Systems and methods for quantum processor topology

Topologies for analog computing systems may include cells of qubits which may implement a tripartite graph and cross substantially orthogonally. Qubits may have an H-shape or an l-shape, qubits may change direction within a cell. Topologies may be comprised of two or more different sub-topologies. Qubits may be communicatively coupled to non-adjacent cells by long-range couplers. Long-range couplers may change direction within a cell. A cell may have two or more different type of long-range couplers. A cell may have shifted qubits, more than one type of inter-cell couplers, more than one type of intra-cell couplers and long-range couplers.

FIELD

This disclosure generally relates to designs, layouts, and topologies for quantum processors comprising qubits.

BACKGROUND

Quantum Computation

Quantum computation and quantum information processing are active areas of research and define classes of vendible products. A quantum computer is a system that makes direct use of at least one quantum-mechanical phenomenon, such as, superposition, tunneling, and entanglement, to perform operations on data. The elements of a quantum computer are not binary digits (bits) but typically are quantum binary digits or qubits.

There are several types of quantum computers. An adiabatic quantum computer is a type of quantum computer that can be used to solve various computational problems including optimization problems, for example. Further details on adiabatic quantum computing systems, methods, and apparatus are described in, for example, U.S. Pat. Nos. 7,135,701 and 7,418,283.

Quantum Devices

Quantum devices are structures in which quantum mechanical effects are observable. Quantum devices include circuits in which current transport is dominated by quantum mechanical effects such as electronic spin and superconductivity. Quantum devices can be used for measurement instruments, in computing machinery, and the like. An analog processor (e.g., a quantum processor) can provide a plurality of quantum devices (e.g., qubits) which are controllably coupled to each other. The design and selection of an analog processor's topology (also referred to herein as the architecture)—that is, the arrangement of qubits and couplers and/or other quantum devices—is an important aspect of an analog processor design. Particular topologies may be better suited to solving certain classes of problems than others. U.S. Pat. No. 8,772,759 provides various examples of analog processor topologies.

Quantum Annealing

Quantum annealing is a computation method that may be used to find a low-energy state of a system, for example the ground state of a system. Quantum annealing may use quantum effects, such as quantum tunneling to reach a global energy minimum. In quantum annealing, thermal effects and other noise may be present. The final low-energy state may not be the global energy minimum.

Adiabatic quantum computation may be considered a special case of quantum annealing for which the system, ideally, begins and remains in its ground state throughout an adiabatic evolution. Thus, those of skill in the art will appreciate that quantum annealing systems and methods may generally be implemented on an adiabatic quantum computer. Throughout this specification and the appended claims, any reference to quantum annealing is intended to encompass adiabatic quantum computation unless the context requires otherwise.

BRIEF SUMMARY

A quantum processor may be summarized as including a first set of qubits, each qubit in the first set of qubits extending parallel to a first major axis along at least a majority of the qubit's length; a second set of qubits, each qubit in the second set of qubits extending parallel to a second major axis along at least a majority of the qubit's length, each qubit in the second set of qubits crossing at least one qubit in the first set of qubits; a third set of qubits, each qubit in the third set of qubits crossing at least one qubit in the first set of qubits and each qubit in the second set of qubits; and a set of intra-cell couplers, each coupler proximate a respective point where a first qubit in the first, second, or third set of qubits crosses a second qubit in a different one of the first, second, and third sets of qubits, each coupler providing communicative coupling between the first and second qubits.

In some implementations, each qubit in the second set of qubits extends parallel to a third major axis and the first, second, and third major axes are non-parallel with each other and non-orthogonal to each other so that the first and second axes meet at a first angle, the first and third axes meet and a second angle, and the second and third axes meet at a third angle. In some implementations, the first, second, and third angles are equal to each other.

In some implementations, the first major axis is orthogonal to the second major axis; each qubit in the third set of qubits comprises a first portion extending parallel to the first major axis and a second portion extending parallel to the second major axis; each qubit in the second set of qubits crosses each qubit in the first set of qubits orthogonally; and each qubit in the first and second sets of qubits crosses at least one qubit in the third set of qubits orthogonally.

In some implementations, at least one qubit of the third set of qubits comprises a third portion between the first and second portions of the at least one qubit, the third portion comprising at least one of: a bend and a curvature. In some implementations, the third portion comprises a first bend proximate to the first portion and a second bend proximate to the second portion. In some implementations, the at least one qubit of the third set of qubits comprises a fourth portion proximate to a crossing between the at least one qubit and at least one qubit of the first set of qubits, the fourth portion extending non-orthogonally to the first and second major axes and extending away from the first and second sets of qubits.

In some implementations, the qubits of the first and second sets of qubits each have a length less than or equal to a threshold length and the at least one qubit of the third set of qubits has a length greater than the threshold length. In some implementations, the qubits of the first and second sets of qubits cross each other in a central region and each qubit of the third set of qubits crosses each of the qubits of the first and second sets of qubits in a boundary region bounding the central region.

In some implementations, the first set of qubits comprises a first plurality of subsets and the second set of qubits comprises a second plurality of subsets, wherein each qubit of the third set of qubits crosses each qubit of at least one subset of the first plurality of subsets and at least one subset of the second plurality of subsets. In some implementations, for each pairing of a first subset of the first plurality of subsets and a second subset of the second plurality of subsets, there is a respective qubit of the third set of qubits crossing each qubit of the first and second subsets.

In some implementations, each qubit of the third set of qubits comprises a third portion between respective first and second portions of the qubit, the third portions of each qubit of the third set of qubits being arranged in a central region, each qubit of the third set of qubits crossing qubits of the first and second sets in a boundary region bounding the central region, each crossing of qubits in the first and second sets also being in the boundary region.

In some implementations, the quantum processor comprises one or more further intra-cell couplers, each coupler proximate third and fourth qubits of the third set of qubits and providing communicative coupling between the third and fourth qubits.

In some implementations, a total length of the at least one qubit of the third subset of qubits is equal to a total length of qubits of the first and second sets of qubits.

In some implementations, the first plurality of subsets comprises a first subset comprising half of the qubits of the first set of qubits and a second subset comprising the other half of the qubits of the first set of qubits and the second plurality of subsets comprises a third subset comprising half of the qubits of the second set of qubits and a fourth subset comprising the other half of the qubits of the second set of qubits; the first, second, third, and fourth subsets being disjoint; and for each qubit of the third set of qubits the first portion crosses each qubit in one of the first subset and the second subset and the second portion crosses each qubit in one of the third subset and the fourth subset.

In some implementations, the quantum processor comprises a plurality of cells tiled over an area such that each cell is positioned proximately adjacent at least one other cell, a first cell comprising the first, second, and third sets of qubits and each other cell of the plurality cells comprising like first, second, and third sets of qubits: a set of inter-cell couplers, each inter-cell coupler providing tunable communicative coupling between pairs of qubits in adjacent cells; wherein the set of inter-cell couplers provide tunable communicative coupling between at least one qubits in the first set of qubits of the first cell and at least one of the qubits in the first set of qubits of a second cell, tunable communicative coupling between at least one of the qubits in the second set of qubits of the first cell and at least one of the qubits in the second set of qubits of a third cell, and tunable communicative coupling between at least one of the qubits in the third set of qubits of the first cell and at least one of the qubits in the third set of qubits of a fourth cell.

In some implementations, the quantum processor comprises a plurality of superconducting qubits, at least a first qubit of the plurality comprising a loop of superconducting material comprising: a central portion extending along a central axis; a first distal portion, the first distal portions arranged at and integrally formed with a first end of the central portion, the first distal portion extending along a first distal axis non-parallel to the central axis; a second distal portion, the second distal portion arranged at and integrally formed with a second end of the central portion, the second end opposing the first end along the central axis, the second distal portion extending along a second distal axis non-parallel to the central axis.

In some implementations, the first and second distal axes are parallel to each other and orthogonal to the central axis. In some implementations, the first qubit has a shape comprising at least one of: an H-shape and an I-shape, wherein the first and second ends of the central portion are proximate central regions of the first and second distal portions along the first and second distal axes, respectively. In some implementations, the first qubit has a shape comprising a U-shape, wherein the first and second ends of the central portion are proximate ends of the first and second distal portions along the first and second distal axes, respectively.

In some implementations, the quantum processor comprises: a plurality of cells tiled over an area such that each cell is positioned proximately adjacent at least one other cell, a first cell comprising the at least one qubit and one or more like qubits; a set of intra-cell couplers for each cell, the intra-cell couplers providing tunable communicative coupling between qubits in the cell; a set of inter-cell couplers, each inter-cell coupler providing tunable communicative coupling between qubits in adjacent cells; wherein a first coupler subset comprising two or more inter-cell couplers communicatively couples the first qubit, via the first distal portion, to a first qubit subset comprising two or more qubits in one or more adjacent cells; and a second coupler subset comprising two or more inter-cell couplers communicatively couples the first qubit, via the second distal portion, to a second qubit subset comprising two or more qubits in one or more adjacent cells.

In some implementations, a first inter-cell coupler of the first coupler subset communicatively couples the first qubit, via the first distal portion, to a first adjacent qubit of the first qubit subset, the first adjacent qubit in a first adjacent cell like the first cell, the first adjacent qubit occupying a position in the first adjacent cell unlike a position of the first qubit in the first cell.

In some implementations, the first inter-cell coupler extends diagonally relative to the first qubit, thereby extending non-orthogonal and non-parallel to the central axis and the first and second distal axes.

In some implementations, the first inter-cell coupler crosses a second inter-cell coupler, the second inter-cell coupler coupling a second qubit in the first cell to a second adjacent qubit in the first adjacent cell, the second qubit proximate to the first qubit and the second adjacent qubit occupying a position in the first adjacent cell corresponding to a position of the first qubit.

In some implementations, the first inter-cell coupler extends substantially parallel to a second inter-cell coupler, the second inter-cell coupler coupling a second qubit in the first cell to a second adjacent qubit in the first adjacent cell, the second qubit proximate to the first qubit and the second adjacent qubit occupying a position in the first adjacent cell corresponding to a position of the first qubit.

In some implementations, the quantum processor comprises a first corner inter-cell coupler communicably coupling a first corner distal portion of a first corner qubit of the first cell to a first adjacent corner qubit of a second cell, the second cell neighbouring one or more cells adjacent to the first cell along at least one of the central axis and first and second distal axes; wherein the first corner inter-cell coupler couples to first end of a distal portion of the first corner qubit, the first end being proximate to an outer boundary of the first cell along the central axis and at least one of the first and second distal axes.

In some implementations, the quantum processor comprises a second corner inter-cell coupler communicably coupling a second corner distal portion of a second corner qubit of the first cell to a second adjacent corner qubit of the second cell, the second corner distal portion extending orthogonally to the first corner distal portion, the second corner inter-cell coupler crossing the first inter-cell coupler.

In some implementations, the quantum processor comprises a second corner inter-cell coupler communicably coupling a second corner distal portion of a second corner qubit of the first cell to a second adjacent corner qubit of a third cell, the second corner distal portion extending orthogonally to the first corner distal portion, the second corner inter-cell coupler extending orthogonal to and non-overlapping with the first inter-cell coupler.

In some implementations, the quantum processor comprises a plurality of superconducting qubits each comprising a loop of superconducting material, the plurality of qubits comprising a first set of qubits and a second set of qubits, the qubits of the first set of qubits extending parallel to a first axis and the qubits of the second set of qubits extending parallel to a second axis orthogonal to the first axis, one or more qubits of the first set of qubits crossing one or more qubits of the second set of qubits at one or more crossing regions; a first set of couplers communicably coupling the one or more qubits of the first set of qubits to the one or more qubits of the second set of qubits at the one or more crossing regions; a second set of couplers comprising at least a first coupler communicably coupling a first qubit of the first set of qubits to a second qubit of the first set of qubits, the first and second qubits non-overlapping, the first coupler comprising a first coupling portion coupling to the first qubit, a second coupling portion coupling to the second qubit, and an extension portion extending orthogonally to the first and second qubits and communicatively coupling the first and second coupling portions.

In some implementations, the first coupler non-communicatively crosses a third qubit of the first set of qubits, the third qubit disposed between the first and second qubits.

In some implementations, each qubit of the first set of qubits is coupled to each qubit of the second set of qubits by a respective coupler of the first set of couplers; each pair of qubits of the first set of qubits is communicatively coupled to each other by a respective coupler of the second set of couplers; and each pair of qubits of the second set of qubits is communicatively coupled to each other by a respective coupler of the second set of couplers.

In some implementations, the quantum processor comprises a plurality of cells tiled over an area such that each cell is positioned proximately adjacent at least one other cell, a first cell comprising the first qubit and one or more like qubits and a second cell comprising the second qubit and one or more like qubits; wherein the second set of couplers comprises: a first subset of inter-cell couplers providing tunable communicative coupling between qubits proximately adjacent to each other in adjacent cells over an inter-cell distance; and a second subset of long-range couplers providing tunable communicative coupling between non-proximately adjacent qubits of the first set of qubits in different cells, a first long-range coupler communicatively coupling the first and second qubits over a long-range distance, the long-range distance greater than the inter-cell distance.

In some implementations, each long-range coupler communicatively couples qubits having like positions in their respective cells.

In some implementations, the first occupies a first position in the first cell and the second qubit occupies a second position in the second cell unlike the first position.

In some implementations, the quantum processor comprises a plurality of cells tiled over an area such that each cell is positioned proximately adjacent at least one other cell, a first cell comprising the first qubit and one or more like qubits and a second cell comprising one or more like qubits including a third qubit; wherein the second set of couplers comprises: a first subset of inter-cell couplers providing tunable communicative coupling between qubits proximately adjacent to each other in adjacent cells over an inter-cell distance; and a second subset of long-range couplers providing tunable communicative coupling between non-proximately adjacent qubits of the first set of qubits in different cells, a first long-range coupler communicatively coupling the first and third qubits over a long-range distance, the long-range distance greater than the inter-cell distance; wherein the first and third qubits extend parallel to respective non-parallel axes.

In some implementations, long-range couplers of the second subset change direction about an axis of symmetry, each of the long-range couplers extending toward the axis of symmetry from a first end along a first portion parallel to a first extension axis, bending at a bent region proximate to the axis of symmetry, and extending toward a second end and away from the axis of symmetry along a second portion parallel to a second extension axis orthogonal to the first extension axis.

In some implementations, the axis of symmetry passes through a central tile, the bent regions of a plurality of long-range couplers disposed in the central cell, each of the long-range couplers disposed entirely on a respective side of the axis of symmetry.

In some implementations, the plurality of qubits comprises a first set of adjacent cells and a second set of long-range cells, the second set of long-range cells comprising the second cell, the first set of adjacent cells comprising a plurality of cells each proximately adjacent to the first cell and mutually non-proximately adjacent to each other.

In some implementations, long-range couplers of the second subset communicatively couple one or more qubits of the first set of qubits in a first adjacent cell to one or more corresponding qubits of the first set of qubits in a second adjacent cell, the one or more qubits of the first adjacent cell being coupled to one or more qubits of the first cell and the one or more qubits of the second adjacent cell indirectly coupled to the first cell at least by the one or more qubits of the first adjacent cell.

In some implementations, the adjacent cells are diagonally offset from each other in the tiled area.

In some implementations, the second set of couplers further comprises a third subset of couplers and, for one or more of the plurality of cells, each pair of qubits of the first set of qubits in the cell is communicatively coupled to each other by a respective coupler of the third set of couplers; and each pair of qubits of the second set of qubits in the cell is communicatively coupled to each other by a respective coupler of the third set of couplers.

In some implementations, the plurality of cells being tiled over the area comprises a subtopology comprising a first set of one or more cells comprising qubits coupled to each other within each cell by the third subset of couplers, the first set of one or more cells disposed adjacent a second set of one or more cells comprising qubits coupled to qubits in other cells by the second subset of long-range couplers, the subtopology tiled over the area.

In some implementations, the first and second sets of qubits each comprise the same number of cells.

In some implementations, the first subset of qubits comprises fewer cells than the second subset of qubits.

In some implementations, the quantum processor comprises: a plurality of superconducting qubits each comprising a loop of superconducting material, the plurality of qubits comprising first and second sets of qubits, the first and second sets of qubits respectively comprising first and second bent qubits, each of the first and second bent qubits respectively comprising a first portion extending parallel to a first axis, a second portion extending parallel to a second axis, and a bent region connecting and communicatively coupling the first and second portions, the first portion of the first bent qubit crossing a first qubit of the first set of qubits at a first crossing region; a first set of couplers comprising at least a first coupler proximate to the respective bent regions of the first and second bent qubits, the first coupler communicably coupling the first and second bent qubits via the respective bent regions; a second set of couplers comprising at least a second coupler proximate to the first crossing region, the second coupler communicatively coupling the first bent qubit and the first qubit.

In some implementations, each qubit of the first and second sets of qubits respectively comprises a first portion extending parallel to a first axis, a second portion extending parallel to a second axis, and a bent region connecting and communicatively coupling the first and second portions; each qubit of the first set of qubits being communicatively coupled to each other qubit of the first set of qubits at a respective crossing region where the qubit and the other qubit cross by a coupler of the second set of couplers.

In some implementations, for each qubit of the first set of qubits, a coupler of the first set of couplers communicatively couples the qubit to a further qubit of the second set of qubits, the coupler proximate to the bent regions of the qubit and the further qubit.

In some implementations, the first axes of the first and second sets of qubits are parallel to each other and the second axes of the first and second sets of qubits are parallel to each other and orthogonal to the first axes.

In some implementations, each qubit of the first set of qubits has a length substantially the same as a length of each other qubit of the first set of qubits.

In some implementations, each of the first and second sets of qubits respectively comprise one or more linear qubits, each linear qubit of the first set extending parallel to a first extension axis, the first extension axis parallel to one of the first axis and the second axis of the first bent qubit, and each linear qubit of the second set extending parallel to a second extension axis, the second extension axis parallel to one of the first axis and the second axis of the second bent qubit.

In some implementations, the first qubit comprises a first linear qubit of the one or more linear qubits, the first linear qubit crossing a number of qubits in both the first and second sets of qubits at a corresponding number of crossing regions, the first linear qubit being communicatively coupled to each of the number of qubits via couplers of the second set of couplers proximate to the corresponding number of crossing regions.

In some implementations, the one or more linear qubits and one or more bent qubits like the first bent qubit are disposed alternatingly between linear and bent qubits along an axis orthogonal to the first extension axis.

In some implementations, the quantum processor comprises a plurality of cells tiled over an area such that each cell is positioned proximately adjacent at least one other cell, each cell comprising: a first set of qubits; a second set of qubits, wherein a portion of at least one qubit in the first set of qubits crosses a portion of at least one qubit in the second set of qubits and wherein a portion of at least one qubits in the first set of qubits crosses a portion of at least one of the qubits in the second set of qubits in an adjacent cell; a first set of inter-cell couplers, wherein each of the inter-cell couplers is located proximate a first end of each of the qubits in the first set of qubits and a first end of each of the qubits in the second set of qubits and wherein each of the inter-cell couplers provides tunable communicative coupling between one of the qubit in the first set of qubits and one of the qubits in the first set of qubits in an adjacent cell or between one of the qubits in the second set of qubits and one of the qubits in the second set of qubits in an adjacent cell; a first set of intra-cell couplers, wherein each of the intra-cell couplers in the first set of intra-cell couplers is positioned proximate a region where one of the qubit in the first set of qubits crosses one of the qubit in the second set of qubits and provides tunable communicative coupling between one of the qubits in the first set of qubits and one of the qubits in the second set of qubits; and a second set of intra-set couplers, wherein each of the intra-cell couplers in the second set of intra-set couplers provides tunable communicative coupling between one qubit in the first set of qubits another one of the qubit in the first set of qubits or between one of the qubits in the second set of qubits and another one of the qubits in the second set of qubits.

In some implementations, each cell further comprises a second set of inter-cell couplers, each of the inter-cell couplers in the second set of inter-cell couplers providing tunable communicative coupling between one of the qubits in the first set of qubits and one of the qubits in the first set of qubits in an adjacent cell, wherein the adjacent cell is positioned along a first direction respective to the cell and the first direction is non-parallel to a longitudinal axis of the first set of qubits or between one of the qubits in the second set of qubits and one of the qubits in the second set of qubits in an adjacent cell, wherein the adjacent cell is positioned along a second direction respective to the cell and the second direction is non-parallel to a longitudinal axis of the second set of qubits.

In some implementations, each of the qubits in the first and the second set of qubits is comprised of a loop of superconductive material interrupted by at least one Josephson junction.

In some implementations, the longitudinal axis of each of the qubits in the first set of qubits is parallel to a third direction and the longitudinal axis of each qubit in the second set of qubits is parallel to a fourth direction.

In some implementations, the third direction is orthogonal to the fourth direction.

In some implementations, each cell comprises twelve qubits in the first set of qubits and twelve qubits in the second set of qubits. A quantum processor may comprise a plurality of cells tiled over an area such that each cell is positioned proximately adjacent at least one other cell, each cell comprises a first set of qubits, a second set of qubits, wherein a portion of at least one qubit in the first set of qubits crosses a portion of at least one qubit in the second set of qubits and wherein a portion of at least one qubits in the first set of qubits crosses a portion of at least one of the qubits in the second set of qubits in an adjacent cell, a first set of inter-cell couplers, wherein each of the inter-cell couplers is located proximate a first end of each of the qubits in the first set of qubits and a first end of each of the qubits in the second set of qubits and wherein each of the inter-cell couplers provides tunable communicative coupling between one of the qubit in the first set of qubits and one of the qubits in the first set of qubits in an adjacent cell or between one of the qubits in the second set of qubits and one of the qubits in the second set of qubits in an adjacent cell, a first set of intra-cell couplers, wherein each of the intra-cell couplers in the first set of intra-cell couplers is positioned proximate a region where one of the qubit in the first set of qubits crosses one of the qubit in the second set of qubits and provides tunable communicative coupling between one of the qubits in the first set of qubits and one of the qubits in the second set of qubits, and a second set of intra-set couplers, wherein each of the intra-cell couplers in the second set of intra-set couplers provides communicative coupling between one qubit in the first set of qubits another one of the qubit in the first set of qubits or between one of the qubits in the second set of qubits and another one of the qubits in the second set of qubits.

Each cell in a quantum processor may further comprise a second set of inter-cell couplers, each of the inter-cell coupler in the second set of inter-cell couplers providing tunable communicative coupling between one of the qubits in the first set of qubits and one of the qubits in the first set of qubits in an adjacent cell, wherein the adjacent cell is positioned along a first direction respective to the cell and the first direction is non-parallel to a longitudinal axis of the first set of qubits or between one of the qubits in the second set of qubits and one of the qubits in the second set of qubits in an adjacent cell, wherein the adjacent cell is positioned along a second direction respective to the cell and the second direction is non-parallel to a longitudinal axis of the second set of qubits.

Each of the qubits in the first and the second set of qubits may be comprised of a loop of superconductive material interrupted by at least one Josephson junction.

The longitudinal axis of each of the qubits in the first set of qubits is parallel to a third direction and the longitudinal axis of each qubit in the second set of qubits is parallel to a fourth direction. The third direction may be orthogonal to the fourth direction.

Each cell may comprise twelve qubits in the first set of qubits and twelve qubits in the second set of qubits.

DETAILED DESCRIPTION

In the following description, some specific details are included to provide a thorough understanding of various disclosed embodiments. One skilled in the relevant art will recognize that embodiments may be practiced without one or more of these specific details, or with other methods, components, materials, etc. Throughout this specification and the appended claims, the words “element” and “elements” are used to encompass, but are not limited to, all such structures, systems, and devices associated with quantum processors, as well as their related programmable parameters.

Reference throughout this specification to “one embodiment” “an embodiment”, “another embodiment”, “one example”, “an example”, “another example”, “one implementation”, “another implementation”, or the like means that a particular referent feature, structure, or characteristic described in connection with the embodiment, example, or implementation is included in at least one embodiment, example, or implementation. Thus, the appearances of the phrases “in one embodiment”, “in an embodiment”, “another embodiment” or the like in various places throughout this specification are not necessarily all referring to the same embodiment, example, or implementation. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments, examples, or implementations.

It should be noted that, as used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the content clearly dictates otherwise. Thus, for example, reference to a system including “a quantum processor” includes a single quantum processor, or two or more quantum processors. It should also be noted that the term “or” is generally employed in its sense including “and/or” unless the content clearly dictates otherwise.

The term “connectivity” describes the number of possible or available communicative coupling paths that are available (e.g., whether active or not) to communicably couple directly between pairs of qubits in a quantum processor without the use of intervening qubits. As an example, a qubit with a connectivity of three is capable of directly communicably coupling to up to three other qubits without any intervening qubits due to the physical topology of the qubits and couplers as manufactured. In other words, there are direct communicative coupling paths available to a maximum of three other qubits, although in any particular application all or less than all of those direct communicative coupling paths may actually be employed depending on the particular problem being solved and/or mapping of that particular problem to the processor or hardware.

Typically, qubits on an outer perimeter (i.e., qubits positioned along the edges of an array) of the architecture or topology layout will have a smaller number of physically available direct connections than qubits located inwardly of the perimeter. The qubits on an outer perimeter of the array are denominated herein as perimeter, or edge, qubits. Where the qubits are arrayed in an array with a polygonal perimeter (e.g., square, rectangular, hexagonal), the qubits at the corners of the perimeter typically have the smallest number of physically available direct connections. These qubits at the corners of the perimeter are denominated herein as corner qubits. Thus, the edge or corner qubits may limit the measure of physical connectivity for any given architecture or topology.

These non-perimeter or non-edge qubits are referred to herein as inner qubits, per the processor design, whether those direct connections are ever used or not in solving any particular problem.

One or more quantum processors are fabricated or manufactured according to a given design. However, in some instances, one or more defects may prevent all of the qubits and/or all of the couplers of any given manufactured quantum processor from being operational or within tolerance of a design specification (i.e., within spec). Thus, the design processor or hardware graph for the design may not be an accurate portrayal of any given instance of the manufactured quantum processor. In fact, different instances of the quantum processors based on a given design may vary from one another due to these manufacturing defects or out of tolerance components.

FIG. 1illustrates a hybrid computing system100including a digital computer105coupled to an analog computer150. In some implementations the analog computer150is a quantum computer. The exemplary digital computer105includes a digital processor (CPU)110that may be used to perform classical digital processing tasks.

Digital computer105may include at least one digital processor (such as central processor unit110with one or more cores), at least one system memory120, and at least one system bus117that couples various system components, including system memory120to central processor unit110.

The digital processor may be any logic processing unit, such as one or more central processing units (“CPUs”), graphics processing units (“GPUs”), digital signal processors (“DSPs”), application-specific integrated circuits (“ASICs”), programmable gate arrays (“FPGAs”), programmable logic controllers (PLCs), etc.

Digital computer105may include a user input/output subsystem111. In some implementations, the user input/output subsystem includes one or more user input/output components such as a display112, mouse113, and/or keyboard114.

System bus117can employ any known bus structures or architectures, including a memory bus with a memory controller, a peripheral bus, and a local bus. System memory120may include non-volatile memory, such as read-only memory (“ROM”), static random access memory (“SRAM”), Flash NAND; and volatile memory such as random access memory (“RAM”) (not shown).

Digital computer105may also include other non-transitory computer- or processor-readable storage media or non-volatile memory115. Non-volatile memory115may take a variety of forms, including: a hard disk drive for reading from and writing to a hard disk, an optical disk drive for reading from and writing to removable optical disks, and/or a magnetic disk drive for reading from and writing to magnetic disks. The optical disk can be a CD-ROM or DVD, while the magnetic disk can be a magnetic floppy disk or diskette. Non-volatile memory115may communicate with digital processor via system bus117and may include appropriate interfaces or controllers116coupled to system bus117. Non-volatile memory115may serve as long-term storage for processor- or computer-readable instructions, data structures, or other data (sometimes called program modules) for digital computer105.

Although digital computer105has been described as employing hard disks, optical disks and/or magnetic disks, those skilled in the relevant art will appreciate that other types of non-volatile computer-readable media may be employed, such a magnetic cassettes, flash memory cards, Flash, ROMs, smart cards, etc. Those skilled in the relevant art will appreciate that some computer architectures employ volatile memory and non-volatile memory. For example, data in volatile memory can be cached to non-volatile memory. Or a solid-state disk that employs integrated circuits to provide non-volatile memory.

Various processor- or computer-readable instructions, data structures, or other data can be stored in system memory120. For example, system memory120may store instruction for communicating with remote clients and scheduling use of resources including resources on the digital computer105and analog computer150.

In some implementations system memory120may store processor- or computer-readable calculation instructions to perform pre-processing, co-processing, and post-processing to analog computer150. System memory120may store at set of analog computer interface instructions to interact with the analog computer150.

Analog computer150may include an analog processor such as quantum processor140. The analog computer150can be provided in an isolated environment, for example, in an isolated environment that shields the internal elements of the quantum computer from heat, magnetic field, and other external noise (not shown).

A quantum processor includes programmable elements such as qubits, couplers, and other devices. Examples of qubits and how they are arranged are shown inFIGS. 3-5andFIGS. 7-23B.

In one implementation, the quantum processor is a superconducting quantum processor including a number of qubits and associated local bias devices. The superconducting quantum processor may also employ couplers providing communicative coupling between qubits. Further details and embodiments of exemplary quantum processors that may be used in conjunction with the present systems methods and apparatus are described in, for example, U.S. Pat. Nos. 7,533,068; 8,008,942; 8,195,596; 8,190,548; and 8,421,053.

Examples of superconducting qubits include superconducting flux qubits, superconducting charge qubits, and the like. In a superconducting flux qubit, the Josephson energy dominates or is equal to the charging energy. In a charge qubit, it is the reverse. Examples of flux qubits that may be used include rf-SQUIDs, which include a superconducting loop interrupted by one Josephson junction, persistent current qubits, which include a superconducting loop interrupted by three Josephson junctions, and the like. In some implementations, the qubits and couplers are controlled by on-chip circuitry. Examples of on-chip control circuitry can be found in U.S. Pat. Nos. 7,876,248; 7,843,209; 8,018,244; 8,098,179; 8,169,231; and 8,786,476.

Throughout this specification and the appended claims, the “architecture” or “topology” of a quantum processor is defined by the relative physical positions of the qubits and couplers in the quantum processor.

A connection is a direct communicative path between two elements (e.g., between two qubits via a single coupler without an intervening qubits). A coupling can be a direct communicative path between two elements (e.g., between two qubits via a single coupler without an intervening qubits) or an indirect communicative coupling between two elements (e.g., between two qubits via another intervening qubit and/or multiple couplers).

In some implementations, the qubits and couplers in a quantum processor are arranged in an architecture (or topology) such that a certain number of qubits are laid out into a number of sub-topologies, each sub-topology also referred to herein as a cell of qubits (hereinafter “cell”). A cell is a repeated sub-topology of a quantum processor topology comprising qubits and couplers. A plurality of cells tiled over an area produces a certain quantum processor architecture or topology. Each qubit in a cell may be included in only one cell such that no qubit may be included in multiple cells and no qubit may be shared among multiple cells.

A qubit within a cell can be communicatively coupled to another qubit within the same cell by a coupler referred to herein as an intra-cell coupler. A qubit in one cell can be communicatively coupled to another qubit in a different cell by a coupler referred to herein as an inter-cell coupler.

Any given coupling may be controllable (e.g., ON/OFF) as specified by a programming configuration of the quantum processor. The programming configuration of the quantum processor may be performed by a non-quantum processor, such as a digital processor. A quantum processor may interact with a digital processor to solve a particular problem.

FIG. 2shows an example graph200of a complete tripartite graph. Example graph200has twelve nodes (210ato210d,220ato220dand230ato230d) or vertices, grouped in three sets210,220and230.

A person skilled in the art will recognize that the terms ‘node’ and ‘vertex’ can be used interchangeably in a graph. Therefore, for the purpose of this specification and the appended claims, the term ‘node’ can be substituted for ‘vertex’ and ‘vertex’ can substituted for ‘node’.

Example graph200is a complete tripartite graph where all the nodes in a set (e.g., set210) are connected to each of the nodes in the other two sets (e.g., sets220and230), but there is no direct connection between nodes in the same set. For example, there is no physical connection between nodes210aand210b. Each node in example graph200is connected to eight other nodes in example graph200, and, therefore, has a connectivity of eight. Physical connections in example graph200are shown as lines240(only one called out for clarity).

Example graph200may represent the connectivity of a tripartite cell in a quantum processor with twelve nodes in accordance with the present systems, methods and apparatus. Example graph200is shown as having four nodes in each set, however, this is not intended to be limiting. Other tripartite graphs may have a smaller or a larger number of nodes.

FIG. 3shows an example cell300forming the basis of a quantum processor topology in accordance with the present systems, devices, and methods. Example cell300includes a first set of qubits310a-310d(collectively310), a second set of qubits320a-320d(collectively320), and a third set of qubits330a-330d(collectively330) representing a complete tripartite graph, such as example graph200. While each set is illustrated as having four qubits, such is not limiting. In other implementations, each set of qubits in a cell may have a larger or smaller number of qubits. In some implementations, the number of qubits in one set (e.g., the second set) does not equal the number of qubits in another set (e.g., the third set).

The qubits310of the first set each have a respective longitudinal or major axis315a, (only one called out, collectively315) along which the superconductive paths or loops of the respective qubits310of the first set extend in a lengthwise direction of the qubit. Likewise, the qubits320of the second set each have a respective longitudinal or major axis316a(only one called out, collectively316) along which the superconductive paths or loops of the qubits320of the second set extend in a lengthwise direction of the qubit. The qubits330of the third set each have a respective longitudinal or major axis317a(only one called out, collectively317) along which the superconductive paths or loops of the qubits330of the third set extend in a lengthwise direction of the qubit. In some implementations, each qubit of a given set shares a single major axis316, rather than (or in addition to) each having an independently-defined major axis.

The qubits310of the first set have loops that are substantially parallel with one another, and with the respective longitudinal or major axes315. The qubits320of the second set have loops that are substantially parallel with one another, and with the respective longitudinal or major axes316. The qubits330of the third set have loops that are substantially parallel with one another, and with the respective longitudinal or major axes317.

The longitudinal or major axis is the axis along which the longest dimension of the loop of a qubit generally extends, whether or not the qubit has one or more bends or changes in directions between ends.

Qubits310, qubits320, and qubits330each may have respective lateral or minor axes (not shown), respectively. The lateral axis may be perpendicular to the major axis.

While the qubits are illustrated as being substantially rectangular loops, such is not intended to be limiting, and the qubits may have any other form, such as, but not limiting to, oval or discorectangular loops. As used herein and in the claims the term substantially parallel means parallel, essentially parallel, or approximately parallel. For example, a longitudinal or major axis of a respective elongated loop of each of at least two qubits is parallel with one another, without reference to any relatively shorter legs or portions of the elongated loops. Another way to describe the geometric relationship between qubits in a set is that corresponding portions of the loops of the qubits are laterally spaced equally from one another.

The longitudinal or major axes315of the qubits310are nonparallel (e.g., meeting at approximately 60 degrees) to the longitudinal or major axes316of the qubits320. The longitudinal or major axes316of the qubits320are nonparallel (e.g., meeting at approximately 60 degrees) to the longitudinal or major axes317of the qubits330. The longitudinal or major axes317of the qubits330are nonparallel (e.g., meeting at approximately 60 degrees) to the longitudinal or major axes315of the qubits310.

In some implementations, the qubits310meet the qubits320at a first angle. In some implementations, the qubits320meet the qubits330at a second angle. In some implementations, the qubits330meet the qubits310at a third angle. Optionally varied in implementation the first angle, the second angle, and the third angle are equal or unequal.

The qubits310may, for instance, be laid out generally left ascending in the plane of the drawing sheet ofFIG. 3, and hence are denominated herein as left ascending qubits for ease of discussion. The qubits320may, for instance, be laid out generally right ascending in the plane of the drawing sheet ofFIG. 3, and hence are denominated as right ascending qubits320for ease of discussion. The qubits330may, for instance, be laid out generally horizontally in the plane of the drawing sheet ofFIG. 3, and hence are denominated as horizontal qubits for ease of discussion.

Example cell300represents a single cell in a quantum processor, whereas the corresponding quantum processor topology may comprise a plurality of example cells300tiled over an area. A complete processor topology may employ a plurality of example cells300where each individual example cell300is positioned adjacent (i.e., neighboring) at least one other example cell300. For example, example cell300suggests a six-connected topology. Example cell300could be positioned next to six neighbors: left, right, upper left, upper right, lower left, and lower right.

A person of skill in the art will appreciate that while twelve qubits are illustrated in example cell300, this number is arbitrary and example cell300may comprise more or fewer than twelve qubits (but must comprise at least three qubits). As well, the number of qubits in example cell300need not be a multiple of three.

Couplers such as couplers350(only one called out in drawing) may provide pair-wise communicative coupling between respective pairs of qubits where one qubit of the pair is selected from one of qubits310, qubits320, or qubits330; and the other qubit of the pair selected from a different one of qubits310, qubits320, or qubits330.

Couplers350can provide tunable communicative coupling between qubits310, qubits320, and/or qubits330. The couplers are located at regions proximate where the qubits310meet qubits320, qubits320meet qubits330, and/or qubits330meet qubits310. As used herein and in the appended claims, the term “meet”, and variants thereof such as meets or meeting, includes cross, overlie, underlie, overlap, come together or are proximate one another (i.e., two elements within an inductive coupling distance of one another, whether both elements reside with one another in a common plane or substrate of a wafer or die, or the elements reside in respective planes or substrates of a wafer or die, the inductive coupling distance being a distance at which inductive coupling occurs between the elements that exceeds a level of background noise, if any, in a circuit to which the elements belong).

Each intersecting pair of qubits may not have a proximate coupler but it is generally regarded as advantageous to have such in an implementation. Each coupler may be a respective loop of superconducting material interrupted by at least one respective Josephson junction. Couplers may be tunable as described in, for example U.S. Pat. Nos. 7,619,437, 7,969,805 and 7,898,282, etc. in that the coupling created between two respective qubits by the coupler may be adjusted during the operation of a quantum processor.

Example cell300may be laid out into an integrated circuit. The integrated circuit may be multi-layered. There may be at least two layers of metal in the integrated circuit. At least a first portion of each qubit in qubits310, qubits320, and qubits330may be laid out in a first metal layer of the integrated circuit. At least a second portion of each qubit in qubits310, qubits320, and qubits330may be laid out in a first metal layer of the integrated circuit. For example, portions of a horizontal qubit (e.g., a qubit in qubits330) and a right ascending qubit (e.g. a qubit in qubits320) may both be laid out in the first metal layer and portions of these qubits may briefly change layers (e.g., switch to the second metal layer) to tunnel under, or bridge over, another qubit. This change of metal layer for tunneling under, or bridging over, another qubit may occur at an approximate position where a first qubit crosses a second qubit.

At least a portion of each coupler350may be laid out in the first metal layer and/or the second metal layer and/or a third metal layer. The third metal layer may be interposed between the first metal layer and the second metal layer. For example, coupler350may exist in the first, second or third metal layer or in the first and second, second and third or first and third metal layers or the first, second and third metal layers. Interconnection between layers, also referred to herein as vias, may be used within qubits310, qubits320, and/or coupler350to electrically and/or superconductingly connect any or all of the first, second and third metal layers together.

FIG. 4shows an example cell400forming the basis of a quantum processor topology in accordance with the present systems methods and apparatus. Example cell400comprises three sets of qubits and couplers between each of the three sets of qubits. Each qubit in one set in example cell400crosses all the other qubits in the other two sets substantially orthogonally, thereby allowing additional space in the region where two qubits cross each other for couplers and/or other electronic devices. Example cell400includes a first set of qubits410a-410d(collectively410), a second set of qubits420a-420d(collectively420), and a third set of qubits430a-430d(collectively430) representing a complete tripartite graph, such as example graph200.

While each set is illustrated as having four qubits, such is not limiting. In other implementations, each set of qubits in a cell may have a larger or smaller number of qubits. In some implementations, the number of qubits in one set (e.g., the second set) does not equal the number of qubits in another set (e.g., the third set).

The qubits410of the first set each have a respective longitudinal or major axis415a(only one called out inFIG. 4, collectively415) along which the superconductive paths or loops of the respective qubits410of the first set extend in a lengthwise direction of the qubit. Likewise, the qubits420of the second set each have a respective longitudinal or major axis425a(only one called out inFIG. 4, collectively425) along which the superconductive paths or loops of the qubits420of the second set extend in a lengthwise direction of the qubit.

The qubits430of the third set have a first longitudinal axis431aand a second longitudinal axis432a(only two called out inFIG. 4, collectively431and432) along which a first segment435aand a second segment436a(only two called out inFIG. 4, collectively435and436) of the superconductive paths or loops of the respective qubits430of the third set extend in a lengthwise direction of the qubit, respectively. Axes431and432are substantially orthogonal to each other (i.e., they meet at approximately 90 degrees). Qubits430may bend one or more times between axis431and432and may bend in other areas of example cell400along lateral axes.

In some implementations, qubits430may bend between the edge of example cell400and first segment435and/or they may bend between second segment436and the edge of example cell400. In some implementations, qubits430may bend at a 45 degree angle between the edge of example cell400and first segment435and/or they may bend at a 45 degree angle between second segment436and the edge of example cell400.

The qubits410of the first set have loops that are substantially parallel with one another, and with the respective longitudinal or major axes415. The qubits420of the second set have loops that are substantially parallel with one another, and with the respective longitudinal or major axes425. The qubits430of the third set have first segment435of the superconductive loops that are substantially parallel to each other and with the respective first axis431. Qubits430of the third set have second segment436of the superconductive loops that are substantially parallel to one another and to the respective second axis432.

The longitudinal or major axes415of the qubits410are substantially orthogonal (i.e., meeting at approximately 90 degrees) to the major or longitudinal axes425of the qubits420. The longitudinal or major axes415of the qubits410are orthogonal (i.e., meeting at 90 degree angle) to second axes432and parallel to first axes431of the qubits430. The longitudinal or major axes425of the qubits420are orthogonal (i.e., meeting at 90 degree) to first axes431and parallel to second axis432of the qubits430.

Qubits410, qubits420, and qubits430may be superconducting flux qubits. Each qubit410-430may be a respective loop of superconducting material where at least a first portion of each loop of superconducting material is elongated along a respective major or longitudinal axis. In one implementation, each qubit410-430is interrupted by at least one respective Josephson junction (not shown).

Qubits410of the first set and qubits420of the second set can have superconducting loops of equal or similar length. Qubits430of the third set can have superconductive loops that are substantially longer than the superconducting loops of the qubits410and420to allow for substantially orthogonal intersection with the first and the second set of qubits410,420.

Couplers450may provide pair-wise communicative coupling between respective pairs of qubits where one qubit of the pair is selected from one of qubits410, qubits420, or qubits430; and the other qubit of the pair selected from a different one of qubits410, qubits420, or qubits430.

Couplers450can provide tunable communicative coupling between qubits410, qubits420, and qubits430. The couplers can be located at regions proximate where the qubits410meet qubits420, qubits420meet qubits430, and qubits430meet qubits410. Each intersecting pair of qubits may not have a proximate coupler but it is generally regarded as advantageous to have such in an implementation. Each coupler may be a respective loop of superconducting material interrupted by at least one respective Josephson junction.

Each qubit410from the first set of qubits may be communicatively coupled to all the qubits420of the second set of qubits and all the qubits430of the second set of qubits. Each qubit420of the second set of qubits may be communicatively coupled to all the qubits410of the first set of qubits and to all the qubits430of the third set of qubits. Each qubit430of the third set of qubits may be communicatively coupled to all the qubits410of the first set and all the qubits420of the second set. Therefore, example cell400may represent a complete tripartite graph, such as example graph200.

Similarly to example cell300, example cell400may be laid out into an integrated multi-layered circuit as discussed above with reference to example cell300.

FIG. 5shows a schematic diagram of an example topology500of a quantum processor according to the present systems, methods and apparatus. Example topology500comprises four cells and couplers between horizontally arranged cells, between vertically arranged cells and between two diagonally arranged cells. Example topology500shows four cells510,520,530and540.

Each cell510,520,530and540is substantially identical to example cell400and may implement a tripartite graph. Each cell (e.g. cell510) has twelve qubits distributed in three sets, where each qubit crosses qubits from the other sets substantially orthogonally (i.e. meeting at approximately 90 degrees). For example, cell510has a first set of qubits511, a second set of qubits512and a third set of qubits513.

Cells510to540are connected to each other by inter-cell couplers, such as couplers550(only one called out inFIG. 5). The cells in example topology500are arranged such that couplers may exist between the first set of a cell and the first set of an adjacent cell, between the second set of a cell and the second set of an adjacent cell and/or between the third set of a cell and the third set of an adjacent cell. For example, each qubit in the first set of qubits511in cell510is communicatively coupled to at least one qubit in the first set of qubits521of cell520(e.g., directly via a single coupler) and each qubit in the second set512of cell510is communicatively coupled to at least one qubit in the second set542of the fourth cell540(e.g., directly via a single coupler), where cells510and520are laid out adjacent to one another and generally horizontally in the plane ofFIG. 5and cells510and540are laid out adjacent to one another and generally vertically in the plane ofFIG. 5. Each qubit in the third set of qubits543in cell540is communicatively coupled to at least one qubit in the third set of qubits523in cell520(e.g., directly via a single coupler), where cells540and520are laid out generally diagonally to each other in the plane ofFIG. 5.

Cells510to540are shown with three groups of four qubits each, however such is not limiting and in a different implementation a larger or smaller number of qubits may be present.

FIG. 6shows an example graph600illustrating the connectivity of a cell implementing a non-complete tripartite graph forming the basis of a quantum processor topology based on the present systems, methods and apparatus. Example graph600implements a non-complete tripartite graph with twelve nodes. The twelve nodes of example cell600are divided into three sets. While example graph600is shown with twelve nodes, such is not meant to be limiting and in a different implementation example graph600may have a smaller or a larger number of nodes while still representing a non-complete tripartite graph.

Example graph600has a first set of nodes610ato610d(collectively610), a second set of nodes620ato620d(collectively620) and a third set of nodes630ato630d(collectively630) representing a tripartite graph. In some implementation the number of nodes in one set (e.g., the second set) does not equal the number of nodes in another sets (e.g., the third set).

Example graph600has a set of edges650(only one called out inFIG. 6) between nodes in example graph600and edges640(only one called out inFIG. 6) between a node in example graph600and a node in other graphs.

Edges650connect each node in the first set of nodes610and each node in the second set of nodes620, each node in the first set of nodes610and at least one node in the third set of nodes630, each node in the second set of nodes620and at least one node in the third set of nodes630and at least two nodes in the third set of nodes630(e.g., there is an edge between node630aand630b).

In at least one implementation, each node in the first set of nodes610is connected by an edge650to two nodes in the third set of nodes630, each node in the second set of nodes620is connected by an edge650to two nodes in the third set of nodes630, and nodes in the third set630are pairwise connected by an edge650.

Edges640connect each node in example graph600and at least one node in another graph (not shown inFIG. 6). In some implementation, each node in example graph600is connected to two nodes that are not within example graph600by an edge640. In some implementations, edges640connect each node in example graph600and one node in an adjacent graph and another node in a different adjacent graph. For example, node610ais connected to a node in an adjacent graph laying on the right of example graph600in the plane of the page ofFIG. 6by an edge640and to another node in an adjacent graph laying on the left of example graph600by another one of edges640.

Therefore example graph600has connectivity of eight (i.e., each node in example graph600is connected to six nodes in example graph600and to two nodes in another graph).

FIG. 7shows a schematic diagram of an example cell700in a quantum processor according to the present systems, method and apparatus. Example cell700has three sets of qubits, where all qubits are substantially equal in length. Qubits in the first, second and third sets cross each other substantially orthogonally. Example cell700has a first set of qubits710ato710d(collectively710), a second set of qubits720ato720d(collectively720) and a third set of qubits730ato730d(collectively730) implementing a non-complete tripartite graph according to the connectivity illustrated inFIG. 6.

While each set is illustrated as having four qubits, such is not limiting. In other implementations, each set of qubits in a cell may have a larger or smaller number of qubits. In some implementations, the number of qubits in one set (e.g., the second set) does not equal the number of qubits in another set (e.g., the third set). In one implementation, each qubit710-730may be interrupted by at least one respective Josephson junction (not shown).

The qubits710of the first set of qubits each have a respective longitudinal or major axis715a(only one called out, collectively715) along which the superconductive paths or loops of the respective qubits710of the first set extend in a lengthwise direction of the qubit. Likewise, the qubits720of the second set of qubits each have a respective longitudinal or major axis725a(only one called out, collectively725) along which the superconductive paths or loops of the qubits720of the second set extend in a lengthwise direction of the qubit.

The qubits730of the third set of qubits have a first axis731aand a second axis732a(only two called out, collectively731and732) along which a first segment735aand a second segment736a(only two called out, collectively735and736) of the superconductive paths or loops of the respective qubits730of the third set extend in a lengthwise direction of the qubit, respectively. Axis731and732are substantially orthogonal to each other (i.e., they meet at approximately 90 degrees). Each qubit730bend at a 90 degree angle between axis731and732.

The qubits710of the first set of qubits have loops that are substantially parallel with one another, and with the respective longitudinal or major axis715. The qubits720of the second set of qubits have loops that are substantially parallel with one another, and with the respective longitudinal or major axis725. The qubits730of the third set of qubits have first segments735of the superconductive loops that are substantially parallel to each other and to the respective first axis731. Qubits730of the third set of qubits have second segments736of the superconductive loops that are substantially parallel to one another and to the respective second axis732.

The longitudinal or major axis715of the qubits710are orthogonal (i.e., meeting at 90 degree angle) to the major or longitudinal axis725of the qubits720. The longitudinal or major axis715of the qubits710are orthogonal (i.e., meeting at 90 degree angle) to second axis732and parallel to first axis731of the qubits730. The longitudinal or major axis725of the qubits720are orthogonal (i.e., meeting at 90 degree angle) to first axis731and parallel to second axis732of the qubits730.

The length of a qubit in a cell can be defined as the longest distance measured between two points over the superconducting loop of a qubit, with one point at one of the borders of the cell and the other point at another one of the borders of the cell.

In one implementation, qubits710of the first set and qubits720of the second set have superconducting loops of equal or similar length. Qubits730of the third set have superconducting loops of equal or similar length to qubits710and720.

Couplers750may provide pair-wise communicative coupling between respective pairs of qubits where one qubit of the pair is selected from one of qubits710, qubits720, or qubits730; and the other qubit of the pair selected from a different one of qubits710, qubits720, or qubits730

Couplers750can provide tunable communicative coupling between qubits710, qubits720, and qubits730. The couplers are located at regions proximate where the qubits710meet qubits720, qubits720meet qubits730, and qubits730meet qubits710. Each intersecting pair of qubits may not have a proximate coupler but it is generally regarded as advantageous to have such in an implementation. Each coupler may be a respective loop of superconducting material interrupted by at least one respective Josephson junction.

Each qubit710from the first set of qubits may be communicatively coupled to all the qubits720of the second set of qubits and at least one of the qubits730of the third set of qubits. Each qubit720of the second set of qubits may be communicatively coupled to all the qubits710of the first set of qubits and to at least one of the qubits730of the third set of qubits.

In some implementations, each qubit710in the first set is communicatively coupled to two qubits730in the third set (e.g. qubit710ais communicatively coupled to qubits730aand730b) and each qubit720in the second set is communicatively coupled to two qubits730in the third set (e.g. qubit720ais coupled to qubits730aand730d).

Couplers exist between at least two qubits730in the third set of qubits. For example there is a coupler754between qubit730aand730b.

In alternative implementations, qubits730in the third set are pairwise connected. Coupler754provides tunable communicative coupling between qubits730aand730b, coupler751provides tunable communicative coupling between qubits730band730c, coupler752provides tunable communicative coupling between qubits730cand730dand coupler753provides tunable communicative coupling between qubits730dand730a.

Similarly to example cell300and example cell400, example cell700may be laid out into an integrated multi-layered circuit as discussed above with reference to example cell300.

FIG. 8Ashows a schematic diagram of an example cell800ain a quantum processor according to the present systems, method and apparatus. Example cell800ahas two sets of qubits, where each qubits is a superconducting loop in an H-shape, or I-shape. Each qubit in example cell800acan be communicatively coupled to two other qubits on each side. Example cell800ahas a first set of qubits811to814(collectively810) and a second set of qubits821to824(collectively820).

While each set is illustrated as having four qubits, such is not limiting. In other implementations, each set of qubits in a cell may have a larger or smaller number of qubits. In some implementations, the number of qubits in first set of qubits810does not equal the number of qubits in second set of qubits820. While inFIG. 8Aexample cell800ais illustrated as having two sets of qubits, such is not limiting and example cell800amay have a larger (e.g. three) number of sets of qubits.

Qubits in example cell800aare shown as having a superconducting loop forming an H-shape or I-shape, however, such is not limiting and qubits may have other form such as, but not limiting to, rectangular or discorectangular loops. In some implementations, each such qubit comprises distal ends connected by a central portion; the distal ends extend orthogonally to the central portion and thereby provide a greater area along a boundary of the cell along which to be coupled to qubits in other cells. In some implementations an H-shape or I-shape loop may represent a segment of a qubit. In one implementation, each qubit810-820is interrupted by at least one respective Josephson junction (not shown).

Qubits of first set of qubits810in example cell800aare substantially parallel to one another and may be laid out generally horizontally in the plane of the page ofFIG. 8Aand may be referred in this specifications and appended claims as horizontal qubits. Qubits of second set of qubits820in example cell800aare substantially parallel to one another and may be laid out generally vertically in the plane of the page ofFIG. 8Aand may be referred in this specifications and appended claims as vertical qubits. Qubits of the first set of qubits810and qubits of the second set of qubits820are substantially non-parallel (e.g. meet at 90 degree). While qubits of the first and the second sets of qubits810and820are illustrated inFIG. 8Aas having one longitudinal or major axis (not shown), such is not limiting and in other implementations qubits of the first set810and/or qubits of the second set820may have two or more longitudinal or major axes.

Couplers such as couplers835(only one called out) may provide pair-wise communicative coupling between respective pairs of qubits where one qubit of the pair is selected from one of the first set of qubits810or one of the second sets of qubits820, and the other qubit of the pair selected from a different one of first set of qubits810or second set of qubits820.

Couplers835can provide tunable communicative coupling between qubits of the first set810and qubits of the second set820. The couplers may be located at regions proximate where the qubits of the first set810meet qubits of the second set820. In some implementations, couplers may be located at some distance from the regions where the qubits of the first set810meet qubits of the second set820.

Each qubit in cell800apresents at least 2 inter-cell couplers, such as couplers842aand842b(only six called out inFIG. 8A, collectively840) connecting a qubit in example cell800awith at least two qubits in neighboring cells. In some implementations, each end of a qubit has at least two couplers. For example, as shown inFIG. 8A, a qubit (such as qubit821) may comprise distal ends which are each coupled to two couplers840, resulting in four couplers840being coupled to the qubit.

In some implementations, horizontal qubits in a cell are communicatively coupled to horizontal qubits in a neighboring cell by couplers840. Likewise, inter-cell couplers840can provide tunable communicative coupling between pairs of vertical qubits in adjacent cells. As shown inFIG. 8A, a qubit812has inter-cell couplers842a,842b,842cand842d. Qubit812is depicted as the second horizontal qubit, from the upper edge of example cell800a. This numbering is arbitrary and for illustration purposes only and not limiting the scope of the present specification and appended claims. Similarly, qubit813may be referred to the third horizontal qubit.

Each inter-cell coupler840can provide tunable communicative coupling between a horizontal or a vertical qubit in example cell800aand horizontal or vertical qubits in a different position in a neighboring cell, respectively. For example, inter-cell coupler842aprovides tunable communicative coupling between second horizontal qubit812and the first horizontal qubit in a neighboring cell, and inter-cell coupler842bprovides tunable communicative coupling between second horizontal qubit812and the third horizontal qubit in a neighboring cell. Likewise, inter-cell coupler842cprovides tunable communicative coupling between second horizontal qubit812and the first horizontal qubit in a neighboring cell and inter-cell coupler842dprovides tunable communicative coupling between second horizontal qubit812and the third horizontal qubit in a neighboring cell.

As illustrated inFIG. 8A, pairs of inter-cell couplers840of parallel and adjacent qubits may cross each other to provide coupling between qubits in a different order in adjacent cells, as described in the previous paragraph. For example, inter-cell coupler842bof qubit812may cross inter-cell coupler843aof qubit813.

As used herein and in the appended claims the term cross, and variants thereof such as crosses or crossing, includes overlie, underlie, and overlap (e.g., where each resides in a respective plane or substrate of a wafer or die, and a normal projection (i.e., normal to the plane or substrate) of at least a portion of a first element in a first plane or first substrate intersects at least a portion a second element in a second plane or second substrate).

Similarly, qubits that are at the four corners of example cell800a(i.e., qubits821,824,811and814) have inter-cell couplers that cross each other and can provide tunable communicative coupling to diagonally adjacent cells, as shown in more details inFIG. 8BandFIG. 8C. In some implementations, where qubits810and820have two or more major or longitudinal axes, example cell800amay have more than four corners.

FIG. 8Bshows a schematic diagram of a portion of an example topology800bof a quantum processor according to the present systems, methods and apparatus. Example topology800bhas four cells with communicative coupling between diagonally adjacent cells. Example topology800bshows four cells801,802,803and804, where each cell is an implementation of example cell800aofFIG. 8.

As mentioned above, inter-cell couplers840(only one called out inFIG. 8B) connect pairs of vertical and pairs of horizontal qubits in adjacent cells. With reference toFIG. 8B, a second horizontal qubit812of cell801is communicatively coupled to first horizontal qubit814and third horizontal qubit816of cell802. Similarly second vertical qubit822of cell801is communicatively coupled to first vertical qubit824and to third vertical qubit826of cell803.

FIG. 8Cis a schematic diagram illustrating a portion800cof the inter-cell connectivity of example topology800b.FIG. 8Cshows portion800cof cells801,802,803and804where pairs of cells laid out diagonally adjacent in the plane of the page ofFIG. 8Care communicatively coupled.

Inter-cell coupler841can provide tunable communicative coupling between fourth horizontal qubit813of cell801and first horizontal qubit819of diagonally laid out unit tile804. Inter-cell coupler842can provide tunable communicative coupling between first horizontal qubit818of cell803and fourth horizontal qubit817of diagonally laid out unit tile802. Inter-cell coupler843can provide tunable communicative coupling between fourth vertical qubit827of cell803and first vertical qubit828of diagonally laid out unit tile802. Inter-cell coupler844can provide tunable communicative coupling between fourth vertical qubit823of cell801and first vertical qubit829of diagonally laid out unit tile804.

Inter-cell couplers that can provide tunable communicative coupling between pairs of diagonally adjacent cells cross each other. In some implementations, inter-cell couplers may cross three other inter-cell couplers.

FIG. 9Ais a schematic diagram of an example cell900ain a quantum processor according to the present systems, method and apparatus. Each qubit in example cell800acan be communicatively coupled to two other qubits on each side. Example cell900ahas two sets of qubits where each qubits is a superconducting loop in an H-shape or I-shape. Each qubit in example cell900acan be communicatively coupled to two other qubits on each side and the couplers do not cross each other. Example cell900ahas a first set of qubits911to914(collectively910) and a second set of qubits921to924(collectively920).

While each set of qubits is illustrated as having four qubits, such is not limiting. In other implementations, each set of qubits in a cell may have a larger or smaller number of qubits. In some implementations, the number of qubits in first set910does not equal the number of qubits in second set920.

Qubits in cell900aare shown as having a superconducting loop forming an H-shape or I-shape, however, such is not limiting and qubits may have other form such as, but not limiting to, rectangular or discorectangular loops. In some implementations an H-shape or I-shape loop may represent a segment of a qubit. Each qubit910-920may be interrupted by at least one respective Josephson junction (not shown).

Qubits of first set of qubits910in example cell900aare substantially parallel to one another and may be laid out generally horizontally in the plane of the page ofFIG. 9Aand may be referred in this specifications and appended claims as horizontal qubits. Qubits of second set of qubits920in example cell900aare substantially parallel to one another and may be laid out generally vertically in the plane of the page ofFIG. 9Aand may be referred in this specifications and appended claims as vertical qubits. Qubits in the first set of qubits910are substantially non-parallel (e.g., meet at 90 degree) to qubits in the second set of qubits920. While qubits in the first set910and qubits in the second set920are illustrated inFIG. 9Aas having one longitudinal or major axis (not shown), such is not limiting and in other implementations qubits from the first set910and/or the second set920may have two or more longitudinal or major axes.

While example cell900ais illustrated as having two sets of qubits, such is not limiting. In other implementations example cell900amay have a larger number of sets (e.g., three sets) of qubits.

Couplers such as couplers935(only one called out) may provide pair-wise communicative coupling between respective pairs of qubits where one qubit of the pair is selected from one of the first set of qubits910or the second set of qubits920, and the other qubit of the pair selected from a different one of first set of qubits910or the second set of qubits920.

Couplers935can provide tunable communicative coupling between qubits of the first set of qubits910and the second set of qubits920. The couplers are located at regions proximate where the qubits of the first set910meet qubits of the second set920. In some implementations couplers may be located at some distance from the regions where the qubits of the first set810meet qubits of the second set820.

Each qubit in unit tile900apresents at least 2 inter-cell couplers, such as couplers942aand942b(only four called out inFIG. 9A, collectively940) connecting a qubit in example cell900awith at least two qubits in neighboring cells.

In some implementations horizontal qubits in a cell are communicatively coupled to horizontal qubits in a neighboring cell via inter-cell couplers940. Likewise, inter-cell couplers940can provide tunable communicative coupling between pairs of vertical qubits in adjacent cells. As shown inFIG. 9A, a qubit912has inter-cell couplers942a,942b,942cand942d. Qubit912is depicted as the second horizontal qubit, from the upper edge of example cell900a. This numbering is arbitrary and for illustration purposes only and not limiting the scope of the present specification and appended claims.

Each inter-cell coupler940provides tunable communicative coupling between a horizontal or vertical qubit in example cell900aand a first horizontal or vertical qubit in a different position in a neighboring cell and a second horizontal or vertical qubit in the same position in a neighboring cell.

For example, inter-cell coupler942aprovides tunable communicative coupling between second horizontal qubit912and a first horizontal qubit in a neighboring cell, and inter-cell coupler942bprovides tunable communicative coupling between second horizontal qubit912and a second horizontal qubit in a neighboring cell. Likewise inter-cell coupler942cprovides tunable communicative coupling between second horizontal qubit912and a first horizontal qubit in a neighboring cell and inter-cell coupler942dprovides tunable communicative coupling between second horizontal qubit812and a second horizontal qubit in a neighboring cell.

Inter-cell couplers940do not cross each other when providing communicative coupling between pairs of horizontal and pairs of vertical qubits in adjacent cells, with the exception of inter-cell couplers between diagonally adjacent cells, as shown in more details inFIG. 9B. In some implementations, inter-cell couplers940may cross each other when providing communicative coupling between pairs of horizontal and pairs of vertical qubits in adjacent cells.

FIG. 9Bshows a schematic diagram of a portion an exemplary topology900bof a quantum processor according to the present systems, methods and apparatus. Example topology900ahas four cells and communicative coupling between two diagonally adjacent cells. Example topology900bshows four cells901,902,903and904, where each cell is an implementation of example cell900aofFIG. 9A.

As mentioned above, inter-cell couplers940connect pairs of vertical and pairs of horizontal qubits in adjacent cells. With reference toFIG. 9B, a second horizontal qubit912of cell901is communicatively coupled to first horizontal qubit914and second horizontal qubit915of cell902. Similarly second vertical qubit922of cell901is communicatively coupled to first vertical qubit924and to second vertical qubit925of cell903.

In some implementations inter-cell couplers941and942cross each other in the space between cells902and903. In some implementations inter-cell couplers941and942cross may each other over or under or within the surface one of the cells901,902,903or904.

FIG. 10shows a schematic diagram of a portion of an example topology1000of a quantum processor according to the present systems, methods and apparatus. Example topology has four cells and no communicative coupling between diagonally adjacent cells. The additional space between diagonally adjacent cells may be occupied by other electronic components. Example topology1000has four cells1001,1002,1003and1004.

Cells1001to1004have a set of horizontal qubits1010(only one called out inFIG. 10) and a set of vertical qubits1020(only one called out inFIG. 10). While qubits of the set of horizontal qubits1010and of the set of vertical qubits1020are illustrated inFIG. 10as having one longitudinal or major axis (not shown), such is not limiting and in other implementations qubits of the set of horizontal qubits1010and/or of the set of vertical qubits1020may have two or more longitudinal or major axes. While each set is illustrated as having four qubits, such is not limiting. In other implementations, each set of qubits in a cell may have a larger or smaller number of qubits. In some implementations, the number of qubits in first or horizontal set1010does not equal the number of qubits in second or vertical set1020. While inFIG. 10each cell in example topology1000is illustrated as having two sets of qubits, such is not limiting and each cell in example topology1000may have a larger (e.g. three sets) number of sets of qubits.

Qubits in example topology1000are shown as having a superconducting loop forming an H-shape or I-shape, however, such is not limiting and qubits may have other form such as, but not limiting to, rectangular or discorectangular loops. In some implementations an H-shape or I-shape loop may represent a segment of a qubit. Each qubit of the set of horizontal qubits1010and/or of the set of vertical qubits1020may be interrupted by at least one respective Josephson junction (not shown).

Similarly to example topology800b, in example topology1000inter-cell couplers1040(only one called out inFIG. 10) connect pairs of vertical and pairs of horizontal qubits in adjacent cells. Unlike example topology800b, diagonally adjacent cells are not communicatively coupled with inter-cell couplers.

As shown inFIG. 10, cell1001and cell1004are laid out diagonally adjacent to each other in the plane of the page ofFIG. 10. Similarly cells1002and1003are laid out diagonally adjacent to each other. This arrangement is shown inFIG. 10for illustration purposes and it is not limiting.

Unlike example topology800b, in example topology1000fourth horizontal qubit1013of cell1001is communicatively coupled to fourth horizontal qubit1017of adjacent cell1002and fourth vertical qubit1023is communicatively coupled to fourth vertical qubit1027of adjacent cell1003. First horizontal qubit1018of cell1003is communicatively coupled to first horizontal qubit1019of adjacent cell1004and first vertical qubit1028of cell1002is communicatively coupled to first vertical qubit1029of adjacent cell1004.

FIG. 11is a schematic diagram of a portion of an example topology1100of a quantum processor according to the present systems, methods and apparatus. Example topology1100has four cells and communicative coupling between two diagonally adjacent cells. Example topology1100has four cells1101,1102,1103and1104.

Cells1101to1104have a set of horizontal qubits1110(only one called out inFIG. 11) and a set of vertical qubits1120(only one called out inFIG. 11). While qubits of the set of horizontal qubits1110and of the set of vertical qubits1120are illustrated inFIG. 11as having one longitudinal or major axis (not shown), such is not limiting and in other implementations qubits of the set of horizontal qubits1110and/or of the set of vertical qubits1120may have two or more longitudinal or major axes. While each set is illustrated as having four qubits, such is not limiting. In other implementations, each set of qubits in a cell may have a larger or smaller number of qubits. In some implementations, the number of qubits in first or horizontal set1110does not equal the number of qubits in second or vertical set1120. While inFIG. 11each cell in example topology1100is illustrated as having two sets of qubits, such is not limiting and each cell in example topology1100may have a larger (e.g. three sets) number of sets of qubits.

Qubits in example topology1100are shown as having a superconducting loop forming an H-shape or I-shape; however, such is not limiting and qubits may have other form such as, but not limiting to, rectangular or discorectangular loops. In some implementations an H-shape or I-shape loop may represent a segment of a qubit. Each qubit1110-1120may be interrupted by at least one respective Josephson junction (not shown).

Similarly to example topology800b, in example topology1100inter-cell couplers1140(only one called out inFIG. 11) connect pairs of vertical and pairs of horizontal qubits in adjacent cells. Unlike example topology1000, diagonally adjacent cells are communicatively coupled to each other but, unlike topology800b, only two diagonally adjacent cells are communicatively coupled. In topology1100couplers may cross when providing communicative coupling between diagonally adjacent cells.

With respect to the plane of the page ofFIG. 11, connectivity between horizontally adjacent cells in example topology1100is similar to the connectivity between horizontally adjacent cells in example topology1000. Connectivity between vertically adjacent cells in example topology1100is similar to the connectivity between vertically adjacent cells in example topology800b.

A person skilled in the art will understand the opposite is also possible and example topology1100can be implemented with connectivity similar to example topology1000between vertically adjacent cells and connectivity similar to example topology800bbetween horizontally adjacent cells. In some implementations where qubits1110and1120have two or more major or longitudinal axes, inter-cell couplers1140can provide tunable communicative coupling between substantially parallel qubits in adjacent cells.

FIG. 12is a schematic diagram illustrating an example cell1200in a quantum processor according to the present systems, method and apparatus. Example cell1200has two sets of qubits and couplers between qubits of the same set. Couplers may provide communicative coupling between qubits that are substantially parallel. Example cell1200has a first set of qubits1211to1214(collectively1210) and a second set of qubits1221to1224(collectively1220). While inFIG. 12example cell1200is illustrated as having two sets of qubits, such is not limiting and example cell1200may have a larger number of sets of qubits (e.g. three sets).

While each set is illustrated as having four qubits, such is not limiting. In other implementations, each set of qubits in a cell may have a larger or smaller number of qubits. In some implementations, the number of qubits in first set1210does not equal the number of qubits in second set1220.

Qubits in example cell1200are shown as having a superconducting loop in a rectangular shape, however, such is not limiting and qubits may have other form such as, but not limiting to, discorectangular or oval loops. In some implementations a rectangular loop may represent a segment of a qubit. In one implementation, each qubit1210-1220is interrupted by at least one respective Josephson junction (not shown inFIG. 12).

Qubits in first set of qubits1210in example cell1200are substantially parallel to one another and may be laid out generally horizontally in the plane of the page ofFIG. 12and may be referred in this specification and appended claims as horizontal qubits. Qubits in second set of qubits1220in example cell1200are substantially parallel to one another and may be laid out generally vertically in the plane of the page ofFIG. 12and may be referred in this specification and appended claims as vertical qubits. Qubits of the set of horizontal qubits1210and qubits of the set of vertical qubits1220are substantially non-parallel (e.g. meet at 90 degree). While qubits of the set of horizontal qubits1210and of the set of vertical qubits1220are illustrated inFIG. 12as having one longitudinal or major axis (not shown), such is not limiting and in other implementations qubits of the set of horizontal qubits1210and/or of the set of vertical qubits1220may have two or more longitudinal or major axes.

Couplers such as couplers1250(only one called out inFIG. 12) may provide pair-wise communicative coupling between respective pairs of qubits where one qubit of the pair is selected from one of qubits of the set of horizontal qubits1210or one of the qubits of the set of vertical qubits1220, and the other qubit of the pair selected from a different one of qubits of the set of horizontal qubits1210or qubits of the set of vertical qubits1220.

Couplers1250may provide tunable communicative coupling between qubits1210and qubits1220. The couplers may be located at regions proximate where qubits1210meet qubits1220. In some implementations couplers1250are located at some distance from the region where qubits1210meet qubits1220.

Example cell1200has eight couplers1241to1248(collectively1240) providing tunable communicative coupling between pairs of horizontal qubits and between pairs of vertical qubits. Some couplers1240can communicatively couple non-adjacent qubits (e.g., qubits1222and1224). Other couplers1240can communicatively couple adjacent qubits (e.g., qubits1223and1224). In some implementations where qubits1210and1220have two or more longitudinal or major axes couplers1240communicatively couple pairs of substantially parallel qubits.

When communicatively coupling non-adjacent qubits, couplers1240may cross over or under other qubits and/or couplers and/or other electronic components in example cell1200and are substantially electrically isolated from them. For example, when coupler1247communicatively couples non-adjacent qubits1222and1224, coupler1247does not communicatively couple to qubit1223or any other qubits, nor does it interfere with the normal operation of other electronic components of example cell1200.

When communicatively coupling adjacent qubits, couplers1240may cross over or under other qubits and/or couplers and/or other electronic components that may be present between horizontal or between vertical qubits in example cell1200and are substantially electrically isolated from them. For example, when coupler1248communicatively couples adjacent qubits1221and1222, coupler1248does not communicatively couple to any other qubit in example cell1200, nor does it interfere with the normal operation of other electronic components of example cell1200.

As shown in example cell1200, each qubit has a connectivity of six. For example, qubit1211is communicatively coupled to each vertical qubit1221to1224through couplers1250, to horizontal qubit1212through coupler1241and to horizontal qubit1213through coupler1242.

In other implementations, qubits in example cell1200have couplers1240that communicatively couple each horizontal qubit1210to each of another of the horizontal qubits1210and/or each vertical qubit1220to each of another of the vertical qubits1220, in addition to couplers1250, thereby implementing a connectivity of seven.

In addition, couplers1240may provide inter-cell communicative coupling from example cell1200to adjacent or non-adjacent cells. Examples of couplers implementing inter-cell connectivity can be found in U.S. Patent application No. 62/288,719.

FIG. 13is a schematic diagram illustrating an example cell1300in a quantum processor according to the present systems, methods and apparatus. Example cell1300comprises two sets of qubit, each qubit having L-shape. Qubits in one set are substantially symmetric to the qubits in the other set with respect to an axis of symmetry. Couplers between the two sets of qubits may be located proximate the regions where the qubits change direction. Example cell1300has a first set of qubits1311to1318(collectively1310) and a second set of qubits1321to1328(collectively1320). While inFIG. 13example cell1300is illustrated as having two sets of qubits, such is not limiting and example cell1300may have a larger (e.g. three) number of sets of qubits.

While each set is illustrated as having eight qubits, such is not limiting. In other implementations, each set of qubits in a cell may have a larger or smaller number of qubits. In some implementations, the number of qubits in first set1310does not equal the number of qubits in second set1320.

Qubits in example cell1300are shown as having a superconducting loop forming an L-shape; however, such is not limiting and qubits may have other form such as, but not limiting to, rectangular, oval or discorectangular loops. An L-shape is defined as having two adjacent segments or portions which are substantially non-parallel (e.g., they meet at 90 degrees). In some implementations an L-shape loop may represent a segment of a qubit. Each qubit1310-1320is interrupted by at least one respective Josephson junction (not shown).

Qubits in example cell1300have a first segment1361(only one called out inFIG. 13) horizontal in the plane of the page ofFIG. 13and a second segment1362(only one called out inFIG. 13) vertical in the plane of the page ofFIG. 13, where each qubit bends between first segment1361and second segment1362, and each qubit has substantially similar length. In some implementations some or all of the qubits in example cell1300may form an included angle or bend at an angle between first segment1361and second segment1362such that first segment1361and second segment1362are non-orthogonal.

In other implementations qubits in example cell1300have more than two segments (e.g., three segments) and adjacent segments (e.g., first segment1361and second segment1362) are substantially parallel to two different axes.

Qubits1310are so arranged in example cell1300so that they bend between the first and the second segment in a different place along their respective lengths so that first qubit1311has the shortest first segment1361and longest second segment1362and eighth qubit1318having the longest first segment1361and shortest second segment1362.

Qubits1320are so arranged in example cell1300so that they have an included angle or bend between the first and the second segment in a different place along their length so that first qubit1321has the longest first segment1361and the shortest second segment1362and eighth qubit1328has the shortest first segment1361and the longest second segment1362.

Couplers such as couplers1360(only one called out inFIG. 13) provide pair-wise tunable communicative coupling between respective pairs of qubits where one qubit of the pair is selected from one of the first set of qubits1310and the other qubit of the pair selected from a different one of the first set of qubits1310, and/or where one of qubits is selected from one of the qubits of the second set of qubits1320and the other qubit is selected from a different one of qubits of the second set of qubits1320. The couplers may be located at regions proximate where qubits of the first set1310meet a different one of the qubits of the first set1310and where qubits of the second set1320meet a different one of qubits of the second set1320. For example coupler1360provides tunable communicative coupling between qubit1321and qubit1328. In some implementations couplers1360may be located at some distance from the region where qubits of the first set1310meet a different one of qubits of the first set1310and where qubits of the second set1320meet a different one of qubits of the second set1320.

Couplers such as couplers1350(only one called out inFIG. 13) provide tunable communicative coupling between one of the qubits of the first set1310and one of the qubits of the second set1320such that each qubit of the first set1310is communicatively coupled to one qubit of the second set1320and each qubit of the second set1320is communicatively coupled to one qubit of the first set1310. For example, coupler1350provides tunable communicative coupling between qubit1318and qubit1328. In example cell1300there are eight couplers1350.

In example cell1300, each qubit has a connectivity of eight. For example qubit1321is communicatively coupled to qubit1311through coupler1350and is communicatively coupled to qubits1322to1328through couplers1360. While inFIG. 13each qubit is illustrated as having a connectivity of eight such is not limiting and in other implementations qubits in example cell1300may have a smaller or larger connectivity.

FIG. 14shows a schematic diagram of an example cell1400in a quantum processor according to the present systems, methods and apparatus. Example cell1400comprises four sets of qubits. Two sets of qubits have substantially rectangular shape and the other two set of qubits have a substantially L-shape. Similarly to example cell1300, one set of L-shaped qubits is symmetric to the other set of L-shaped qubits with respect to an axis of symmetry and couplers may be present proximate the regions where the L-shape qubits change direction. Unlike example cell1300, rectangular qubits may be coupled to L-shaped qubits. Example cell1400has a first set of qubits1411to1414(collectively1410), a second set of qubits1421to1424(collectively1420), a third set of qubits1431to1434(collectively1430) and a fourth set of qubits1441to1444(collectively1440). While inFIG. 14example cell1400is illustrated as having four sets of qubits, such is not limiting and example cell1400may have a larger (e.g. five sets) number of sets of qubits.

While each set is illustrated as having four qubits, such is not limiting. In other implementations, each set of qubits in a cell may have a larger or smaller number of qubits. In some implementations, the number of qubits in one set (e.g. the first set) does not equal the number of qubits in another set (e.g. the third set). Each qubit in the first, the second, the third and/or the fourth set of qubits1410-1440may be interrupted by at least one respective Josephson junction (not shown). In some implementations some or all of qubits in the first, the second, the third and/or the fourth set of qubits1410-1440may represent a segment of a qubit.

Qubits of first set of qubits1410in example cell1400are substantially parallel to one another and may be laid out generally horizontally in the plane of the page ofFIG. 14and may be referred in this specification and appended claims as horizontal qubits. Qubits of second set of qubits1420in example cell1400are substantially parallel to one another and may be laid out generally vertically in the plane of the page ofFIG. 14and may be referred in this specification and appended claims as vertical qubits. Qubits in the first set1410are substantially non-parallel (e.g. meet at 90 degree) to qubits in the second set1420.

Qubits of the first set1410each have a respective longitudinal or major axis1473, (only one called out inFIG. 14) along which the superconductive paths or loops of the respective qubits of the first set1410extend in a lengthwise direction of the qubit. Likewise, the qubits of the second set1420each have a respective longitudinal or major axis1472(only one called out inFIG. 14) along which the superconductive paths or loops of the qubits of the second set1420extend in a lengthwise direction of the qubit.

While each of the qubits1410and1420is illustrated inFIG. 14as having one longitudinal or major axis (1473and1474, respectively) such is not limiting and in other implementations, some or all of the qubits of the first set1410and/or the second set1420may have two or more longitudinal or major axes.

Qubits1430of third set and qubits1440of fourth set are shown as having a superconducting loop forming an L-shape; however, such is not limiting and qubits may have other form such as, but not limiting to, rectangular, oval or discorectangular loops. An L-shape is defines as having two adjacent segments or portions which are substantially non-parallel (e.g., they meet at 90 degrees).

Qubits of third set1430and qubits of fourth set1440have a first segment1481(only one called out inFIG. 14) horizontal in the plane of the page ofFIG. 14and a second segment1482(only one called out inFIG. 14) vertical in the plane of the page ofFIG. 14, where each qubit forms an included angle or bends between first segment1481and second segment1482, and each qubit has substantially similar length. In some implementations some or all of the qubits of the third set1430and the fourth set1440in example cell1400may form an included angle or bend at an angle between first segment1481and second segment1482such that first segment1481and second segment1482are non-orthogonal.

In other implementations qubits of the third set1430and the fourth set1440in example cell1400have more than two segments (e.g. three segments) and adjacent segments (e.g. first segment1481and second segment1482) are substantially parallel to two different axes.

Qubits in the third set1430are so arranged in example cell1400so that they form an included angle or bend between the first and the second segment in a different place along their length so that first qubit1431has the shortest first segment1481and longest second segment1482and fourth qubit1434having the longest first segment1481and shortest second segment1482; therefore, qubits of the first set, the second set, the third set and the fourth set1410-1440are substantially equal in length.

Qubits of the fourth set1440are so arranged in example cell1400so that they bend between the first and the second segment in a different place along their length so that first qubit1441has the longest first segment1481and the shortest second segment1482and fourth qubit1444has the shortest first segment1481and the longest second segment1482.

Qubits of the third set1430and the fourth set1440are symmetric along axis1471, e.g., first segment1481of qubit1431and second segment1482of qubit1441are substantially equal in length.

Couplers such as couplers1460(only one called out inFIG. 14) may provide pair-wise tunable communicative coupling between respective pairs of qubits where one qubit of the pair is selected from one set of qubits (e.g. the fourth set1440) and the other qubit of the pair selected from a different one of the same set of qubits (e.g. the fourth set1440) or a different set of qubits (e.g. the first set1410). The couplers may be located at regions proximate where qubits in example cell1400meet another qubit. In some implementations, couplers may be located at some distance from the region where qubits in example cell1400meet another qubit. For example coupler1460provides tunable communicative coupling between qubit1411and qubit1444.

Couplers such as couplers1450(only one called out inFIG. 14) may provide tunable communicative coupling between one of the qubits of the third set1430and one of the qubits of the fourth set1440such that each qubit in the third set1430is communicatively coupled to one qubit in the fourth set1440and each qubit in the fourth set1440is communicatively coupled to one qubit the third set1430. For example, coupler1450provides tunable communicative coupling between qubit1434and qubit1444. In example cell1400there are four couplers1450. Couplers1450may be located where qubits1430and1440come closest to each other; however, in other implementations couplers1450may be located at some distance from the region where qubits1430and1440come closest to each other.

In example cell1400, each qubit has a connectivity of eight. For example qubit1434is communicatively coupled to qubit1444through coupler1450and is communicatively coupled to qubits1421to1424and to qubits1431to1433through couplers1460. While inFIG. 14each qubit is illustrated as having a connectivity of eight such is not limiting and in other implementations qubits in example cell1400may have a smaller or larger connectivity.

FIG. 15shows a schematic diagram of an example topology1500of a quantum processor according to the present systems, methods and apparatus. Example topology1500comprises four cells. Couplers may provide communicative coupling between vertical qubits and between horizontal qubits in adjacent cells. Vertical qubits are communicatively coupled between cells tiled horizontally in the plane of the page ofFIG. 15and horizontal qubits are communicatively coupled between cells tiled vertically in the plane of the page ofFIG. 15. Example topology1500has four cells1501to1504; however such is not limiting and example topology1500may have a greater or smaller number of cells.

Each cell in example topology1500has a first set of qubits1510(only one called out inFIG. 15) and a second set of qubits1520(only one called out inFIG. 15). While each set is illustrated as having four qubits, such is not limiting. In other implementations, each set of qubits in a cell may have a larger or smaller number of qubits. In some implementations, the number of qubits in first set1510does not equal the number of qubits in second set1520. While inFIG. 15each cell in example topology1500is illustrated as having two sets of qubits, such is not limiting and each cell in example topology1500may have a larger (e.g. three sets) number of sets of qubits.

Qubits in example topology1500are shown as having a rectangular superconducting loop; however, such is not limiting and qubits may have other form such as, but not limiting to, discorectangular or oval loops. In some implementations, a rectangular loop may represent a segment of a qubit. Each qubit1510-1520may be interrupted by at least one respective Josephson junction (not shown).

Qubits of first set of qubits1510cin example topology1500are substantially parallel to one another and may be laid out generally horizontally in the plane of the page ofFIG. 15and may be referred in this specification and appended claims as horizontal qubits. Qubits of second set of qubits1520in example cell1500are substantially parallel to one another and may be laid out generally vertically in the plane of the page ofFIG. 15and may be referred in this specification and appended claims as vertical qubits. Qubits in the first or horizontal set1510and qubits in the second or vertical set1520are substantially non-parallel (e.g. meet at 90 degree).

While qubits in the first set1510and the second set1520are illustrated inFIG. 15as having one longitudinal or major axis (not shown), such is not limiting and in other implementations qubits of the first set1510and/or the second set1520may have two or more longitudinal or major axes.

Couplers such as couplers1540(only one called out inFIG. 15) provide pair-wise tunable communicative coupling between respective pairs of qubits where one qubit of the pair is selected from the first set1510and the other qubit of the pair selected from the second set1520.

Couplers1540may provide tunable communicative coupling between qubits of the first set1510and qubits of the second set1520. The couplers may be located at regions proximate where the qubits of the first set1510meet qubits of the second set1520. In some implementations the qubits are located at some distance from the regions where qubits of the first set1510meet qubits of the second set1520.

Long-range couplers may directly couple over a greater physical distance than inter-cell couplers, and so may communicatively couple with qubits in a way which provides greater coupling strength. Long-range couplers1530ato1530p(collectively1530) provide tunable communicative coupling between qubits of the first set of qubits1510in one cell (e.g., cell1501) and qubits of the first set of qubits1510in an adjacent cell (e.g., cell1504) and between qubits of the second set of qubits1520in one cell (e.g., cell1501) and qubits of the second set of qubits1520in an adjacent cell (e.g., cell1502). Each qubit inFIG. 15is illustrated as having one long-range coupler1530; however such is not limiting. In other implementations each qubit may have two or more long-range coupler1530. Alternatively or in addition, each qubit may have one or more long-range coupler that is different from long-range couplers1530. For example, couplers1240may be employed in addition or instead of long-range couplers1530.

When long-range couplers1530provide tunable communicative coupling between horizontal qubits, they provide tunable communicative coupling between cells that are positioned vertically in the plane of the page ofFIG. 15and when long-range couplers1530provide tunable communicative coupling between vertical qubits, they provide tunable communicative coupling between cells that are positioned horizontally in the plane of the page ofFIG. 15.

In other implementations, long-range couplers1530may provide tunable communicative coupling between horizontally or vertically positioned cells that are not adjacent to each other.

FIG. 16shows a schematic diagram of an example topology1600of a quantum processor according to the current systems, methods and apparatus. Example topology1600comprises two sub-topologies of equal size tiled over the plane of the page ofFIG. 16. In some implementations, example topology1600is comprised of example topology1500and a second topology1200a, where topology1200ais comprised of four example cells1200, while in other implementations example topology1600is comprised of sub-topologies that are substantially different from sub-topologies1200aand1500.

While inFIG. 16example topology1600is illustrated as having two sub-topologies, this is not limiting and in other implementations example topology1600may have three or more sub-topologies.

In example topology1600, each sub-topology is comprised of four cells; however, such is not meant to be limiting and each sub-topology may have a larger or smaller number of cells.

In example topology1600each sub-topology is comprised of the same number (i.e., four) cells; however, such is not limiting and the number of cells in one sub-topology (e.g., topology1500) may not be equal the number of cells in another sub-topology (e.g., topology1200a) in example topology1600.

Couplers (not shown inFIG. 16) provide tunable communicative coupling between pairs of adjacent sub-topologies. In some implementations couplers provide tunable communicative coupling between pairs of non-adjacent sub-topologies.

FIG. 17shows a schematic diagram of an example topology1700of a quantum processor according to the present systems, methods and apparatus. Example topology1700comprises two sub-topologies of different size tiled over the plane of the page ofFIG. 17. In some implementations example topology1700comprises example topology1500and topology1200b, where the number of cells in one sub-topology (e.g., topology1500) does not equal the number of cells in another sub-topology (e.g.,1200b) and topology1500is substantially different from topology1200b. Topology1200bis comprised of one or more example cells1200.

While inFIG. 17topology1200bis illustrated as having one cell and topology1500is illustrated as having four cells1501to1504(only one called out inFIG. 17), such is not limiting. In other implementations topologies1500and1200bmay have a smaller or larger number of cells.

The outline of example topology1500and topology1200bare shown in a dashed outline for clarity and are not intended to imply any physical structure.

In other implementations, example topology1700is comprised of sub-topologies that are substantially different from topology1500and1200b. In other implementations, example topology1700may have a larger number (e.g. three) of sub-topologies.

Couplers (not shown inFIG. 17) provide tunable communicative coupling between pairs of adjacent sub-topologies. In some implementations couplers provide tunable communicative coupling between pairs of non-adjacent sub-topologies.

FIG. 18shows a schematic diagram of an example topology1800of a quantum processor according to the present systems, methods and apparatus. Example topology1800comprises four cells of qubits. Couplers may provide communicative coupling between qubits in adjacent cells and between qubits in non-adjacent cells. Couplers that communicatively couple qubits in adjacent cell may communicatively couple a vertical qubit to a horizontal qubit in adjacent cells or a horizontal qubit to a vertical qubit in adjacent cells. Couplers that provide communicative coupling between qubits in non-adjacent cells may cross one or more cells. Such couplers may be long-range couplers. Example topology1800comprises four cells1801to1804; however, such is not limiting and example topology1800may have a greater or smaller number of cells.

Each cell in example topology1800has a first set of qubits1810(only one called out inFIG. 18) and a second set of qubits1820(only one called out inFIG. 18). While each set1810,1820is illustrated as having four qubits, such is not limiting. In other implementations, each set of qubits1810,1820in a cell may have a larger or smaller number of qubits. In some implementations, the number of qubits in first set1810does not equal the number of qubits in second set1820. While inFIG. 18each cell in example topology1800is illustrated as having two sets of qubits, such is not limiting and each cell in example topology1800may have a larger (e.g., three sets) number of sets of qubits.

Qubits in example topology1800are shown as having rectangular superconducting loops; however, such is not limiting and qubits may have other form such as, but not limiting to, discorectangular or oval loops. In some implementations a rectangular loop may represent a segment of a qubit. Each qubit in the first set1810and the second set1820may be interrupted by at least one respective Josephson junction (not shown).

Qubits of first set of qubits1810in example topology1800are substantially parallel to one another and may be laid out generally horizontally in the plane of the page ofFIG. 18and may be referred in this specification and appended claims as horizontal qubits. Qubits of second set of qubits1820in example cell1800are substantially parallel to one another and may be laid out generally vertically in the plane of the page ofFIG. 18and may be referred in this specifications and appended claims as vertical qubits. Qubits in the first or horizontal set1810are substantially non-parallel (e.g. meet at 90 degree) to qubits in the second or vertical set1820.

While qubits in the first set1810and second set1820are illustrated inFIG. 18as having one longitudinal or major axis (not shown), such is not limiting and in other implementations qubits in the first set1810and/or the second set1820may have two or more longitudinal or major axes.

Couplers such as couplers1870(only one called out inFIG. 18) provide pair-wise communicative coupling between respective pairs of qubits where one qubit of the pair is selected from one of qubits in the first set1810and the other qubit of the pair selected from one of qubits in the second set1820in the same cell.

Couplers1870provide tunable communicative coupling between qubits in the first set1810and qubits in the second set1820. Couplers1870are located at regions proximate where the qubits in the first set1810meet qubits in the second set1820. In some implementations, couplers1870are located at some distance from the regions where qubits in the first set1810meet qubits in the second set1820.

Long-range couplers1830a-1830i(only nine called out inFIG. 18, collectively1830) providing tunable communicative coupling between qubits of the first set of qubit1810in one cell (e.g. cell1801) and qubits in the first set1810in a non-adjacent cell and between qubits in the second set of qubits1820in one cell (e.g. cell1801) and qubits in the second set of qubits1820in a non-adjacent cell.

Long-range couplers1830provide tunable communicative coupling between horizontal qubits in non-adjacent cells, and between vertical qubits in non-adjacent cells.

For example, long-range coupler1830eprovides tunable communicative coupling between a third horizontal qubit1810in cell1801and a fourth horizontal qubit in a cell positioned on the right of cell1802in the plane of the page ofFIG. 18and long-range coupler1830iprovides tunable communicative coupling between a first vertical qubit1820in cell1803and a second vertical qubit1820in a cell positioned above cell1802in the plane of the page ofFIG. 18.

While qubits are illustrated inFIG. 18as having one long-range coupler1830such is not limiting and in some implementations qubits in example topology1800may have two or more long-range couplers1830.

Couplers such as long-range couplers1840a-1840g(only seven called out inFIG. 18, collectively1840) provide tunable communicative coupling between first set of qubits1810in one cell (e.g., cell1801) and second set of qubits1820in an adjacent cell (e.g., cell1804) and between second set of qubits1820in one cell (e.g., cell1802) and first set of qubits in an adjacent cell (e.g., cell1803).

Long-range couplers1840are shown inFIG. 18in a dash line for clarity; that depiction is not intended to imply any physical structure.

Long-range couplers1840provide tunable communicative coupling between vertical and horizontal qubits in adjacent cells and/or between horizontal and vertical qubits in adjacent cells. For example, long-range coupler1840aprovides tunable communicative coupling between a first vertical qubit1820in cell1802and a third horizontal qubit1810in cell1803.

While inFIG. 18qubits are illustrated as having one long-range coupler1840such is not limiting and in some implementation qubits in example topology18may have two or more long-range couplers1840.

In some implementations, long-range couplers1840may provide tunable communicative coupling between horizontal and vertical qubits in non-adjacent cells.

In some implementations, one or more of long-range couplers1830may be replaced in example topology1800by one or more of long-range couplers1840, or one or more long-range couplers1840may be replaced by one or more long-range couplers1830.

FIG. 19shows a schematic diagram of an example topology1900of a quantum processor according to the present systems, methods and apparatus. Example topology1900employs long-range couplers that change direction around an axis of symmetry. Additional space may be available proximate the regions where the long-range couplers change direction for other electronic components of a quantum processor. Example topology1900comprises seven cells1901to1907tiled over the plane of the page ofFIG. 19in the shape of a cross; however such is not limiting and example topology1900may have a greater or smaller number of cells. In example topology1900a central cell1903has a cell on the right (cell1907) and a cell on the left (cell1906) in the plane of the page ofFIG. 19. Central cell1903has two cells (1901and1902) above and two cells (1904and1905) below in the plane of the page ofFIG. 19. In some implementations the cells in example topology19can be positioned to form a different shape in the plane of the page ofFIG. 19. A full topology of a quantum processor may comprise one or more instances of example topology1900tiled over an area. In some implementations, one or more instances of example topology1900may overlap over an area.

In example topology1900each cell has a first set of qubits1910(only one called out inFIG. 19) and a second set of qubits1920(only one called out inFIG. 19). While each set is illustrated as having four qubits, such is not limiting. In other implementations, each set of qubits in a cell may have a larger or smaller number of qubits. In some implementations the number of qubits in first set1910does not equal the number of qubits in second set1920. While inFIG. 19each cell in example topology1900is illustrated as having two sets of qubits, such is not limiting and each cell in example topology1900may have a larger (e.g. three sets) number of sets of qubits.

Qubits in example topology1900are shown as having a rectangular superconducting loop; however, such is not limiting and qubits may have other form such as, but not limiting to, discorectangular or oval loops. In some implementations a rectangular loop may represent a segment of a qubit. Each qubit in the first set1910and/or the second set1920may be interrupted by at least one respective Josephson junction (not shown).

Qubits of first set of qubits1910in example topology1900are substantially parallel to one another and may be laid out generally horizontally in the plane of the page ofFIG. 19and may be referred in this specification and appended claims as horizontal qubits. Qubits of second set of qubits1920in example cell1900are substantially parallel to one another and may be laid out generally vertically in the plane of the page ofFIG. 19and may be referred in this specification and appended claims as vertical qubits. Qubits in the first set1910are substantially non-parallel (e.g. meet at 90 degree) to qubits in the second set1920.

While qubits in the first set1910and the second set1920are illustrated inFIG. 19as having one longitudinal or major axis (not shown), such is not limiting and in other implementations qubits in the first set1910and/or the second set1920may have two or more longitudinal or major axes.

Couplers such as couplers1970(only one called out inFIG. 19) may provide pair-wise communicative coupling between respective pairs of qubits where one qubit of the pair is selected from one of qubits of the first set1910and the other qubit of the pair selected from one of qubits of the second1920in the same cell.

Couplers1970provide tunable communicative coupling between qubits of the first set1910and qubits of the second set1920. The couplers are located at regions proximate where the qubits of the first set1910meet qubits of the second set1920. In some implementations the qubits are located at some distance from the respective regions where qubits of the first set1910meet qubits of the second set1920.

Long-range couplers1930a-1930h(collectively1930) provide tunable communicative coupling between qubits of the first set of qubits1910in one cell (e.g., cell1906) and qubits of the second set of qubits1910in a non-adjacent cell (e.g., cell1901) and between qubits of the second set of qubits1920in one cell (e.g., cell1905) and qubits of the first set of qubits1910in a non-adjacent cell (e.g.,1907).

Long-range couplers1930provide tunable communicative coupling between horizontal and vertical qubits in non-adjacent cells, where the long-range couplers1930route around an axis1960in center cell1903, so that no long-range coupler1930substantially crosses axis1960.

Long-range couplers1930have a first segment1981(only one called out inFIG. 19) and a second segment1982(only one called out inFIG. 19). First segment1981and second segment1982are substantially non-parallel (e.g., they the form an included angle or meet at 90 degrees). First segment1981may have different length than second segment1982. For example, in coupler1930hfirst segment1981is shorter than second segment1982. Therefore, long-range couplers1930or groups of long-range couplers1930have substantially similar length.

For example, long-range coupler1930aprovides tunable communicative coupling between a first qubit of the second or vertical set of qubits1920in cell1901and a fourth qubit of the first or horizontal set of qubits1910in cell1906and long-range coupler1930eprovides tunable communicative coupling between a first qubit of the second or vertical set of qubits1920in cell1905and a fourth qubit of the first or horizontal set qubits1910in cell1907.

While inFIG. 19qubits in cells1901,1906,1905and1907are illustrated as having one long-range coupler1930such is not limiting and in some implementations qubits in cells1901,1906,1905and1907in example topology1900may have two or more long-range couplers1930.

While inFIG. 19qubits in cells1902,1903and1904are illustrated as having no long-range couplers1930, such is not limiting and in some implementations qubits in cells1902,1903and1904in example topology1900have one or more long-range coupler1930. Alternatively or in addition, each qubit may have one or more long-range coupler that is different from long-range couplers1930. For example, couplers1240or1530may be employed in addition or instead of long-range couplers1930.

FIG. 20shows a schematic diagram of an example topology2000of a quantum processor according to the present systems, methods and apparatus. Example topology2000employs two different type of couplers to provide communicative coupling between qubits in diagonally adjacent cells and between qubits in non-adjacent cells. Example topology2000comprises five cells2001to2005tiled over the plane of the page ofFIG. 20in the shape of a cross; however, such is not limiting and example topology2000may have a greater or smaller number of cells. In example topology2000a central cell2003has a cell above (i.e., cell2001), a cell on the right (i.e., cell2004), a cell below (i.e., cell2004) and a cell on the left (i.e., cell2002) in the plane of the page ofFIG. 20. In some implementations the cells in example topology20can be positioned to form a different shape in the plane of the page ofFIG. 20. A full topology of a quantum processor may comprise one or more instances of topology2000tiled over an area.

Each cell in example topology2000has a first set of qubits2010(only one called out inFIG. 20) and a second set of qubits2020(only one called out inFIG. 20). While each set is illustrated as having four qubits, such is not limiting. In other implementations, each set of qubits in a cell may have a larger or smaller number of qubits. In some implementations, the number of qubits in first set2010does not equal the number of qubits in second set2020. While inFIG. 20each cell in example topology2000is illustrated as having two sets of qubits, such is not limiting and each cell in example topology2000may have a larger (e.g. three sets) number of sets of qubits.

Qubits in example topology2000are shown as having a rectangular superconducting loop; however, such is not limiting and qubits may have other form such as, but not limiting to, discorectangular or oval loops. In some implementations a rectangular loop may represent a segment of a qubit. Each qubit in the first set2010and the second set2020may be interrupted by at least one respective Josephson junction (not shown).

Qubits of first set of qubits2010in example topology2000are substantially parallel to one another and may be laid out generally horizontally in the plane of the page ofFIG. 20and may be referred in this specification and appended claims as horizontal qubits. Qubits of second set of qubits2020in example cell2000are substantially parallel to one another and may be laid out generally vertically in the plane of the page ofFIG. 20and may be referred in this specifications and appended claims as vertical qubits. Qubits in the first set2010are substantially non-parallel (e.g. meet at 90 degree) to qubits in the second set2020.

While qubits in the first set2010and the second set2020are illustrated inFIG. 20as having one longitudinal or major axis (not shown), such is not limiting and in other implementations qubits in the first set2010and/or second set2020may have two or more longitudinal or major axes.

Couplers such as couplers2070(only one called out inFIG. 20) may provide pair-wise communicative coupling between respective pairs of qubits where one qubit of the pair is selected from one of qubits of the first set2010and the other qubit of the pair selected from one of qubits of the second set2020in the same cell.

Couplers2070may provide tunable communicative coupling between qubits of the first set2010and qubits of the second set2020. The couplers may be located at regions proximate where the qubits of the first set2010meet qubits of the second set2020. In some implementations the qubits are located at some distance from the respective regions where qubits of the first set2010meet qubits of the second set2020.

Long-range couplers2030a-2030p(collectively2030) provide tunable communicative coupling between qubits of the first set of qubits2010in central cell2003and qubits of the first set of qubits2010in a non-adjacent cell and between qubits of the second set of qubits2020in central cell2003and qubits of the second set of qubits2020in a non-adjacent cell.

Long-range couplers2030provide tunable communicative coupling between horizontal qubits in non-adjacent cells, and between vertical qubits in non-adjacent cells. Long-range couplers2030may pass over or under or across the surface area of cells2001,2002,2004, and/or2005and are electrically isolated from other electronic components, such that long-range couplers2030do not interfere with the operation of other electronic components in cells2001,2002,2003and2004.

For example, long-range coupler2030aprovides tunable communicative coupling between a first qubit of the second or vertical set of qubits2020in central cell2003and a first qubit of the second or vertical set of qubits2020in a cell positioned above cell2001in the plane of the page ofFIG. 20. Long-range coupler2030eprovides tunable communicative coupling between a first qubit of the first or horizontal set of qubits2010in central cell2003and a first qubit of the first or horizontal set of qubits2010in a cell positioned on the right of cell2004in the plane of the page ofFIG. 20.

While each qubit in central cell2003is illustrated inFIG. 20as having two long-range couplers2030such is not limiting. In some implementations each qubit in cell2003can have a smaller or larger (e.g., three) number of long-range couplers2030. Alternatively or additionally, each qubit may have one or more long-range coupler that is different from long-range couplers2030. For example, couplers1240or1530may be employed in addition or instead of long-range couplers2030.

Couplers such as long-range couplers2040a-2040d(only four called out inFIG. 20, collectively2040) provide tunable communicative coupling between horizontal qubits in diagonally adjacent cell and between vertical qubits in diagonally adjacent cells.

In example topology2000vertical qubits in cells2001are communicatively coupled to vertical qubits in cells2002and to vertical qubits in cell2004. Likewise vertical qubits in cell2005are communicatively coupled to vertical qubits2002and to vertical qubits2004. Horizontal qubits in cell2002are communicatively coupled to horizontal qubits in cell2001and to horizontal qubits in cell2005. Likewise horizontal qubits in cell2004are communicatively coupled to horizontal qubits in cell2001and to horizontal qubits in cell2005.

While vertical qubits in cells2001and2005are illustrated inFIG. 20as having a connectivity of three (i.e., are communicatively coupled to three other qubits), such is not limiting and vertical qubits in cells2001and2005may have a smaller or a larger number of long-range couplers2040. While horizontal qubits in cells2002and2004are illustrated as having a connectivity of three (i.e., are communicatively coupled to three other qubits) such is not limiting and horizontal qubits in cells2002and2004may have a smaller or a larger number of long-range couplers2040. Alternatively or in addition, each qubit may have one or more long-range coupler that is different from long-range couplers2040. For example, couplers1240or1530may be employed in addition or instead of long-range couplers2040.

FIG. 21Ashows a schematic diagram of an example qubit2100ain a quantum processor according to the present systems, methods and apparatus. Example qubit2100amay form the basis of a topology of a quantum processor. Example qubits2100ahas one or more coupling devices to communicatively couple to adjacent qubits and qubits in the same cell and one or more long-range couplers to communicatively couple to qubits in other regions of the quantum processor.

Example qubit2100ais illustrated inFIG. 21Aas having a superconductive loop in an elongated rectangular shape; however, such is not limiting and other forms, such as, but not limiting to, oval or discorectangular are also possible. In some implementations a rectangular loop may represent a segment of a qubit. Example qubit2100amay be interrupted by at least one respective Josephson junction (not shown).

Example qubit2100ahas two long-range couplers2101aand2101b(collectively,2101) that provide tunable communicative coupling between example qubit2100aand a qubit in a non-adjacent cell. InFIG. 21Along-range couplers2101are illustrated as placed approximately symmetrically from the middle of the length of example qubit2100a; however, such is not limiting and in other implementations long-range couplers2101may be placed at other regions on a length of example qubit2100a.

In some implementations, example qubit2100amay have a larger or a smaller number of long-range couplers2101. In some implementations, long-range couplers2101provide tunable communicative coupling between example qubit2100aand a qubit in a non-adjacent cell.

Couplers such as couplers2102ato2102n(collectively,2102) provide tunable communicative coupling between qubit2100aand a qubit in the same cell or a qubit in an adjacent cell.

Example qubit2100ais illustrated inFIG. 21Aas having fourteen couplers2102; however such is not limiting and in other implementations example qubit2100amay have a larger or a smaller number of couplers. With reference toFIG. 21A, couplers2102d,2102g,2102i,2102kand2102mmay provide tunable communicative coupling between qubit2100aand a non-adjacent qubit. With reference toFIG. 21A, couplers2102ato2102c,2102e,2102f,2102jand21021to2102nprovide tunable communicative coupling between qubit2100aand an adjacent qubit.

FIG. 2100Bshows a schematic diagram of a group2100bof example qubits2100ain a quantum processor according to the present systems, methods and apparatus. Group2100bis comprised of a first qubit2100a-1and second qubit2100a-2, where each qubit is substantially similar to example qubit2100aofFIG. 21A.

Qubits in group2100bare positioned respective to each other so that they are substantially parallel to each other in the plane of the page ofFIG. 21Band one qubit (e.g., qubit2100a-2) is rotated with respect to the other qubit (e.g.,2100a-1). In some implementations qubit2100a-2is rotated 180 degrees with respect to qubit2100a-1.

Group2100bis illustrated inFIG. 21Bas having two qubits2100a-1and2100a-2; however, such is not limiting and group2100bmay have a larger number of qubits.

At least one coupler2102provides tunable communicative coupling between qubit2100a-1and qubit2100a-2. InFIG. 21B, coupler2102hcommunicatively couples qubits2100a-1and2100a-2. In other implementations another one of couplers2102(e.g., coupler2102f) may communicative couple qubits2100a-1and2100a-2.

FIG. 21Cshows a schematic diagram of an example cell2100cof a quantum processor according to the present systems, methods and apparatus. Example cell2100cis illustrated inFIG. 21Cas having two groups2100b-1and2100b-2of qubits; however, in some implementations example cell2100cmay have a larger number of groups of qubits. Example cell2100chas two groups of two qubits tiled to form an L-shape, with one group of qubits (e.g., the vertically tiled group) turned over with respect with the other group of qubits (e.g., the horizontally tiled group).

Groups2100b-1and2100b-2are positioned in the plane of the page ofFIG. 21Csuch that they are substantially non-parallel (e.g., they form an included angle or meet at 90 degree). In some implementations one group of qubits (e.g., group2100b-2) is rotated according to an axis of symmetry at the mid-point of coupler2102h-2, such that the region the group that faced toward the inside of the page inFIG. 21Cfaces towards the outside of the page ofFIG. 21C.

At least one of couplers2102(e.g.,2102j) provides tunable communicative coupling between pairs of qubits were one qubit of the pair is selected from a group (e.g., group2100b-1) and the other qubit is selected from a qubit in a different group (e.g., group2100b-2).

Example cell2100cmay for the basis of a topology of a quantum processor where cells are tiled over the surface of an area.

FIG. 22shows a schematic diagram of an example topology2200of a quantum processor according to the present systems, methods and apparatus. Example topology2200employs two different couplers to provide communicative coupling between qubits in non-adjacent cells. Some of the couplers may be long-range couplers that change direction over the region of a central cell, thereby allowing space for additional electronic components that may be present in a quantum processor. Example topology2200has five cells2201to2205; however, such is not limiting and in other implementations example topology2200may have a larger or smaller number of cells.

In example topology2200, a central cell2203has a cell2201above and a cell2205below in the plane of the page ofFIG. 22, and a cell2202on the left and a cell2204on the right in the plane of the page ofFIG. 22.

Each cell in example topology2200has a first set of qubits2210and a second set of qubits2220. While each set is illustrated as having four qubits such is not limiting. In other implementations each set of qubits in a cell may have a larger or smaller number of qubits. In some implementations the number of qubits in one set (e.g., set2210) does not equal the number of qubits in another set (e.g., set2220). In some implementations, cells in example topology2200may have more than two sets of qubits.

Qubits in example topology2200are shown as having a superconducting loop in a rectangular shape; however, such is not limiting. In other implementations qubits in example topology2200may have other forms such as, but not limited to, discorectangular or oval. In some implementations, a rectangular loop may represent a segment of a qubit. Each qubit in the first set2210and the second set2220may be interrupted by at least one respective Josephson junction (not shown).

Qubits in first set of qubits2210in cells in example topology2200are substantially parallel to one another and may be laid out generally horizontally in the plane of the page ofFIG. 22and may be referred in this specification and appended claims as horizontal qubits. Qubits in second set of qubits2220in cells in example topology2200are substantially parallel to one another and may be laid out generally vertically in the plane of the page ofFIG. 22and may be referred in this specification and appended claims as vertical qubits. Qubits2210are substantially non-parallel (e.g., have an included angle or meet at 90 degree) to qubits2220.

While qubits in the first or horizontal set2210and the second or vertical set2220are illustrated inFIG. 22as having one longitudinal or major axis (not shown), such is not limiting and in other implementations qubits of the first or horizontal set2210and/or qubits of the second or vertical set2220may have two or more longitudinal or major axes.

Couplers such as couplers2250(only one called out inFIG. 22) may provide pair-wise communicative coupling between respective pairs of qubits where one qubit of the pair is selected from one of qubits of the first set2210or qubits of the second set2220in a cell (e.g. cell2202in example topology2200), and the other qubit of the pair selected from a different one of the qubits of the second set of qubits2220or qubits of the first set of qubits2210in the same cell, respectively.

Couplers2250may provide tunable communicative coupling between qubits of the first set2210and qubits of the second set2220within the same cell. The couplers are located at regions proximate where qubits of the first set2210meet qubits of the second set2220. In some implementations couplers2250are located at some distance from the respective regions where qubits of the first set2210meet qubits of the second set2220.

Central cell2203has sixteen long-range couplers2230ato2230p(collectively,2230) that provide tunable communicative coupling between a qubit in central cell2203and qubit in a non-adjacent cell. For example long-range coupler2230pprovides tunable communicative coupling between a fourth qubit of the first or horizontal set of qubits2210in central cell2203and a fourth qubit of the first or horizontal set of qubits2210in a cell on the right of cell2204in the plane of the page ofFIG. 22. Alternatively, or in additionally, long-range coupler2230pmay communicatively couple to a central cell in a non-adjacent example topology2200on the right of cell2204in the plane of the page ofFIG. 22.

While inFIG. 22each qubit in central cell is illustrated as having two long-range couplers2230, such is not limiting. In other implementations qubits in central cell2203may have a larger or smaller number of long-range couplers2230, such that central cell2203may have a larger or a smaller number of long-range couplers. Alternatively or in addition, each qubit may have one or more long-range coupler that is different from long-range couplers2230. For example, couplers1240or1530may be employed in addition or instead of long-range couplers2230.

Qubits in cells2201,2202,2204and2205have couplers such as couplers2240ato2240p(collectively,2240) providing tunable communicative coupling between pairs of horizontal qubits and vertical qubits in non-adjacent cells. For example, coupler2240cprovides tunable communicative coupling between first qubit of the second or vertical set of qubits2220in cell2201and a third qubit of the first or horizontal set of qubits in a cell on the left of cell2202in the plane of the page ofFIG. 22.

With reference to cell2201inFIG. 22, two couplers2240communicatively couple vertical qubits2220to horizontal qubits in a cell on the left of cell2202and two couplers2240communicatively couple vertical qubits2220to horizontal qubits in a cell on the right of cell2204in the plane of the page ofFIG. 22. Therefore, one or more of couplers2240in cell2201bends toward the right of cell2204and/or one or more of couplers2240bends toward the left of cell2202.

With reference to cell2202inFIG. 22, two couplers2240communicatively couple horizontal qubits2210to vertical qubits in a cell below cell2205and two couplers2240communicatively couple horizontal qubits2210to vertical qubits in a cell above cell2201in the plane of the page ofFIG. 22. Therefore, one or more of couplers2240in cell2202bends or is angled toward the top of cell2201and/or one or more of couplers2240bends or is angled toward the bottom of cell2205.

With reference to cell2204inFIG. 22, two couplers2240communicatively couple horizontal qubits2210to vertical qubits in a cell below cell2205and two couplers2240communicatively couple horizontal qubits2210to vertical qubits in a cell above cell2201in the plane of the page ofFIG. 22. Therefore, one or more of couplers2240in cell2204bends or is angled toward the top of cell2201and/or one or more of couplers2240bends or is angled toward the bottom of cell2205.

With reference to cell2205inFIG. 22, two couplers2240communicatively couple vertical qubits2220to horizontal qubits in a cell on the left of cell2202and two couplers2240communicatively couple vertical qubits2220to horizontal qubits in a cell on the right of cell2204in the plane of the page ofFIG. 22. Therefore, one or more of couplers2240in cell2205bends or is angled toward the right of cell2240and/or one or more of couplers2240bends or is angled toward the left of cell2202.

In some implementations some cell may have a larger or smaller number of couplers2240. In some implementations couplers2240communicatively couple qubits in diagonally-adjacent cells. Alternatively or in addition, each qubit may have one or more coupler that is different from couplers2240. For example, couplers1240or1530may be employed in addition or instead of couplers2240.

Couplers2240may cross over or under other qubits or other electronic components in example topology2200and are substantially electrically isolated from them. For example, when long-range coupler22401communicatively couple non-adjacent qubits from cell2205to a cell on the right of cell2204in the plane of the page ofFIG. 22, coupler22401does not communicatively couple to any other qubits, nor does it interfere with the normal operation of other electronic components of example topology2200.

FIG. 23Ais a schematic diagram of an example cell2300aof a quantum processor according to the present systems, methods and apparatus. Example cell2300acomprises four types of couplers and shifted qubits. In example cell2300a, the physical position of at least some of the qubits is shifted with respect to some of the other qubits so that a portion of some of the qubits may cross at least a portion of another qubit in an adjacent cell.

Example cell2300ahas a larger connectivity than a K4,4cell in a Chimera topology—a description of Chimera topologies can be found in U.S. Pat. No. 9,170,278. Example cell2300amay therefore be suitable for solving larger problems and reducing the need for employing embedding techniques—and therefore more software resources—to overcome a limited connectivity.

In one implementation, example cell2300amay have a connectivity of up to sixteen, or fifteen if example cell2300ais positioned at the edge of a quantum processor, although a lower number of connections is also possible.

In one implementation, example cell2300acomprises twelve qubits2302a-23021(collectively2302) in a first set of qubits and twelve qubits2304a-23041(collectively2304) in a second set of qubits, although in other implementations the number of qubits can be lower or higher than twelve in each set or the number of qubits in one set (e.g., the first set) may be different from the number of qubits in the other set (e.g., he second set). Qubits2302of the first set have loops that are substantially parallel with one another and qubits2304of the second set have loops that are substantially parallel with one another. Qubits2302in the first set of qubits are non-parallel (e.g. orthogonal) to qubits2304of the second set of qubits. Without loss of generality and for the purpose of this specification and the appended claims, qubits2302in the first set of qubits may be referred to as vertical qubits2302and qubits2304in the second set of qubits may be referred to as horizontal qubits2304.

At least one of the vertical qubits2302is shifted longitudinally with respect to other vertical qubits and at least one of the horizontal qubits2304is shifted with respect to other horizontal qubits. Therefore, a portion of at least one of vertical qubits2302and a portion of at least one of horizontal qubits2304extends in an adjacent cell, crossing a portion of at least one horizontal or vertical qubit in an adjacent cell, respectively. InFIG. 23A, qubits2302a-2302dare shifted longitudinally with respect to other qubits2302and similarly, qubits2304a-2304dare shifted longitudinally with respect to other qubits2304.

The description of which qubit is longitudinally shifted with respect to other qubits may be arbitrary and is used in its relative sense. When a first qubit is longitudinally shifted with respect to a second qubit it is understood that the second qubits may be considered shifted with respect to the first qubit. Similarly, a first group of qubits may be shifted with respect to a second group of qubits within the same set of qubits.

The amount by which each qubit is shifted with respect to other qubits may influence the communicative coupling with other qubits and therefore influence the topology of a quantum processor. InFIG. 23A, a group of qubits (e.g., qubits2302a-2302d) are shifted by the same amount (approximately 50% of their total length), however in other implementations, the amount of shift and the number of qubits that are shifted by the same amount may vary. Alternatively, or in addition, one or more qubits may be shifted by a different amount than another one or more qubits within the same cell (e.g., qubits2302a-2302dare shifted by 50% of their length and qubits2302e-2302hare shifted by more than 50% of their length in example cell2300a).

Each qubit may be a loop of superconducting material and may be interrupted by at least one respective Josephson junction (not shown).

Example cell2300ahas a grid of twelve by twelve couplers2306(only one called out inFIG. 2300a) that provide tunable communicative coupling between pairs of orthogonal qubits. For example, vertical qubit2302dis communicatively coupled via one of couplers2306to horizontal qubit2304a. In one implementation, each qubit in example cell2300ais communicatively coupled to an orthogonal qubit via exactly ten couplers2306. Where example cell2300ais located at one of the edges of a quantum processor the number of couplers2306per qubit may be lower.

Given that some horizontal and some vertical qubits are shifted in example cell2300a, some of couplers2306may communicatively couple pairs of orthogonal qubits that are not in the same cell, as better illustrated inFIG. 23B.

Example cell2300ahas twelve couplers2308(only one called out inFIG. 23Ato reduce clutter), six aligned at the right edge of example cell2300aand six at the top edge of cell2300a. Couplers2308provide tunable communicative coupling between two adjacent horizontal qubits (e.g., horizontal qubits2304kand2304j) or two adjacent vertical qubits (e.g., vertical qubits2302aand2302b) within example cell2300a. In one implementation of example cell2300a, there is exactly one coupler2308per qubit, although in other implementations the number of couplers2308per qubit may be higher than one.

Example cell2300acomprises twelve couplers2310(only one called out inFIG. 23A), six that provide direct tunable communicative coupling between pairs of vertically aligned qubits in vertically adjacent cells and six that provide tunable direct communicative coupling between pairs of horizontally aligned qubits in horizontally adjacent cells. Example cell2300acomprises exactly one coupler2310per qubit, so that each vertical qubit2302not at the edge of a quantum processor is communicatively coupled to two vertical qubits in vertically adjacent cells (i.e., one above and one below with respect to the plane of the page ofFIG. 23A) and each horizontal qubit2304not at the edge of a quantum processor is communicatively coupled to two horizontal qubits in horizontally adjacent cells (i.e., one at the right and one at the left with respect to the plane of the page ofFIG. 23A). Where example cell2300ais located at one of the edges of a quantum processor some of the qubits may be coupled to only one other qubit via coupler2310.

Example cell2300amay comprise up to twelve long-range couplers2312, where six long-range couplers2312provide tunable direct communicative coupling between two non-adjacent vertical qubits2302in horizontally adjacent cells and six long-range couplers2312that provide tunable direct communicative coupling between two non-adjacent horizontal qubits2304in vertically adjacent cells. In some implementations, example cell2300amay have no long-range couplers2312or less than twelve long-range couplers2312.

In alternative implementations where example cell2300ahas less than twelve horizontal and twelve vertical qubits, the number of couplers2306,2308,2310and2312is reduced accordingly. For example, if one implementation of example cell2300acomprises six horizontal and six vertical qubits, example cell2300amay comprise a grid of six by six couplers2306, six couplers2308(three at the top edge of example cell2300aand three at the right edge of example cell2300a), six couplers2310and at the most six long-range couplers2312(for example three horizontal and three vertical).

Similarly, in alternative implementations where example cell2300ahas more than twelve horizontal and twelve vertical qubits, the number of couplers2306,2308,2310and2312is increased accordingly. For example, if one implementation of example cell2300acomprises twenty-four horizontal and twenty-four vertical qubits, example cell2300amay comprises a grid of twenty-four by twenty-four couplers2306, twenty-four couplers2308(twelve at the top edge of example cell2300aand twelve at the right edge of example cell2300a), twenty-four couplers2310and at the most twenty-four long-range couplers2312(for example twelve horizontal and twelve vertical).

FIG. 23Bis a schematic diagram of a portion of an example topology2300bcomprising a grid of example cells2300aofFIG. 23A(only one called out inFIG. 23A). In the implementation shown inFIG. 23B, example topology2300bcomprises a grid of three by three example cells2300a(the dashed lines shows the approximate outline of the cells and are for illustration purposes only given that some horizontal and some vertical qubits may be shifted and therefore extend into an adjacent cell), although a different arrangement of cells is also possible.

In topology2300bcouplers2306(only one called out inFIG. 23Bto reduce clutter) in cells not at the bottom or the left edge of the processor are used to tunably communicatively couple one horizontal and one vertical qubits from two different cells, thereby increasing the overall connectivity of a quantum processor with topology2300b.

Many techniques for using quantum processors to solve computational problems involve finding ways to directly map a representation of a problem to the quantum processor itself. Given the generally fixed topology and/or fixed connectivity of a hardware processor, some classes of problem may benefit from embedding techniques. Examples of embedding techniques are described in U.S. Pat. Nos. 7,984,012, 8,244,662 and US Patent Publication 2014/0250288. One example of a fixed topology is the Chimera topology. Examples of quantum processor topologies, including Chimera topologies, are described in greater detail in International Patent Application WO2006066415, U.S. Pat. Nos. 9,170,278 and 9,178,154.

A clique embedding can be defined as embedding a clique in a graph representing the structure of a hardware processor. Methods and algorithms exist for finding clique embeddings in Chimera graphs. An example of a method or algorithm for finding clique embedding is Chimera graph is described in Boothby et al. (see http://arxiv.org/abs/1507.04774). It is possible to employ existing methods to construct clique embeddings topology graphs described in this specification by constructing logical or virtual ‘sub-qubits’ joined together with logical or virtual couplers to produce Chimera-like graph on which to run existing algorithms. It will be understood that clique embeddings may be found in Chimera graph by employing any suitable method or algorithm and the present specification and appended claims are not restricted to a particular method or algorithm.

On topologies described in this specification, for example topology800b,900b,1000or1100or other topology here described, a digital or classical processor may partition the quantum processor topology so that all the horizontally aligned qubits are grouped into a ‘horizontally aligned group’ and all the vertically aligned qubits are grouped into a ‘vertically aligned group’. Every pair of qubits where one member of the pair is selected from the ‘horizontally aligned group’ and the other member is selected from the ‘vertically aligned group’ has the property that either all the qubits in the ‘vertically aligned group’ are communicatively coupled to all the qubits in the ‘horizontally aligned group’ or none of the qubits in the ‘vertically aligned group’ are communicatively coupled to any of the qubits in the ‘horizontally aligned group’.

A person skilled in the art will understand that when a quantum processor topology includes more than two sets of qubits (e.g. horizontal qubits, vertical qubits and diagonally oriented qubits) the digital processor may partition the quantum processor topology in more than two sets. Similarly, the digital processor will account for qubits that have two or more longitudinal or major axes.

A digital processor can then partition each qubit in the ‘horizontally aligned group’ and each qubit in the ‘vertically aligned group’ into ‘horizontally aligned sub-qubits groups’ and ‘vertically aligned sub-qubits groups’. Each sub-qubit in a ‘horizontally aligned sub-qubits group’ is communicatively coupled to all the sub-qubit in exactly one ‘vertically aligned sub-qubit group’. Likewise, each sub-qubit in a ‘vertically aligned sub-qubits group’ is communicatively coupled to all the sub-qubit in exactly one ‘horizontally aligned sub-qubit group’. Some sub-qubits may not be communicatively coupled to orthogonal qubits if they are on the boundary of the processor or disabled.

The digital processor may then add virtual or fictional couplers between sub-qubits such that physically adjacent qubits are communicatively coupled by virtual or fictional couplers to construct a Chimera graph on a non-Chimera topology. The digital processor may then run any suitable embedding methods or algorithms on the constructed Chimera graph to find clique embeddings.

The various embodiments described above can be combined to provide further embodiments. To the extent that they are not inconsistent with the specific teachings and definitions herein, all of the U.S. patents, U.S. patent application publications, U.S. patent applications, referred to in this specification and/or listed in the Application Data Sheet and commonly assigned to D-Wave Systems Inc., including but not limited to U.S. application Ser. No. 62/346,917 filed Jun. 7, 2016; and U.S. application Ser. No. 62/400,990 filed Sep. 28, 2016, are incorporated herein by reference, in their entirety. Aspects of the embodiments can be modified, if necessary, to employ systems, circuits and concepts of the various patents, applications and publications to provide yet further embodiments.