Patent ID: 12206404

DETAILED DESCRIPTION OF THE INVENTION

A “persistent current qubit”, as used herein, is a qubit having a state that is characterized by a persistent current circulating within the qubit. Examples of persistent current qubits include the flux qubit and the fluxonium qubit.

Two quantities are “about equal” when they are equal within fabrication tolerances. Two values for an applied flux are “about equal” when they are with five-hundredths of the flux quantum. A negative value for an applied flux is a flux applied in a direction that opposed an arbitrarily chosen direction associated with positive values for an applied flux.

FIG.1illustrates system100for providing a multi-body interaction among a plurality of persistent current qubits102,104, and106. In the illustrated implementation, the system100includes three persistent current qubits102,104, and106as an example, although it will be appreciated that the system100can be implemented to provide a multi-body interaction among more than three qubits. In this example, each of the persistent current qubits102,104, and106have at least two Josephson junctions in one loop with sufficiently large shunt capacitance to prohibit quantum tunneling of superconducting phase, as to provide a periodic double-well potential for the qubit. In one implementation, each of the persistent current qubits102,104, and106, can be implemented as a fluxonium qubit.

Each of the plurality of persistent current qubits (e.g.,102) is galvanically coupled to two other persistent current qubits (e.g.,104and106) as to form a superconducting loop110including the persistent current qubits. The superconducting loop110is interrupted by a Josephson junction112between two of the persistent current qubits (e.g.,104and106). It will be appreciated that the Josephson junction110can be implemented, in some examples, as a compound Josephson junction comprising multiple Josephson junctions arranged in parallel to allow for additional tunability of the system100. In some implementations, additional inductors (not shown) can be including in the galvanic connections between the other pairs of persistent current qubits. For example, in this example using three qubits, the inductors could be implemented between qubits102102and106and between qubits102and104.

FIG.2illustrates a first example of a persistent current qubit circuit200that can be used in the system ofFIG.1, specifically a fluxonium qubit. The circuit includes a superconducting loop210interrupted by a Josephson junction212and an inductor214and shunted by a capacitor216. The inductor214can be implemented using any appropriate structure, for example, a geometric inductance or a series of Josephson junctions. Since the inductor214can itself be formed from a series of Josephson junctions in some implementations, the Josephson junction212of a fluxonium qubit is often referred to as the “black sheep” junction, as it is generally implemented with a smaller critical current than any Josephson junctions used to provide the inductor214. In the illustrated implementation, however the Josephson junction212can be fabricated to have a relatively large critical current, for example, a critical current greater than one hundred fifty nanoamps. In another example, the “black sheep” Josephson junction212can be fabricated to have a critical current within twenty percent of the critical current of one of a series of inductors used to fabricate the inductor214. In a further example, the “black sheep” Josephson junction212can be fabricated to have a critical current about equal to the critical current of one of a series of inductors used to fabricate the inductor214.

FIG.3is a chart300illustrating a simulation of the persistent current circulating in a fluxonium qubit, represented on a vertical axis302in nanoamps, as a function of the critical current of the Josephson junction212, represented on a horizontal axis304in nanoamps. In the simulation, a large shunt capacitance is used and small flux bias from an operating point at half a flux quantum are added so that the ground state wavefunction is localized in one well. Specifically, the simulation assumes an inductance of two hundred nanohenries for the inductor214, a capacitance for the capacitor216of one hundred femtofarads, and a 0.1 mΦ0, deviation of the flux bias from 0.5 Φ0, where Φ0is the flux quantum. As can be seen from the plot306, an increase in the critical current of the Josephson junctions does not greatly increase the persistent current, and therefore does not significantly increase flux-noise induced dephasing when the qubit is operating away from a “sweet spot” frequency at which tunnel-coupling is present and a fluxonium qubit is generally operated. In fact, the persistent current increases by only sixteen percent when the critical current is increased by over an order of magnitude. Thus, the qubits discussed here with larger junction212critical currents may have similar dephasing to a standard fluxonium circuit, with its smaller junction critical current, when operated off the standard sweet spot. This increased dephasing may be acceptable in applications where a strong, pure ZZZ interaction is desired, and can be mitigated to some degree by increasing the inductance of the inductor214.

FIG.4shows another example of a persistent current qubit circuit400that can be used in the ZZZ coupling arrangement ofFIG.1. The illustrated persistent current qubit400comprises a superconducting loop410comprising a first inductor412, a second inductor414, a first Josephson junction416, and a second Josephson418. The two Josephson junctions416and418have about identical critical currents and have much larger critical currents than the typical black sheep junction. With half a flux quantum in the loop, the circuit exhibits a double-well potential that is periodic in the phase on the top junction. This periodicity gives rise to two inequivalent tunneling paths between the two wells, which, in turn, gives rise to Aharonov-Casher interference for some device parameters. With a sufficiently large shunt capacitance across the junctions (not shown), this tunneling and the associated interference is highly suppressed.

FIG.5is a chart500illustrating an energy splitting between the two lowest energy levels for the qubit ofFIG.4, represented on a vertical axis502in megahertz, as a function of an offset charge at the node of the circuit between the two Josephson junctions412and414, represented on the horizontal axis504in units of twice the electron charge. For this example, the inductances of the inductors412and414are each one hundred twenty-five nanohenries with a five femtofarad shunt capacitance, and the Josephson junctions416and418have critical current of two hundred nanoamps. Each plot506-509represents a different shunt capacitance across the junctions416and418, with a first plot506representing a shunt capacitance of one femtofarad, a second plot507representing a shunt capacitance of two femtofarads, a third plot508representing a shunt capacitance of three femtofarads, and a fourth plot509representing a shunt capacitances of fifteen femtofarads. With one-half of a flux quantum provided to the superconducting loop210, a double well potential is formed with two inequivalent tunnelling paths between wells. Tunneling exhibits Aharonov-Casher interference, which is controlled by the offset charge, and is suppressed by increasing the junction shunt capacitances. With fifteen femtofarad capacitive shunts, tunnel-splitting is suppressed well below 0.1 kHz for any offset charge, while the gap to the next highest states is 6.4 GHz. These simulations provide evidence that the energy potential for the qubit400exhibits a periodicity of period π as a function of a Josephson phase associated with the node of the circuit between the two Josephson junctions412and414, such that the energy potential contains two minima in the interval zero to 21.

FIG.6illustrates another example of a qubit600that can be used in the ZZZ coupling arrangement ofFIG.1. The qubit600, is implemented as a fluxonium qubit and includes a superconducting loop601containing four inductors602-605and two Josephson junctions606and608. The inductors602-605will be selected to have inductances that are significantly larger than the inductances associated with the Josephson junctions and can be implemented, for example, via Josephson junction chains, high kinetic inductance superconducting material, or long superconducting wires. In the illustrated example, a first Josephson junction606is implemented as a compound junction to allow for tuning of a tunnel barrier height of the energy potential of the qubit via applied flux. The second Josephson junction608is included to manifest a desired periodicity in the circuit's potential energy as a function of superconducting phase difference between the nodes of the circuit labelled as A and B. In the illustrated implementation, the critical current of the first Josephson junction606is about equal to the critical current of the second Josephson junction. The first Josephson junction606is configured to receive flux from a first control line610comprising a first current source612and a first transformer614. Similarly, the superconducting loop is configured to receive flux from a second control line620comprising a second current source622and a second transformer624. In the illustrated example, the second transformer624includes one of the inductors605.

FIG.7illustrates a system700implementing a ZZZ coupling arrangement using the qubit600ofFIG.6. The system700includes three tunable fluxonium qubits710,720, and730, each implemented as illustrated inFIG.6and connected to one another at circuit nodes A and B to form a loop740. Each of the three tunable fluxonium qubits710,720, and730includes a compound Josephson junction712,722, and732configured to receive flux via a control line (not shown). The loop740is interrupted by a Josephson junction742on a connection between two of the fluxonium qubits (e.g.,710and720) and configured to receive flux from a control line750comprising a current source752and a transformer754. In some implementations, the remaining connections between the qubits (e.g., between720and730and between710and730) can include inductors (not shown), for example, implemented in a manner similar to the inductors602-605in the qubits.

During operation, the system700can be provided with flux at the compound Josephson junctions712,714, and716in each qubit as well as in the main loop740itself. The potential minima of the system700as a function of phase difference across the fluxonium qubits forms a lattice in three-dimensional space, where each vertex is a potential minimum. A representation of this lattice800is illustrated asFIG.8, where the potential, Ep, can be represented in simplified form as

EP=cos⁡(2⁢x)+cos⁡(2⁢y)+cos⁡(2⁢z)-a*cos⁡(2⁢πΦΦ0-x-y-z),
where each cosine term represents a potential of one of the three qubits710,720, and730, Φ is a value of a flux applied to the loop740, Φ0is the flux quantum, and a is a relative coupling strength. A first axis802represents a value for x, a second axis804represents a value for y, and a third axis806represents a value for z. Each potential energy minimum of the system corresponds to specific persistent currents of the three qubits, where 0/1 corresponds to clockwise/counter-clockwise circulating current. For example, the minimum labeled 000 has an associated quantum state |000> in which all three qubits have clockwise circulating current.

Connecting the qubits710,720, and730in the loop740constrains the sum of the phases across each qubit. The constraint forms a plane in the three-dimensional space of the qubit phases that is translated by flux in the multi-qubit ring. When a flux of about 0.25 Φ0, is provided to the loop740, four phase minima lie in the plane which correspond to the ground states of the ZZZ interaction, specifically |011>, |101>, |110>, and |000>. When a flux of about −0.25 Φ0, is provided to the loop740. The sign of the interaction is flipped for ring flux of −0.25 Φ0, with the plane representing the ground states translated to include the states |100>, |010>, |001>, and |111>. For qubits710,720, and730having an inductance of two hundred nanohenries for the inductor, a capacitance for the capacitor of one hundred femtofarads, and Josephson junctions having a critical current about equal to one hundred fifty milliamps, the system700can provide a coupling strength greater than one gigahertz.

In view of the foregoing structural and functional features described above, a method in accordance with various aspects of the present invention will be better appreciated with reference toFIG.9. While, for purposes of simplicity of explanation, the method ofFIG.9is shown and described as executing serially, it is to be understood and appreciated that the present invention is not limited by the illustrated order, as some aspects could, in accordance with the present invention, occur in different orders and/or concurrently with other aspects from that shown and described herein. Moreover, not all illustrated features may be required to implement a method in accordance with an aspect the present invention.

FIG.9illustrates a method900for providing a ZZZ coupling among three persistent current qubits galvanically connected to one another to form a superconducting loop. At902, an applied flux is provided to the superconducting loop with a first value to provide a first ZZZ coupling among the three persistent current qubits. The first ZZZ coupling has a first set of four lowest energy states. The applied flux can be provided to the superconducting loop by providing a current to a control line inductively coupled to the superconducting loop. At904, the applied flux is provided to the superconducting loop with a second value to provide a second ZZZ coupling among the three persistent current qubits. The second ZZZ coupling has a second set of four lowest energy states. At906, the applied flux is provided to the superconducting loop with a third value to avoid a ZZZ coupling among three persistent current qubits.

What have been described above are examples of the present invention. It is, of course, not possible to describe every conceivable combination of components or methodologies for purposes of describing the present invention, but one of ordinary skill in the art will recognize that many further combinations and permutations of the present invention are possible. Accordingly, the present invention is intended to embrace all such alterations, modifications, and variations that fall within the scope of the appended claims.