Patent Description:
In quantum computing it has become common to use the term qubit to designate not only the basic unit of information but also the information storage element that is used to store one qubit of information. As an example, a superconductive memory circuit with one or more qubits (i.e. qubit-sized information storage elements) can be considered. In such an example the qubit is an anharmonic oscillator, such as a transmon, and it may be coupled to a nearby readout resonator for facilitating the readout of the state of the qubit stored therein.

To implement a quantum gate it is essential that there are controllable couplings between qubits, so that the states of the qubits can interact with each other in a controlled manner. In the case of electrical qubits that have a characteristic resonance frequency, a relatively simple way to control the coupling between adjacent qubits involves frequency tuning, so that the qubits are tuned to (or close to) resonance for strong coupling (on-position) and detuned for small coupling (off-position). Such an arrangement imposes an upper bound on the gate on-off ratio for given gate speed. There is no known scalable method to cancel out the unwanted entanglement of idling qubits that results from the weak always-on interaction.

A more versatile way is to use a tunable coupling element between the two qubits, as described for example in <NPL>. However, the known way of using tunable coupling elements involves drawbacks that relate to distances and dimensioning. Sufficient capacitance is needed also between the qubits themselves, not only between each individual qubit and the tunable coupling element, which advocates keeping the qubits relatively close to each other. At the same time, the short qubit-to-qubit distance increases the coupling between also unwanted pairs of qubits, as well as between qubits and control leads, introducing crosstalk. The short qubit-to-qubit distance also restricts the amount of space available for other required components, such as readout resonators for example.

<CIT> discloses a tunable qubits. The bus comprises a tunable coupler connected to non-tunable parts. The bus is connected to qubits via capacitive coupling. <CIT>discloses a tunable coupler and non-galvanic connections between constant coupling waveguides.

There is a need for structural and functional solutions that enable sufficiently strong, yet controllable coupling between qubits while simultaneously eliminating unwanted crosstalk and giving large freedom in the way in which the circuit hardware is designed and implemented.

It is an objective to provide an arrangement that enables strong, yet controllable coupling between qubits while simultaneously eliminating unwanted crosstalk and giving large freedom in the way in which the circuit hardware is designed and implemented.

The objectives of the invention are achieved by utilizing tunable couplers with separate coupling extenders to implement the coupling between qubits that can be made to implement a gate in quantum computing.

Advantageous embodiments of the invention are described in more detail in the depending claims.

According to a first aspect there is provided a tunable coupler for making a controllable coupling to at least a first qubit. The tunable coupler comprises a first constant coupling element and a tunable coupling element, with a coupling between the first and tunable coupling elements. Said first constant coupling element forms a non-galvanic coupling interface to at least said first qubit at a first extremity of said first constant coupling element distant from said tunable coupling element, for a strong coupling due to a close proximity of the first constant coupling element and said first qubit at said first non-galvanic coupling interface. Said tunable coupling element is located adjacent to a second non-galvanic coupling interface formed to a further circuit element at a second extremity of said first constant coupling element. There is a coupling between said tunable coupling element and said further circuit element and a strong coupling due to a close proximity of the first constant coupling element and said further circuit element at said second non-galvanic coupling interface. Said tunable coupling element is configured to be tuned in order to adapt a coupling strength of the coupling between the tunable coupling element and the first constant coupling element and a coupling strength of the coupling between the tunable coupling element and the further circuit element. Said further circuit element is a second constant coupling element or a second qubit.

According to an embodiment said first constant coupling element is a waveguide. This involves the advantage that the length of the first constant coupling element can be utilized to make the distances between other circuit elements sufficiently long.

According to an embodiment said first constant coupling element is a waveguide resonator. In addition to the advantages mentioned above, this involves the additional advantage that the resonance characteristics of the first constant coupling element may be utilized in setting the strength of each electromagnetic coupling to which the first constant coupling element takes part.

According to an embodiment said first constant coupling element is a lumped element resonator. This involves the advantage that the characteristic impedance of the first constant coupling element may be selected in a very wide range, enabling it to mediate a very strong coupling between qubits.

According to an embodiment said first constant coupling element is a conductor island. This involves the advantage that its dimensions can be very effectively utilized in particular together with quantum dot qubits.

According to an embodiment the the tunable coupler comprises the further circuit element, which is the second constant coupling element. The second constant coupling element then forms a non-galvanic coupling interface to said second qubit at an extremity of said second constant coupling element distant from said tunable coupling element, for a strong coupling due to a close proximity of the second constant coupling element and said second qubit at said third non-galvanic coupling interface. The tunable coupling element may then be located adjacent to a non-galvanic coupling interface formed between said first and second constant coupling elements. This involves the advantage that there may be a coupling between the first and second constant coupling elements, and the tunable coupling element may be used to affect the strength of that coupling.

According to an embodiment said second constant coupling element is one of: waveguide, waveguide resonator, lumped element resonator, conductor island. Each of these alternatives involves similar advantages that were already mentioned above with respect to the first constant coupling element.

According to an embodiment said first and second constant coupling elements are waveguides or waveguide resonators, and each of them comprises a respective coupling area at the respective extremity adjacent to which the tunable coupling element is located. The respective coupling areas of the first and second constant coupling elements both comprise a first edge adjacent to the first edge of the other coupling area and a second edge adjacent to a respective edge of the tunable coupling element. This involves the advantage that the couplings between the various elements can be designed at great accuracy and reproducibility.

According to an embodiment the tunable coupling element occupies a first sector of an annular two-dimensional region, and each of said respective coupling areas of the first and second constant coupling elements occupies a respective further sector of said annular two-dimensional region. Said further sectors may then be adjacent sectors of said annular two-dimensional region. Together said first sector and said further sectors may cover the whole of said annular two-dimensional region. This involves the advantage that the desired characteristics of the elements may be realized in a very compact size and shape.

According to an embodiment the tunable coupler comprises a chain of consecutive constant coupling elements, of which said first constant coupling element is one, with non-galvanic coupling interfaces formed between consecutive constant coupling elements in said chain. The tunable coupler may then comprise at least two tunable coupling elements, each of said at least two tunable coupling elements being adjacent to a respective one of said non-galvanic coupling interfaces formed between consecutive constant coupling elements in said chain. This involves the advantage that even very large quantum computing circuits may be designed using the principles explained above.

According to a second aspect there is provided a quantum computing circuit that comprises a tunable coupler of the kind explained above and at least the first qubit or the second qubit.

According to an embodiment the quantum computing circuit comprises the first qubit and the second qubit. This involves the advantage that an accurately controllable coupling can be formed between said two qubits while minimizing crosstalk and other disadvantageous effects that were typical to prior art solutions.

<FIG> is an example of how the coupling between two qubits <NUM> and <NUM> can be affected by tuning the qubits. Assuming that the qubits <NUM> and <NUM> form a standard two-qubit gate, its on and off positions correspond to strong and weak coupling between the qubits. In <FIG> there is a dedicated tuning input for each of the qubits <NUM> and <NUM>, which can be used to change the resonance frequency of the corresponding qubit. For the off position, the qubits are detuned. Such an arrangement exhibits the disadvantageous features referred to above in the description of prior art.

<FIG> is an example of using a tunable coupling element <NUM> to affect the coupling between two qubits <NUM> and <NUM>. <FIG> illustrates the same in the form of a schematic circuit diagram. The capacitive couplings 1C, C2, and <NUM> of <FIG> appear as the capacitors C1C, C2C, and C12 drawn in <FIG> respectively. The tuning inputs shown in <FIG> are left out of <FIG> for graphical clarity. Detuning between the first qubit <NUM> and the tunable coupling element <NUM> affects the coupling 1C. Similarly, detuning between the second qubit <NUM> and the tunable coupling element <NUM> affects the coupling C2. The mutual tuning of the two qubits <NUM> and <NUM> affects the coupling <NUM>. In addition to tuning, also the physical distance between each pair of circuit elements has an important effect on their coupling.

It is important to understand that for the appropriate operation of the arrangement shown in <FIG>, the qubits <NUM> and <NUM> and the tunable element <NUM> must be relatively close to each other, so that in addition to the capacitances 1C and C2 there would also be the capacitance C12 of sufficient magnitude. This in turn results in the couplings between also unwanted pairs of qubits and control leads getting too large in a system with more qubits.

In many of the following drawings the simplified form of a plus-sign is used for qubits (and in some cases also for tunable coupling elements). <FIG> is provided to give and explanation of how such a plus-formed circuit element may look like in practice. <FIG> is a top view of a piece of a quantum computing circuit, in which a substrate (such as silicon or sapphire for example) has layers and patterns of conductive and/or superconductive materials deposited on a surface thereof. Cross-hatched areas in <FIG> illustrate bare portions of the substrate surface, while solid white areas illustrate conductive and/or superconductive material.

Most of the surface of the substrate is filled with a ground plane <NUM>, made of superconductive material and patterned with a matrix of small openings in order to reduce the effect of unwanted eddy currents. The plus-formed area <NUM> of superconductive material constitutes the capacitive part of a qubit, while the detailed patterns at <NUM> comprise the Josephson junction(s). Two examples are shown of how another circuit element in the quantum computing circuit may form a non-galvanic coupling interface to the qubit. At the top, the fork-formed area <NUM> implements a capacitive coupling through the top branch of the plus-formed area <NUM>. At the bottom, the end of a transmission line <NUM> forms another kind of non-galvanic coupling interface to that part of the qubit where the Josephson junction(s) is/are located.

<FIG> shows how the principle of using tunable coupling elements for qubit-to-qubit coupling explained above with reference to <FIG> may be utilized in an array of qubits. Here the cross-hatched plus signs are qubits and the simply hatched plus signs therebetween are the tunable coupling elements. <FIG> shows another example, in which the tunable coupling elements are not plus-shaped but simple line-shaped and appear adjacent to the mutually facing branches of the plus-shaped qubits the coupling of which they affect. Irrespective of the shape of the tunable coupling element, the distance between the qubits cannot be increased since this would reduce the direct capacitance (shown as C12 in <FIG>) between the qubits. As a result, both in <FIG> and in <FIG> the qubits must be relatively close to each other, which introduces crosstalk between qubits. The tight spacing also restricts the amount of space available on the surface of the substrate for other necessary circuit elements, such as readout resonators that are not shown in the schematic representation in <FIG>.

The distance between adjacent qubits is also linked to the size and shape of the tunable coupling element. When the qubits are close to each other, the direct capacitance between two qubits is large enough even if the tunable coupling element is plus-shaped (the same shape as the qubits themselves). Using a line-shaped or slab-shaped tunable coupling element, like in <FIG>, the qubits can be brought even closer to each other. This means increased coupling between the qubits and consequently faster gates, but at the price of even more qubit-qubit crosstalk.

<FIG> illustrates the concept of a quantum bus, which is essentially an extended conductor <NUM>, the ends of which each form a non-galvanic coupling interface to a respective qubit. Such an extended conductor <NUM> may also be called a constant coupling element, because it is not tunable. In the graphical representation a different kind of a simple hatch (sparser, and inclined to left) is used to emphasize the difference to the tunable coupling elements shown in <FIG>. The left end of the extended conductor <NUM> forms a non-galvanic coupling interface to a first qubit <NUM>, and the right end of the extended conductor <NUM> forms a non-galvanic coupling interface to a second qubit <NUM>. The quantum bus is a way of increasing the distance between two qubits, thus reducing crosstalk and crowding issues on the surface of the substrate, while maintaining sufficient qubit-to-qubit capacitive coupling.

<FIG> illustrates the principle of a tunable coupler for making a controllable coupling to (or between) two qubits <NUM> and <NUM>. The tunable coupler comprises a first constant coupling element <NUM> and a tunable coupling element <NUM>. In the embodiment of <FIG> the tunable coupler comprises also a second constant coupling element <NUM>.

The first constant coupling element <NUM> forms a non-galvanic coupling interface to the first qubit <NUM>. The non-galvanic coupling interface to the first qubit <NUM> is formed at a first extremity of the first constant coupling element that is distant from the tunable coupling element <NUM>.

The tunable coupling element <NUM> is located adjacent to a non-galvanic coupling interface formed to a further circuit element (here: to the second constant coupling element <NUM>) at a second extremity of the first constant coupling element <NUM>. This feature can be considered in more detail by comparing to <FIG>.

In <FIG> the two qubits <NUM> and <NUM> are plus-formed, as is the tunable coupling element <NUM> in the middle. The constant coupling elements <NUM> and <NUM> are line- or slab-formed. The mutual arrangement of the elements in <FIG> is otherwise like that described above with reference to <FIG>, but the tunable coupling element <NUM> is not located adjacent to a non-galvanic coupling interface formed to a further circuit element at a second extremity of the first constant coupling element <NUM>. Rather, in <FIG> the tunable coupling element <NUM> is located between, and fills a gap between, the "second extremity" (i.e. right end) of the first constant coupling element <NUM> and the closest part of the second constant coupling element <NUM>. As a result, there is a relatively weak direct coupling between the constant coupling elements <NUM> and <NUM> in <FIG>.

In <FIG> the tunable coupling element <NUM> is line- or slab-formed, and located adjacent to a non-galvanic coupling interface formed to a further circuit element at the second extremity of the first constant coupling element <NUM>. Namely, the first extremity of the first constant coupling element <NUM> is its left end, where a non-galvanic coupling interface is formed to the first qubit <NUM>. The second extremity of the first constant coupling element <NUM> is its right end, where - in <FIG> - a non-galvanic coupling interface is formed to the second constant coupling element <NUM>.

In the embodiment of <FIG> the second constant coupling element <NUM> forms a non-galvanic coupling interface to the second qubit <NUM> at an extremity of the second constant coupling element <NUM> distant from the tunable coupling element <NUM>. The tunable coupling element <NUM> is located adjacent to the non-galvanic coupling interface formed between the first and second constant coupling elements <NUM> and <NUM> in the middle.

The couplings between the various elements are schematically shown in the upper part of <FIG>. Here we may particularly compare to <FIG>. There is a direct qubit-to-qubit coupling <NUM>, but - due to the relatively large distance between the qubits <NUM> and <NUM> in <FIG> - it is relatively weak. Quite to the contrary, the close proximity of the respective element pairs means that there are a number of couplings that are strong: the coupling <NUM> between the first qubit <NUM> and the first constant coupling element <NUM>, the coupling <NUM> between the first and second constant coupling elements <NUM> and <NUM>, and the coupling <NUM> between the second coupling element <NUM> and the second qubit <NUM>. The strength of the couplings <NUM> and <NUM> between the constant coupling elements <NUM> and <NUM> and the tunable coupling element <NUM> respectively depends on how the tunable coupling element <NUM> is tuned. If the constant coupling elements <NUM> and <NUM> are resonators, also they can be tuned, which further affects the strength of the couplings <NUM> and <NUM>. If the constant coupling elements <NUM> and <NUM> are coupler islands, short waveguides, or other such elements that cannot themselves be tuned, the effective coupling <NUM> resulting from all the other couplings will depend on how the qubits <NUM>, <NUM> and the tunable coupling element <NUM> are tuned.

<FIG> illustrate another embodiment. Compared to <FIG> the second constant coupling element <NUM> is missing. Rather, in <FIG> the further circuit element to which there is formed a non-galvanic coupling interface at the second extremity of the first constant coupling element <NUM> is the second qubit <NUM>. In the embodiment of <FIG> there are two couplings that may be relatively strong due to the close proximity of the respective element pairs are: the coupling <NUM> between the first qubit <NUM> and the first constant coupling element <NUM>, and the coupling <NUM> between the first constant coupling element <NUM> and the second qubit <NUM>. The strength of the couplings <NUM> and <NUM> between the first constant coupling element <NUM> and the tunable coupling element <NUM> and between the last-mentioned and the second qubit <NUM> depends on how the first qubit <NUM>, the tunable coupling element <NUM>, and the second qubit <NUM> are tuned.

The effect of the constant coupling element (as element <NUM> in <FIG>) or the chain of constant coupling elements (as elements <NUM> and <NUM> in <FIG>) is that sufficient effective qubit-to-qubit coupling, comparable to C12 in <FIG>, is achieved even if the qubits <NUM> and <NUM> are relatively far apart. The tunable coupling element <NUM> does not mediate the coupling between the qubits directly (as it did in the embodiments of <FIG>, <FIG>). Instead, it mediates the coupling between the two constant coupling elements (as in <FIG>), between the constant coupling element and one of the qubits (as in <FIG>), or between the constant coupling element and some other kind of further circuit element.

Constant coupling elements of the kind described above with respect to <FIG> can alternatively be called coupling extenders. They allow placing the qubits further apart than in previously known solutions, which in turn gives space for larger ground planes, vias, or bump bonds to other ground layers in between the qubits. More grounding in between the qubits means lower crosstalk.

Any of the constant coupling elements described above may be a waveguide resonator, which means that the coupling element in question has a length comparable to the characteristic wavelength at a given frequency of interest. Waveguides are particularly convenient for use as constant coupling elements for transmon qubits. This is because the typical characteristic dimension of a transmon qubit is about one twentieth of the wavelength at resonance frequency, while a recommendable minimum distance between two transmon qubits for low crosstalk is around <NUM> times the characteristic dimension of the transmon qubit.

The coupling strength between a waveguide (which is used as a constant coupling element or, in other words, a coupling extender) and a qubit is enhanced if the length of the waveguide is close to an integer number of half-wavelengths on the frequency of interest. If this is the case, the waveguide (or the constant coupling element the dimensions of which make it a waveguide) is a waveguide resonator. While such a higher coupling strength allows faster two-qubit gates, the coupling is enhanced for the resonant frequency only. This phenomenon, called frequency dispersion, makes the circuit design more sensitive to imprecision in dimensioning and manufacturing.

According to another embodiment, any of the constant coupling elements may be a lumped element resonator. In addition to the coupling enhancement at resonance frequencies as for waveguide resonators, a lumped element resonator allows designing the characteristic impedance in a much wider range, enabling even stronger coupling between the qubits. However, in addition to strong frequency dispersion, the self-resonance frequency of a lumped element resonator can be very sensitive to the geometry of other circuit elements nearby, which may make designing the quantum computing circuit quite challenging.

According to yet another embodiment, any of the constant coupling elements may be a conductor island. A conductor island is a circuit element that has an insignificant self-inductance and coupling to the ground. Conductor islands are particularly useful as constant coupling elements for quantum dot qubits, because the practical distance between them may be much smaller than the wavelength at the typical resonant frequency of the qubit for a realistic coupling element geometry.

<FIG> illustrates a tunable coupler according to an embodiment, as well as two qubits <NUM> and <NUM>. The tunable coupler comprises a first constant coupling element <NUM>, a tunable coupling element <NUM>, and a second constant coupling element <NUM>. The first constant coupling element <NUM> forms a non-galvanic coupling interface to the first qubit <NUM> at its first extremity, which is the one distant from the tunable coupling element <NUM>. The second constant coupling element <NUM> forms a non-galvanic coupling interface to the second qubit <NUM> at its extremity distant from the tunable coupling element <NUM>. The tunable coupling element <NUM> is located adjacent to the non-galvanic coupling interface formed between the first and second constant coupling elements <NUM> and <NUM>. In other words, the last-mentioned non-galvanic coupling interface is between those extremities of the first and second constant coupling elements <NUM> and <NUM> that are closest to the tunable coupling element <NUM>. Ground planes and tuning connections are not shown in <FIG> to maintain graphical clarity. Capacitors shown in dashed lines illustrate the capacitive couplings between elements with the same reference designators as above in <FIG>.

In the embodiment of <FIG> each of the first and second constant coupling elements <NUM> and <NUM> is a waveguide. Each of them comprises a respective coupling area at that extremity adjacent to which the tunable coupling element <NUM> is located. These coupling areas are shown with reference designators <NUM> and <NUM> in <FIG>. Their form is suitable for creating the respective capacitive couplings between the two constant coupling elements <NUM> and <NUM> on one hand, and between each of them and the tunable coupling element <NUM> on the other hand. In particular, the respective coupling areas <NUM> and <NUM> of the first and second constant coupling elements both comprise a first edge adjacent to the first edge of the other coupling area and a second edge adjacent to a respective edge of the tunable coupling element <NUM>.

A generally annular geometry is used for the tunable coupling element <NUM> and the coupling areas <NUM> and <NUM> in <FIG>. The tunable coupling element <NUM> occupies a first sector of an annular two-dimensional region. Each of the respective coupling areas <NUM> and <NUM> of the first and second constant coupling elements <NUM> and <NUM> occupies a respective further sector of said annular two-dimensional region. These further sectors are adjacent sectors of said annular two-dimensional region. Together said first sector and said further sectors cover the whole of said annular two-dimensional region. Capacitance-enhancing forms, like the interleaved fingers in <FIG>, can be used at any of the edges of adjacent sectors.

The generally annular geometry, if used, does not need to mean a round annular form, but various polygonal shapes may be used. Also, even if the intertwined-finger-type forms (which as such constitute only an example of capacitance-enhancing forms that can be used) are used between the tunable coupling element <NUM> and the coupling areas <NUM> and <NUM> respectively in <FIG>, this is not an essential feature. <FIG> shows an alternative embodiment where an annular, hexagonal form is used for the tunable coupling element <NUM> and the coupling areas <NUM> and <NUM>. Also, in the embodiment of <FIG> the intertwined-finger-type forms are used between the coupling areas <NUM> and <NUM> in addition to their use between the tunable coupling element <NUM> and each individual coupling area <NUM> and <NUM>. The generally annular geometry can also be used without using the intertwined-finger-type forms between any of the areas involved.

<FIG> illustrates an example of how tunable couplers conformant with the principles described above can be used in a quantum computing circuit that comprises a number of qubits. As an example, the rightmost column of qubits <NUM> to <NUM> can be considered. The tunable coupler to their right comprises a chain of consecutive constant coupling elements. The one closest to the top qubit <NUM> may be called a first constant coupling element <NUM>. Non-galvanic coupling interfaces are formed between consecutive constant coupling elements in said chain: as an example, following said chain one may jump over non-galvanic coupling interfaces from the first constant coupling element <NUM> to the vertically directed constant coupling element <NUM> and to a further constant coupling element <NUM>. The tunable coupler comprises at least two tunable coupling elements, of which the tunable coupling elements <NUM> and <NUM> are examples. Each of these tunable coupling elements is adjacent to a respective one of said non-galvanic coupling interfaces formed between consecutive constant coupling elements in said chain.

As shown in the example of <FIG>, at least some of the constant coupling elements in the tunable coupler may constitute a shared bus, through which connections to and from a number of different qubits is possible.

Claim 1:
Tunable coupler for making a controllable coupling to at least a first qubit (<NUM>, <NUM>), comprising:
- a first constant coupling element (<NUM>, <NUM>), and
- a tunable coupling element (<NUM>, <NUM>), there being a coupling between said first (<NUM>, <NUM>) and tunable (<NUM>, <NUM>) coupling elements;
wherein:
- said first constant coupling element (<NUM>, <NUM>) forms a first non-galvanic coupling interface to at least said first qubit (<NUM>, <NUM>) at a first extremity of said first constant coupling element (<NUM>, <NUM>) distant from said tunable coupling element (<NUM>, <NUM>), for a strong coupling due to a close proximity of the first constant coupling element (<NUM>, <NUM>) and said first qubit (<NUM>, <NUM>) at said first non-galvanic coupling interface, and
- said tunable coupling element (<NUM>, <NUM>) is located adjacent to a second non-galvanic coupling interface formed to a further circuit element (<NUM>, <NUM>, <NUM>) at a second extremity of said first constant coupling element (<NUM>, <NUM>), there being a coupling between said tunable coupling element (<NUM>, <NUM>) and said further circuit element (<NUM>, <NUM>, <NUM>) and a strong coupling due to a close proximity of the first constant coupling element (<NUM>, <NUM>) and said further circuit element (<NUM>, <NUM>, <NUM>) at said second non-galvanic coupling interface;
wherein said tunable coupling element (<NUM>, <NUM>) is configured to be tuned in order to adapt a coupling strength of the coupling between the tunable coupling element (<NUM>, <NUM>) and the first constant coupling element (<NUM>, <NUM>) and a coupling strength of the coupling between the tunable coupling element (<NUM>, <NUM>) and the further circuit element (<NUM>, <NUM>, <NUM>);
and wherein said further circuit element (<NUM>, <NUM>, <NUM>) is a second constant coupling (<NUM>, <NUM>) element or a second qubit.