Reduction of Floating Coupling via Multi-Junction Cubits

Abstract

Systems and techniques are provided that facilitate the reduction of stray coupling through multi-junction qubits. In various embodiments, a device may include a first qubit having a plurality of Josephson junctions respectively between a plurality of capacitor pads. In various aspects, the device may further include a plurality of second qubits respectively coupled to different ones of the plurality of capacitor pads, such that no two of the plurality of second qubits are coupled to the same one of the plurality of capacitor pads. (FIG. 1)

Description

Background Art

[0001] The present disclosure relates to the reduction of stray coupling through qubits, and more specifically, multi-junction qubits.

[0002] Quantum computing is facilitated by executing quantum circuits on qubits arranged within a qubit lattice. The type / contents of the quantum circuits that can be executed depend on which qubits are coupled to each other within the qubit lattice. Higher-order coupling topologies among the qubits in the qubit lattice enable more interesting / useful quantum circuits to be executed. However, such higher-order coupling topologies also generate significant stray coupling, which may not be desirable.

[0003] Accordingly, systems and / or techniques that can address one or more of these technical problems may be desirable.

Summary of the Invention

[0004] A summary is presented below to provide a basic understanding of one or more embodiments of the invention. This summary is not intended to identify key or essential elements, nor to define any scope of either particular embodiments or the scope of any claims. Its sole purpose is to present concepts in a simplified form as a prelude to the more detailed description that is presented later. In one or more embodiments described herein, devices, systems, computer-implemented methods, apparatuses, and / or computer program products are described that can facilitate the reduction of stray coupling through multi-junction qubits.

[0005] According to one or more embodiments, a device is provided. In various aspects, the device may include a first qubit having a plurality of Josephson junctions respectively between a plurality of capacitor pads. In various aspects, the device may further include a plurality of second qubits respectively coupled to different ones of the plurality of capacitor pads, such that no two of the plurality of second qubits are coupled to the same one of the plurality of capacitor pads. In various instances, the device may further include a plurality of inductive loops respectively between the plurality of capacitor pads, and a plurality of third qubits respectively coupled to different ones of the plurality of inductive loops, such that no two of the plurality of third qubits are coupled to the same one of the plurality of inductive loops. In various cases, different ones of the plurality of Josephson junctions may be sized differently.

[0006] According to one or more embodiments, a system is provided. In various embodiments, the system may include a qubit lattice. In various aspects, the system may further include at least one qubit within the qubit lattice coupled to three or more adjacent qubits within the qubit lattice. In various instances, the at least one qubit may have three or more coupling elements respectively corresponding to the three or more adjacent qubits. In various cases, no two of the three or more adjacent qubits may be coupled to the same one of the three or more coupling elements. In various aspects, the coupling element may be a capacitor pad or an inductive loop. In various instances, the qubit lattice may exhibit a double hexagonal tiling layout.

[0007] In various embodiments, the above-described device and / or system may be implemented as a method.

[0008] Various other details of the various embodiments described herein are provided in the following items.

[0009] Item 1: A device comprising: a first qubit having a plurality of Josephson junctions respectively disposed between a plurality of capacitor pads; and a plurality of second qubits respectively coupled to different ones of the plurality of capacitor pads. As described herein, when the plurality of second qubits are respectively coupled to different ones of the plurality of capacitor pads, there may be no stray coupling (e.g., crosstalk) and / or a differently improved level of stray coupling between each pair of the plurality of second qubits.

[0010] Item 2: The device of any preceding item specified in the general description, wherein two of the plurality of second qubits are not coupled to the same one of the plurality of capacitor pads. Again, as described herein, this can eliminate and / or otherwise reduce the stray coupling between the plurality of second qubits.

[0011] Item 3: The device of any preceding item specified in the general description, further comprising: a plurality of inductive loops respectively disposed between the plurality of capacitor pads; and a plurality of third qubits respectively coupled to different ones of the plurality of inductive loops. As described herein, when the plurality of third qubits are respectively coupled to different ones of the plurality of inductive loops, there may be no stray coupling (e.g., crosstalk) and / or a differently improved level of stray coupling between each pair of the plurality of third qubits.

[0012] Item 4: The device of any preceding item specified in the general description, wherein two of the plurality of third qubits are not coupled to the same one of the plurality of inductive loops. Again, as described herein, this can eliminate and / or otherwise reduce the stray coupling between the plurality of third qubits.

[0013] Item 5: The first qubit has a first Josephson junction between a first capacitor pad and a second capacitor pad, and the first qubit further has a second Josephson junction between the second capacitor pad and a third capacitor pad, the device of any preceding item specified in general terms.

[0014] Item 6: The plurality of second qubits includes a first transmon qubit coupled to the first capacitor pad and not coupled to either the second capacitor pad or the third capacitor pad, a second transmon qubit coupled to the second capacitor pad and not coupled to either the first capacitor pad or the third capacitor pad, and a third transmon qubit coupled to the third capacitor pad and not coupled to either the first capacitor pad or the second capacitor pad, the device of any preceding item specified in general terms.

[0015] Item 7: The plurality of second qubits are each coupled to different ones of the plurality of capacitor pads by flux-tunable couplers, the device of any preceding item specified in general terms.

[0016] Item 8: Different ones of the plurality of Josephson junctions are sized differently, the device of any preceding item specified in general terms. As described herein, such different (e.g., asymmetric) sizes of the plurality of Josephson junctions can implement different operating modes as compared to the same (e.g., symmetric) sizing of the plurality of Josephson junctions.

[0017] In various aspects, any combination and / or any combination of Items 1 to 8 can be implemented.

[0018] Step 9: providing a first qubit having a plurality of Josephson junctions respectively between a plurality of capacitor pads; and coupling a plurality of second qubits to different ones of the plurality of capacitor pads. As described herein, when a plurality of second qubits are respectively coupled to different ones of the plurality of capacitor pads, there may be no stray coupling (e.g., crosstalk) and / or an otherwise improved level of stray coupling between each pair of the plurality of second qubits.

[0019] Step 10: The method of any preceding item specified in the summary, wherein two of the plurality of second qubits are not coupled to the same one of the plurality of capacitor pads. Again, as described herein, this can eliminate and / or otherwise reduce the stray coupling between the plurality of second qubits.

[0020] Step 11: The method of any preceding item specified in the summary, further comprising coupling a plurality of third qubits to different ones of the plurality of inductive loops, wherein the plurality of inductive loops are respectively between the plurality of capacitor pads. As described herein, when a plurality of third qubits are respectively coupled to different ones of the plurality of inductive loops, there may be no stray coupling (e.g., crosstalk) and / or an otherwise improved level of stray coupling between each pair of the plurality of third qubits.

[0021] Step 12: The method of any preceding item specified in the summary, wherein two of the plurality of third qubits are not coupled to the same one of the plurality of inductive loops. Again, as described herein, this can eliminate and / or otherwise reduce the stray coupling between the plurality of third qubits.

[0022] Item 13: The method of any preceding item specified in the summary, wherein the first qubit has a first Josephson junction between a first capacitor pad and a second capacitor pad, and the first qubit further has a second Josephson junction between the second capacitor pad and a third capacitor pad.

[0023] Item 14: The method of any preceding item specified in the summary, wherein the plurality of second qubits include a first transmon qubit coupled to the first capacitor pad and not coupled to either the second capacitor pad or the third capacitor pad, a second transmon qubit coupled to the second capacitor pad and not coupled to either the first capacitor pad or the third capacitor pad, and a third transmon qubit coupled to the third capacitor pad and not coupled to either the first capacitor pad or the second capacitor pad.

[0024] Item 15: The method of any preceding item specified in the summary, wherein the plurality of second qubits are each coupled to different ones of the plurality of capacitor pads by flux-adjustable couplers.

[0025] Item 16: The method of any preceding item specified in the summary, wherein different ones of the plurality of Josephson junctions are sized differently. As described herein, such different (e.g., asymmetric) sizes of the plurality of Josephson junctions can implement different operating modes as compared to the same (e.g., symmetric) sizing of the plurality of Josephson junctions.

[0026] In various aspects, any combination and / or any combination of items 9 to 16 can be implemented.

[0027] Item 17: A system comprising a qubit lattice; and at least one qubit within the qubit lattice coupled to three or more adjacent qubits within the qubit lattice, wherein the at least one qubit has three or more coupling elements respectively corresponding to the three or more adjacent qubits, and two of the three or more adjacent qubits are not coupled to the same one of the three or more coupling elements, and the coupling elements are capacitor pads or inductive loops. As described herein, when two of the three or more adjacent qubits are not coupled to the same one of the three or more coupling elements, there may be no stray coupling (e.g., crosstalk) between each pair of the three or more adjacent qubits and / or an otherwise improved level of stray coupling.

[0028] Item 18: The system of any preceding item specified in the general description, wherein the at least one qubit is coupled to three adjacent qubits, the at least one qubit has two Josephson junctions in series between three capacitor pads, and the three adjacent qubits are respectively coupled to different ones of the three capacitor pads.

[0029] Item 19: The system of any preceding item specified in the general description, wherein the at least one qubit is coupled to five adjacent qubits, the at least one qubit has two Josephson junctions in series between three capacitor pads and two inductive loops, and the five adjacent qubits are respectively coupled to different ones of the three capacitor pads and the two inductive loops. As described herein, such embodiments can significantly increase the number of adjacent qubits that can be coupled to any given qubit without experiencing an excessive increase in stray coupling between such adjacent qubits.

[0030] Item 20: The system of any preceding item specified in the summary, wherein the qubit lattice exhibits a double hexagonal tiling layout.

[0031] In various aspects, any combination and / or any combination of items 17 to 20 may be implemented.

Brief Description of the Drawings

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DETAILED DESCRIPTION OF THE INVENTION

[0038] The following detailed description is merely exemplary and is not intended to limit the embodiments and / or the application or use of the embodiments. Further, there is no intention to be bound by any explicit or implicit information presented in the foregoing Background or Summary of the Invention sections, or in the Detailed Description of the Invention section.

[0039] Here, one or more embodiments are described with reference to the drawings, and throughout, like reference numerals are used to refer to like elements. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a more thorough understanding of one or more embodiments. However, it is apparent that in various instances, one or more embodiments may be practiced without these specific details.

[0040] Quantum computing can be facilitated by executing a quantum circuit (e.g., a sequence of parallel and / or sequential quantum gates such as Pauli X gate, Pauli Y gate, Pauli Z gate, phase gate, controlled NOT gate, and / or controlled phase gate) on qubits (e.g., superconducting qubits such as transmon qubits) arranged within a qubit lattice. The type / content of the quantum circuit that can be executed on the qubit lattice can depend on which qubits within the qubit lattice are coupled to each other. For example, entangling gates (e.g., controlled NOT gate, controlled phase gate) can only be executed on two qubits that are coupled together, and cannot be executed on any two qubits that are not coupled together. Thus, the quantum circuits implementable on a qubit lattice can be limited by the coupling topology of the qubit lattice.

[0041] Higher-order coupling topologies among the qubits in a qubit lattice can enable more interesting and / or useful quantum circuits to be executed on the qubit lattice. In other words, it may be desirable to couple more qubits within the qubit lattice to each other. However, such higher-order coupling topologies have the negative side effect of generating a significant amount of stray coupling (e.g., spectator crosstalk). Existing techniques do not provide solutions for such elevated levels of stray coupling other than completely avoiding higher-order coupling topologies and the more interesting / useful quantum circuits supported by such topologies.

[0042] Accordingly, a system and / or technique that can address one or more of these technical problems may be desirable.

[0043] The various embodiments described herein can address one or more of these technical problems. In particular, the various embodiments described herein can provide systems and / or techniques that can facilitate the reduction of stray coupling via multi-junction qubits. More specifically, the inventors of the various embodiments described herein have determined how / why higher-order coupling topologies give rise to increased levels of stray coupling, and further devised techniques that can utilize multi-junction qubits to reduce and / or otherwise improve stray coupling in such higher-order coupling topologies. Still more specifically, the inventors have realized that increased stray coupling plagues existing technologies. This is because whenever three or more adjacent qubits are coupled to a given qubit according to such existing technologies, some of such three or more adjacent qubits are coupled to the same coupling element of the given qubit (e.g., to the same capacitor pad and / or the same inductive loop). In various aspects, the inventors have realized that such increased stray coupling can be avoided and / or otherwise reduced when the given qubit is a multi-junction qubit. This is because such multi-junction qubits can have more coupling elements (e.g., can have one coupling element per adjacent qubit), and as a result, two adjacent qubits are not coupled to the same coupling element of the given qubit (e.g., as a result, two adjacent qubits do not share the same coupling element of the given qubit).

[0044] As a non-limiting example, consider qubit A, qubit B, qubit C, and qubit D. In various cases, each of qubit A, qubit B, qubit C, and qubit D can be a transmon qubit. In various aspects, a transmon qubit can be a superconducting qubit formed by a Josephson junction shunted by two capacitor pads (e.g., planar capacitor pads, trench capacitor pads, and / or any other suitable type of capacitor pads). In various instances, a transmon qubit can have a charging energy that is significantly smaller (e.g., more than one order of magnitude smaller) than its Josephson energy. Thus, qubit A can be considered to be made by Josephson junction A shunted by two capacitor pads, capacitor pad A1 and capacitor pad A2. Similarly, qubit B can be considered to be made by Josephson junction B shunted by two capacitor pads, capacitor pad B1 and capacitor pad B2. Similarly, qubit C can be considered to be made by Josephson junction C shunted by two capacitor pads, capacitor pad C1 and capacitor pad C2. Finally, qubit D can be considered to be made by Josephson junction D shunted by two capacitor pads, capacitor pad D1 and capacitor pad D2.

[0045] In any case, assume that it is desired to couple qubit A to each of qubit B, qubit C, and qubit D. In various embodiments, this can be facilitated by capacitively coupling one of two capacitor pads A1 and A2 directly and / or indirectly (in a fixed and / or flux-adjustable manner) to one of two capacitor pads B1 and B2, by capacitively coupling one of two capacitor pads A1 and A2 directly and / or indirectly (in a fixed and / or flux-adjustable manner) to one of two capacitor pads C1 and C2, and by capacitively coupling one of two capacitor pads A1 and A2 directly and / or indirectly (in a fixed and / or flux-adjustable manner) to one of two capacitor pads D1 and D2.

[0046] Note that such a configuration inevitably results in capacitively coupling one of the two capacitor pads A1 and A2 to two different qubits, which can lead to increased stray coupling (e.g., resulting in degraded spectator crosstalk) between those two different qubits. For example, without loss of generality, one of the two capacitor pads B1 and B2 of qubit B can be coupled to capacitor pad A1, and one of the two capacitor pads C1 and C2 of qubit C can be coupled to capacitor pad A2. In such a case, one of the two capacitor pads D1 and D2 of qubit D can be coupled to either capacitor pad A1 or capacitor pad A2. If one of the two capacitor pads D1 and D2 of qubit D is coupled to capacitor pad A1, then capacitor pad A1 can be considered to be coupled to both qubit B and qubit D, which can unnecessarily cause excessive crosstalk between qubit B and qubit D. That is, if both qubit B and qubit D are coupled to capacitor pad A1, an entangling gate configured to entangle qubit A with qubit B can erroneously cause an entanglement interaction to occur between qubit B and qubit D. Similarly, if both qubit B and qubit D are coupled to capacitor pad A1, an entangling gate configured to entangle qubit A with qubit D can erroneously cause an entanglement interaction to occur between qubit B and qubit D.

[0047] On the other hand, when one of the two capacitor pads D1 and D2 of the qubit D is coupled to the capacitor pad A2, next, the capacitor pad A2 can be regarded as being coupled to both the qubit C and the qubit D, which can unnecessarily generate excessive crosstalk between the qubit C and the qubit D. That is, when both the qubit C and the qubit D are coupled to the capacitor pad A2, an entangling gate configured to entangle the qubit A with the qubit C can erroneously cause an entanglement interaction to occur between the qubit C and the qubit D. Similarly, when both the qubit C and the qubit D are coupled to the capacitor pad A2, an entangling gate configured to entangle the qubit A with the qubit D can erroneously cause an entanglement interaction to occur between the qubit C and the qubit D.

[0048] Thus, if it is desired to couple a transmon qubit to three or more other transmon qubits according to existing techniques, enhanced stray coupling may be inevitable. In fact, as the inventors have realized, this can be due to the fact that a transmon qubit has only two coupling elements (e.g., two capacitor pads), such that coupling three or more neighbors to a transmon qubit necessarily forces some of those three or more neighbors to couple to the same one of those two coupling elements. Put another way, when existing techniques are implemented, such enhanced stray coupling can only be avoided and / or mitigated by implementing a ring topology in which no more than two transmon qubits are coupled to any given transmon qubit. That is, since a transmon qubit has only two coupling elements (e.g., two capacitor pads), coupling two or fewer neighbors to a transmon qubit enables each of those two or fewer neighbors to be coupled to its own corresponding one of those two coupling elements. Unfortunately, a very large number of quantum circuits of interest cannot be implemented with respect to such a ring topology.

[0049] The inventor has realized that this significant technical problem can be avoided, mitigated, and / or otherwise improved by leveraging multi-junction qubits. This is because such multi-junction qubits can have a higher number of coupling elements (e.g., a higher number of capacitor pads). A non-limiting example of a multi-junction qubit can be a two-junction transmon qubit. In various aspects, a two-junction transmon qubit can be a superconducting qubit that includes two capacitively shunted Josephson junctions coupled in series (e.g., a two-junction transmon qubit can be formed by connecting and / or coupling two single-junction transmon qubits in series). In other words, a two-junction transmon qubit can include a first Josephson junction and a second Josephson junction, where the first Josephson junction is coupled in series between a first capacitor pad and a second capacitor pad, and where the second Josephson junction is coupled in series between the second capacitor pad and a third capacitor pad. In various aspects, the second capacitor pad can be referred to as the central capacitor pad of the two-junction transmon qubit, and the first capacitor pad and the third capacitor pad can be referred to as the end capacitor pads of the two-junction transmon qubit. In various cases, a two-junction transmon qubit can also be referred to as an adjustable coupler qubit.

[0050] In various instances, a two-junction transmon qubit can support and / or exhibit two distinct excitation modes, a dark mode and a bright mode. In various aspects, these two distinct excitation modes can have two different spatial symmetries and / or two different transition frequencies (e.g., a transition frequency of the dark mode and a transition frequency of the bright mode). More specifically, the dark mode of a two-junction transmon qubit can be a higher-frequency excitation mode that has no net dipole moment. In other words, the dark mode can avoid coupling to the overall electric field. In contrast, the bright mode of a two-junction transmon qubit can be a lower-frequency excitation mode that has a net dipole moment. That is, the bright mode can couple to the overall electric field. In various instances, a two-junction transmon qubit can be encoded either in the dark mode (and thus can have a transition frequency of the dark mode) or in the bright mode (and thus can have a transition frequency of the bright mode). In various aspects, short microwave pulses can be used to switch the two-junction transmon qubit between encodings (e.g., suitable microwave pulses can be applied to the two-junction transmon qubit to switch it from the dark mode to the bright mode and / or from the bright mode to the dark mode).

[0051] In any case, the inventor has noticed that the implementation of two-junction transmon qubits in a qubit lattice can help reduce and / or mitigate stray coupling. Consider again the above non-limiting example where qubit A is desired to be coupled to each of qubit B, qubit C, and qubit D. As described above, qubit B, qubit C, and qubit D can all be transmon qubits. As further explained above, when qubit A is also a transmon qubit, excessive stray coupling can occur because one of the capacitor pads of qubit A is forced to be coupled to at least two other qubits. However, the inventor has noticed that this problem can be avoided and / or mitigated when qubit A is a two-junction transmon qubit. That is, assume that qubit A has a first Josephson junction between capacitor pad A1 and capacitor pad A2, and further assume that qubit A has a second Josephson junction between capacitor pad A2 and capacitor pad A3. In other words, qubit A can be considered to have three capacitor pads instead of just two. Here, without loss of generality, one of the two capacitor pads B1 and B2 of qubit B can be coupled to capacitor pad A1, one of the two capacitor pads C1 and C2 of qubit C can be coupled to capacitor pad A2, and one of the two capacitor pads D1 and D2 of qubit D can be coupled to capacitor pad A3. Note that in such a configuration, none of the three capacitor pads of qubit A need to be coupled to more than one of qubit B, qubit C, and qubit D. In other words, none of qubit B, qubit C, and qubit D need to be coupled to the same capacitor pad (e.g., the same coupling element) of qubit A. Therefore, such a configuration where qubit A is a two-junction transmon can experience significantly reduced stray coupling (e.g., significantly reduced spectator crosstalk) compared to a configuration where qubit A is a single-junction transmon.

[0052] Furthermore, as described above, since two-junction transmon qubits can exhibit different excitation modes, qubit A can exhibit such different excitation modes as bright and dark modes when qubit A is a two-junction transmon qubit. In various embodiments, such different excitation modes can be utilized and / or exploited according to the relative sizes of the two Josephson junctions of qubit A. As a non-limiting example, assume that the first Josephson junction and the second Josephson junction of qubit A are sized symmetrically (e.g., having the same dimensions as each other). In such a case, the above-described configuration in which qubit B is coupled to capacitor pad A1, qubit C is coupled to capacitor pad A2, and qubit D is coupled to capacitor pad A3 can be considered to couple all of qubit B, qubit C, and qubit D to the dark mode of qubit A. In contrast and as another non-limiting example, assume that the first Josephson junction and the second Josephson junction of qubit A are sized asymmetrically (e.g., one junction may be twice as large as the other). In such a case, the above-described configuration in which qubit B is coupled to capacitor pad A1, qubit C is coupled to capacitor pad A2, and qubit D is coupled to capacitor pad A3 can be considered to couple all of qubit B, qubit C, and qubit D to the bright mode of qubit A. In various cases, coupling to the bright mode in this way can be beneficial because the anharmonicity of the bright mode may be greater in the asymmetric case than in the symmetric case (e.g., the greater anharmonicity can help avoid frequency collisions).

[0053] In any case and as the above non-limiting examples serve to illustrate, the inventor has noticed that existing techniques accurately generate excessive stray couplings in higher-order coupling topologies. This is because whenever a qubit is coupled to three or more neighbors, such existing techniques force some of those three or more neighbors to be coupled to the same coupling element of the qubit (e.g., the same capacitor pad). Further, the inventor has noticed that whenever a qubit is coupled to three or more neighbors, such excessive stray couplings can be reduced by configuring that qubit as a multi-junction qubit (e.g., as a two-junction transmon). After all, a multi-junction qubit can have more coupling elements (e.g., more capacitor pads), which can help ensure that each neighbor is coupled to its own corresponding coupling element (e.g., can help ensure that two neighbors are not coupled to the same coupling element). When each neighbor is coupled to its own corresponding coupling element (e.g., when two neighbors are not coupled to the same coupling element), the spectator crosstalk between neighbors can be reduced.

[0054] The disclosure herein mainly describes various embodiments of the coupling elements of qubits as capacitor pads, which is merely a non-limiting example for ease of explanation. In various aspects, the coupling element of a qubit can be any other suitable circuit structure and / or circuit component of the qubit to which another qubit (e.g., an adjacent qubit) can be coupled. As a non-limiting example, a qubit can be fabricated using one or more capacitor pads as well as one or more inductive loops. In such cases, all of the one or more capacitor pads and one or more inductive loops can be considered and / or otherwise referred to as coupling elements of the qubit. After all, a neighbor can be capacitively coupled directly and / or indirectly to one or more capacitor pads of a qubit, and / or a neighbor can be inductively coupled directly and / or indirectly to one or more inductive loops of a qubit.

[0055] In any case, the inventors have noticed that stray couplings within higher-order coupling topologies can be reduced and / or otherwise mitigated by implementing multi-junction qubits. This is because such multi-junction qubits can include a larger number of coupling elements compared to single-junction qubits (e.g., can include more capacitor pads and / or more inductive loops), and such a larger number of coupling elements can help ensure that two neighbors are not coupled to the same coupling element.

[0056] The various embodiments described herein can be employed to solve problems that are not essentially highly technical (e.g., facilitating the reduction of stray coupling via multi-junction qubits), not abstract, not mere natural laws, not mere natural phenomena, and cannot be implemented as a set of mental activities by humans, and instead, use hardware and / or software. Instead, the various embodiments described herein include tangible electrical circuit structures / architectures that can be implemented to reduce stray coupling in a qubit lattice and / or methodologies related to such tangible electrical circuit structures / architectures. In fact, as described above, whenever three or more adjacent qubits are coupled to a given qubit according to existing techniques, the inventor has noticed that such existing techniques involve some of those three or more neighbors being coupled to the same coupling element of a given qubit (e.g., to the same capacitor pad, to the same inductive loop), resulting in increased stray coupling (e.g., increased spectator crosstalk).

[0057] In contrast, the various embodiments described herein can address such technical problems. Specifically, the systems / techniques described herein can reduce stray coupling by implementing multi-junction qubits. In particular, the inventor has noticed that whenever three or more adjacent qubits are coupled to a given qubit, the stray coupling can be significantly reduced when the given qubit is a multi-junction qubit (e.g., a two-junction transmon). In fact, when a given qubit is a multi-junction qubit, the given qubit can have a higher number of coupling elements than would be possible if the given qubit were instead a single-junction qubit (e.g., it can have more capacitor pads and / or inductive loops). Thus, when a given qubit has a higher number of coupling elements, it may be possible to prevent any two neighbors from coupling to the same coupling element of the given qubit (e.g., the total number of coupling elements of a given qubit may be greater than or equal to the total number of neighbors desired to be coupled to the given qubit). Therefore, when two neighbors do not couple to the same coupling element of a given qubit (e.g., when two neighbors do not couple to the same capacitor pad of a given qubit and / or when two neighbors do not couple to the same inductive loop of a given qubit), the stray coupling between neighbors (e.g., the crosstalk of a spectator) can be improved. Since the various embodiments described herein can mitigate these technical problems (e.g., excessive stray coupling) associated with existing technologies, such embodiments naturally constitute a specific tangible technical improvement in the field of qubits.

[0058] Furthermore, the various embodiments described herein can control tangible, hardware-based, and / or software-based devices based on the disclosed teachings. For example, the embodiments described herein can include tangible qubits (e.g., superconducting qubits created with Josephson junctions, capacitor pads, and / or inductive loops) that can be fabricated on a tangible quantum substrate (e.g., a silicon wafer).

[0059] It should be recognized that the disclosure in the drawings and the specification describes non-limiting examples of various embodiments. It should be further recognized that the drawings are not necessarily drawn to scale.

[0060] FIG. 1 shows a structural diagram of an exemplary and non-limiting system 100 that can facilitate the reduction of stray coupling through a multi-junction qubit according to one or more embodiments described herein. As shown, system 100 may include a multi-junction qubit 102.

[0061] In various embodiments, multi-junction qubit 102 may include Josephson junctions 104, 106, capacitor pads 108, 110, and / or 112. In various aspects, as shown, Josephson junction 104 may be coupled to capacitor pads 108 and 110, such that capacitor pad 108, Josephson junction 104, and capacitor pad 110 may all be considered to be in series with each other. Thus, in various instances, capacitor pads 108 and 110 may be collectively considered to form a capacitance that shunts Josephson junction 104.

[0062] Similarly, in various cases, as shown, Josephson junction 106 may be coupled to capacitor pads 110 and 112, such that capacitor pad 110, Josephson junction 106, and capacitor pad 112 may all be considered to be in series with each other. Therefore, in various aspects, capacitor pads 110 and 112 may be collectively considered to form a capacitance that shunts Josephson junction 106.

[0063] Also, in various cases, as shown, capacitor pads 108, Josephson junctions 104, capacitor pads 110, Josephson junctions 106, and capacitor pads 112 can all be considered to be in series with each other. Thus, in various cases, capacitor pads 108 and capacitor pads 112 can be collectively considered to form a capacitance that shunts both Josephson junction 104 and Josephson junction 106.

[0064] Thus, in various aspects, the multi-junction qubit 102 can be considered to be a two-junction transmon formed by two single-junction transmons coupled in series. In particular, capacitor pads 108, Josephson junction 104, and capacitor pads 110 can be collectively considered to form a first single-junction transmon. Similarly, capacitor pads 110, Josephson junction 106, and capacitor pads 112 can be collectively considered to form a second single-junction transmon that is in series with the first single-junction transmon. As can be seen, the first single-junction transmon and the second single-junction transmon can be considered to share capacitor pad 110. Thus, in various cases, capacitor pad 110 can be referred to as the central pad of the multi-junction qubit 102, and / or capacitor pads 108 and capacitor pads 112 can be referred to as the end pads of the multi-junction qubit 102. In any case, since the multi-junction qubit 102 can be considered to be a two-junction transmon in the non-limiting example of FIG. 1, the multi-junction qubit 102 can be considered to have multiple excitation modes (e.g., dark mode and bright mode).

[0065] In various cases, capacitor pad 108, Josephson junction 104, capacitor pad 110, Josephson junction 106, and / or capacitor pad 112 can be fabricated and / or manufactured via any suitable microfabrication and / or nanofabrication techniques (e.g., photolithography, deposition, etching, double angle evaporation) with respect to any suitable quantum substrate (e.g., a silicon wafer (not shown)). In various instances, capacitor pad 108, Josephson junction 104, capacitor pad 110, Josephson junction 106, and / or capacitor pad 112 can be fabricated and / or manufactured from any suitable superconducting material and / or combination of superconducting materials as desired.

[0066] FIG. 1 shows Josephson junction 104 and Josephson junction 106 as being identical to each other (e.g., identically sized and / or identically structured), which is merely a non-limiting example for ease of illustration and / or description. In various aspects, Josephson junction 104 and Josephson junction 106 can have the same and / or different sizes, shapes, spatial dimensions, and / or material compositions from each other in various aspects.

[0067] Similarly, FIG. 1 shows capacitor pad 108, capacitor pad 110, and capacitor pad 112 as being identical to each other (e.g., identically sized and / or identically structured), which is merely a non-limiting example for ease of illustration. In fact, in various instances, capacitor pad 108, capacitor pad 110, and capacitor pad 112 can have the same and / or different sizes, shapes, spatial dimensions, and / or material compositions from each other.

[0068] In various embodiments, as shown, a qubit 114 may be present. In various aspects, the qubit 114 may include a Josephson junction 116, a capacitor pad 118, and / or a capacitor pad 120. In various instances, as shown, the Josephson junction 116 may be coupled to the capacitor pad 118 and the capacitor pad 120, such that the capacitor pad 118, the Josephson junction 116, and the capacitor pad 120 may all be considered to be in series with each other. Thus, in various cases, the capacitor pad 118 and the capacitor pad 120 may be collectively considered to form a capacitance that shunts the Josephson junction 116. Thus, in various aspects, the qubit 114 may be considered a single-junction transmon.

[0069] In various aspects, any suitable microfabrication and / or nanofabrication techniques may be implemented to fabricate the capacitor pad 118, the Josephson junction 116, and / or the capacitor pad 120.

[0070] FIG. 1 shows the Josephson junction 116 as being the same as the Josephson junctions of the multi-junction qubit 102, but this is merely a non-limiting example for ease of illustration and / or description. In various instances, the Josephson junction 116 may have the same and / or different size, shape, spatial dimension, and / or material composition as the Josephson junctions of the multi-junction qubit 102 in various aspects.

[0071] Similarly, FIG. 1 shows the capacitor pad 118 and the capacitor pad 120 as being the same as each other and / or the same as the capacitor pads of the multi-junction qubit 102, but this is merely a non-limiting example for ease of illustration. In fact, in various aspects, the capacitor pad 118 and / or the capacitor pad 120 may have the same and / or different size, shape, spatial dimension, and / or material composition as each other and / or the capacitor pads of the multi-junction qubit 102.

[0072] In various instances, as shown, the multi-junction qubit 102 can be coupled to the qubit 114 by a direct capacitive coupler 122. In particular, the direct capacitive coupler 122 can be any suitable wire, cable, and / or circuit structure that can be spatially proximate to the capacitor pad 112 of the multi-junction qubit 102 and spatially proximate to the capacitor pad 120 of the qubit 114. Since the direct capacitive coupler 122 can be spatially proximate to both the capacitor pad 112 and the capacitor pad 120, the direct capacitive coupler 122 can be considered to form a capacitance between the capacitor pad 112 and the capacitor pad 120. In other words, the direct capacitive coupler 122 can be considered to capacitively couple the capacitor pad 112 to the capacitor pad 120.

[0073] In various cases, the direct capacitive coupler 122 can be fabricated via any suitable microfabrication and / or nanofabrication techniques. In various instances, the direct capacitive coupler 122 can have any suitable size, shape, spatial dimension, and / or material composition (e.g., can be made of any suitable superconducting material).

[0074] FIG. 1 shows the capacitor pad 112 capacitively coupled to the capacitor pad 120 by the direct capacitive coupler 122, which is merely a non-limiting example for ease of illustration and / or description. In various aspects, any other suitable capacitive coupler (e.g., an indirect capacitive coupler), whether fixed or flux-tunable, can be implemented instead of and / or in addition to the direct capacitive coupler 122.

[0075] In various embodiments, as shown, a qubit 124 may be present. In various aspects, the qubit 124 may include a Josephson junction 126, a capacitor pad 128, and / or a capacitor pad 130. In various instances, as shown, the Josephson junction 126 may be coupled to the capacitor pad 128 and the capacitor pad 130, such that the capacitor pad 128, the Josephson junction 126, and the capacitor pad 130 may all be considered to be in series with each other. Thus, in various cases, the capacitor pad 128 and the capacitor pad 130 may be collectively considered to form a capacitance that shunts the Josephson junction 126. Thus, in various aspects, the qubit 124 may be considered to be a single-junction transmon.

[0076] Again, in various cases, any suitable microfabrication and / or nanofabrication techniques may be implemented to fabricate the capacitor pad 128, the Josephson junction 126, and / or the capacitor pad 130.

[0077] FIG. 1 shows the Josephson junction 126 as being the same as the Josephson junction of the multi-junction qubit 102 and / or the Josephson junction of the qubit 114, which is merely a non-limiting example for ease of illustration and / or description. In various aspects, the Josephson junction 126 may have the same and / or different size, shape, spatial dimension, and / or material composition as the Josephson junction of the multi-junction qubit 102 and / or the Josephson junction of the qubit 114 in various aspects.

[0078] Similarly, FIG. 1 shows the capacitor pads 128 and 130 being the same as each other, the same as the capacitor pads of the multi-junction qubit 102, and / or the same as the capacitor pads of the qubit 114, but this is merely a non-limiting example for ease of illustration. In fact, in various cases, the capacitor pad 128 and / or the capacitor pad 130 may have the same and / or different sizes, shapes, spatial dimensions, and / or material compositions from each other, the capacitor pads of the multi-junction qubit 102, and / or the capacitor pads of the qubit 114.

[0079] In various cases, as shown, the multi-junction qubit 102 may be coupled to the qubit 124 by a direct capacitive coupler 132. In particular, the direct capacitive coupler 132 can be any suitable wire, cable, and / or circuit structure that can be spatially proximate to the capacitor pad 110 of the multi-junction qubit 102 and spatially proximate to the capacitor pad 128 of the qubit 124. Since the direct capacitive coupler 132 can be spatially proximate to both the capacitor pad 110 and the capacitor pad 128, the direct capacitive coupler 132 can be considered to form a capacitance between the capacitor pad 110 and the capacitor pad 128. That is, the direct capacitive coupler 132 can be considered to capacitively couple the capacitor pad 110 to the capacitor pad 128 (e.g., to transmit a capacitive interaction between the capacitor pad 110 and the capacitor pad 128).

[0080] Just as described above, in various embodiments, the direct capacitive coupler 132 can be fabricated via any suitable microfabrication and / or nanofabrication techniques. In various cases, the direct capacitive coupler 132 can have any suitable size, shape, spatial dimension, and / or material composition (e.g., can be made of any suitable superconducting material) as desired (e.g., can have the same and / or different sizes, shapes, dimensions, and / or compositions as the direct capacitive coupler 122).

[0081] FIG. 1 shows the capacitor pad 110 capacitively coupled to the capacitor pad 128 directly by the capacitive coupler 132, which is merely a non-limiting example for ease of illustration and / or description. In various aspects, any other suitable capacitive coupler (e.g., an indirect capacitive coupler), whether fixed or flux-adjustable, can be implemented instead of and / or in addition to the direct capacitive coupler 132.

[0082] In various embodiments, as shown, a qubit 134 may be present. In various aspects, the qubit 134 may include a Josephson junction 136, a capacitor pad 138, and / or a capacitor pad 140. In various cases, as shown, the Josephson junction 136 may be coupled to the capacitor pad 138 and the capacitor pad 140, such that the capacitor pad 138, the Josephson junction 136, and the capacitor pad 140 may all be considered to be in series with each other. Thus, in various cases, the capacitor pad 138 and the capacitor pad 140 may be collectively considered to form a capacitance that shunts the Josephson junction 136. Thus, in various aspects, the qubit 134 may be considered a single-junction transmon.

[0083] Once again, in various cases, any suitable microfabrication and / or nanofabrication techniques may be implemented to fabricate the capacitor pad 138, the Josephson junction 136, and / or the capacitor pad 140.

[0084] FIG. 1 shows Josephson junction 136 as being the same as the Josephson junctions of multi-junction qubit 102, the Josephson junction of qubit 114, and / or the Josephson junction of qubit 124, but this is merely a non-limiting example for ease of illustration and / or description. In various embodiments, Josephson junction 136 may have the same and / or different sizes, shapes, spatial dimensions, and / or material compositions as the Josephson junctions of multi-junction qubit 102, the Josephson junction of qubit 114, and / or the Josephson junction of qubit 124 in various embodiments.

[0085] Similarly, FIG. 1 shows capacitor pads 138 and 140 as being the same as each other, the same as the capacitor pads of multi-junction qubit 102, the same as the capacitor pads of qubit 124, and / or the same as the capacitor pads of qubit 114, but this is merely a non-limiting example for ease of illustration. In fact, in various cases, capacitor pad 138 and / or capacitor pad 140 may have the same and / or different sizes, shapes, spatial dimensions, and / or material compositions as each other, the capacitor pads of multi-junction qubit 102, the capacitor pads of qubit 114, and / or the capacitor pads of qubit 124.

[0086] In various instances, as shown, the multi-junction qubit 102 can be coupled to the qubit 134 by a direct capacitive coupler 142. In particular, the direct capacitive coupler 142 can be any suitable wire, cable, and / or circuit structure that can be spatially proximate to the capacitor pad 108 of the multi-junction qubit 102 and spatially proximate to the capacitor pad 140 of the qubit 134. Since the direct capacitive coupler 142 can be spatially proximate to both the capacitor pad 108 and the capacitor pad 140, the direct capacitive coupler 142 can be considered to form a capacitance between the capacitor pad 108 and the capacitor pad 140. That is, the direct capacitive coupler 142 can be considered as something that capacitively couples the capacitor pad 108 to the capacitor pad 140 (e.g., something that transmits the capacitive interaction between the capacitor pad 108 and the capacitor pad 140).

[0087] Just as described above, in various aspects, the direct capacitive coupler 142 can be fabricated via any suitable microfabrication and / or nanofabrication techniques. In various instances, the direct capacitive coupler 142 can have any suitable size, shape, spatial dimension, and / or material composition (e.g., can be made of any suitable superconducting material) as desired (e.g., can have the same and / or different size, shape, dimension, and / or composition as the direct capacitive coupler 122 and / or the direct capacitive coupler 132).

[0088] FIG. 1 shows the capacitor pad 108 capacitively coupled to the capacitor pad 140 by the direct capacitive coupler 142, which is merely a non-limiting example for ease of illustration and / or explanation. In various aspects, any other suitable capacitive coupler (e.g., an indirect capacitive coupler), whether fixed or flux-adjustable, can be implemented instead of and / or in addition to the direct capacitive coupler 142.

[0089] In any case, as shown, the capacitor pads of the multi-junction qubit 102 can be considered to be individually and / or independently coupled to three other qubits (e.g., 114, 124, and 134) such that no two of those three other qubits are coupled to the same capacitor pad. More specifically, qubit 114 can be considered to be coupled to capacitor pad 112 and not coupled to either capacitor pad 110 or capacitor pad 108. Similarly, qubit 124 can be considered to be coupled to capacitor pad 110 and not coupled to either capacitor pad 112 or capacitor pad 108. Also, qubit 134 can be considered to be coupled to capacitor pad 108 and not coupled to either capacitor pad 110 or capacitor pad 112. Thus, none of qubit 114, qubit 124, and qubit 134 can be considered to be coupled to the same capacitor pad as one another. In other words, qubit 114, qubit 124, and qubit 134 can all be considered to be coupled to different and / or respective capacitor pads of the multi-junction qubit 102. Accordingly, stray coupling (e.g., spectator crosstalk) between qubit 114 and qubit 124, between qubit 114 and qubit 134, and / or between qubit 124 and qubit 134 can be present at a reduced, mitigated, and / or otherwise improved level.

[0090] Note that such reduced, mitigated, and / or improved stray coupling would not be possible if the multi-junction qubit 102 were instead a single-junction qubit. In fact, if the multi-junction qubit 102 were instead a single-junction qubit (e.g., a single-junction transmon), then, instead of having three, it would simply have two capacitor pads. In such a case, at least two of qubit 114, qubit 124, and qubit 134 would need to be coupled to the same capacitor pad as one another, which increases the stray coupling.

[0091] FIG. 1 shows a multi-junction qubit 102 as a two-junction transmon having three capacitor pads, each of which is coupled to a different adjacent transmon, but this is merely a non-limiting example for ease of illustration and / or description. In various embodiments, the multi-junction qubit 102 may have three or more capacitor pads, thereby ensuring that each corresponding capacitor pad of the multi-junction qubit 102 can be allocated to each adjacent qubit to which the multi-junction qubit 102 is to be coupled. For example, for any suitable positive integer

Number

[0092] As described above, a two-junction transmon can exhibit a bright excitation mode and a dark excitation mode. Thus, since the multi-junction qubit 102 can be a two-junction transmon in some cases, the multi-junction qubit 102 can exhibit a bright excitation mode and a dark excitation mode in such cases. In some embodiments in which those two different excitation modes are implemented and / or activated, it may depend on the relative dimensions between the Josephson junction 104 and the Josephson junction 106. For example, assume that the Josephson junction 104 and the Josephson junction 106 have the same and / or symmetric dimensions (e.g., as measured within any suitable threshold margin of error). In such a case, the coupling structure shown in FIG. 1 can couple all of the qubits 114, 124, and 134 to the dark excitation mode of the multi-junction qubit 102. As another example, assume that the Josephson junction 104 and the Josephson junction 106 instead have different and / or asymmetric dimensions (e.g., as measured within any suitable threshold margin of error). For example, without loss of generality, the Josephson junction 104 may be twice as large (e.g., twice as thick, twice as long, twice as wide) as the Josephson junction 106. In such a case, the coupling structure shown in FIG. 1 can couple all of the qubits 114, 124, and 134 to the bright excitation mode of the multi-junction qubit 102. Thus, the difference in the relative sizes between the Josephson junction 104 and the Josephson junction 106 can affect and / or otherwise control which excitation mode is implemented (e.g., symmetric sizes can implement the dark mode, while asymmetric sizes can implement the bright mode).

[0093] In any case, whenever it is desired to couple three or more adjacent transmons to a given qubit as shown in FIG. 1, the stray coupling can be reduced when the given qubit is a multi-junction qubit having at least one dedicated capacitor pad for each of three or more adjacent transmons.

[0094] FIG. 2 shows a circuit diagram 200 of an exemplary and non - limiting system that can facilitate the reduction of stray coupling through a multi - junction qubit, according to one or more embodiments described herein. In particular, FIG. 2 shows a circuit diagram corresponding to the physical structure / architecture shown in FIG. 1.

[0095] In various embodiments, as shown, the circuit diagram of the multi - junction qubit 102 can be considered to include the Josephson junction 104 shunted by the capacitor 204, further include the Josephson junction 106 shunted by the capacitor 206, and / or further include both the Josephson junction 104 and the Josephson junction 106 shunted by the capacitor 202. In various aspects, the capacitor 204 can be considered as a capacitive interaction occurring between the capacitor pads 108 and 110. Similarly, the capacitor 206 can be considered as a capacitive interaction occurring between the capacitor pads 110 and 112. Similarly, the capacitor 202 can be considered as a capacitive interaction occurring between the capacitor pads 108 and 112. In various cases, the value of the capacitor 202, the capacitor 204, and / or the capacitor 206 (e.g., measured in farads) can depend on the size, shape, dimensions, and / or material composition of the capacitor pad 108, the capacitor pad 110, and / or the capacitor pad 112.

[0096] In various aspects, as shown, the circuit diagram of the qubit 114 can be considered to include the Josephson junction 116 shunted by the capacitor 208. In various cases, the capacitor 208 can be considered as a capacitive interaction occurring between the capacitor pads 118 and 120. In various situations, the value of the capacitor 208 (e.g., measured in farads) can depend on the size, shape, dimensions, and / or material composition of the capacitor pad 118 and / or the capacitor pad 120.

[0097] In various cases, as shown, there can be a capacitance 210 between the multi-junction qubit 102 and the qubit 114. In various situations, the capacitance 210 can be an equivalent capacitive interaction that occurs between the capacitor pad 112 and the capacitor pad 120 due to the direct capacitive coupler 122. More specifically, there can be a first configured capacitive interaction between the capacitor pad 112 and the direct capacitive coupler 122, and a second configured capacitive interaction between the capacitor pad 120 and the direct capacitive coupler 122. In various cases, those two configured capacitive interactions can be considered to be combined (e.g., according to the law of combining capacitors in series) to result in the capacitance 210. In various aspects, the value of the capacitance 210 (e.g., measured in farads) can depend on the size, shape, dimensions, and / or material composition of the capacitor pad 112, the capacitor pad 120, and / or the direct capacitive coupler 122.

[0098] In various aspects, as shown, the circuit diagram of the qubit 124 can be considered to include a Josephson junction 126 shunted by a capacitance 212. In various cases, just as described above, the capacitance 212 can be considered to be a capacitive interaction that occurs between the capacitor pad 128 and the capacitor pad 130. Therefore, in various situations, the value of the capacitance 212 (e.g., measured in farads) can depend on the size, shape, dimensions, and / or material composition of the capacitor pad 128 and / or the capacitor pad 130.

[0099] In various cases, as further shown, a capacitance 214 may exist between the multi-junction qubit 102 and the qubit 124. In various situations, the capacitance 214 may be an equivalent capacitive interaction that occurs between the capacitor pad 110 and the capacitor pad 128 due to the direct capacitive coupler 132. In particular, a first configured capacitive interaction may exist between the capacitor pad 110 and the direct capacitive coupler 132, and a second configured capacitive interaction may exist between the capacitor pad 128 and the direct capacitive coupler 132. In various cases, just as above, those two configured capacitive interactions may be considered to be combined (e.g., according to the law of combining capacitors in series) to result in the capacitance 214. Again, in various aspects, the value of the capacitance 214 (e.g., measured in farads) may depend on the size, shape, dimensions, and / or material composition of the capacitor pad 110, the capacitor pad 128, and / or the direct capacitive coupler 132.

[0100] In various aspects, as further shown, the circuit diagram of the qubit 134 may be considered to include a Josephson junction 136 shunted by a capacitance 216. In various cases, just as above, the capacitance 216 may be considered to be a capacitive interaction that occurs between the capacitor pad 138 and the capacitor pad 140. Therefore, in various situations, the value of the capacitance 216 (e.g., measured in farads) may depend on the size, shape, dimensions, and / or material composition of the capacitor pad 138 and / or the capacitor pad 140.

[0101] In various instances, as further shown, a capacitance 218 may exist between the multi-junction qubit 102 and the qubit 134. In various cases, the capacitance 218 may be an equivalent capacitive interaction that occurs between the capacitor pad 108 and the capacitor pad 140 due to the direct capacitive coupler 142. Specifically, a first configured capacitive interaction may exist between the capacitor pad 108 and the direct capacitive coupler 142, and a second configured capacitive interaction may exist between the capacitor pad 140 and the direct capacitive coupler 142. In various cases, just as above, those two configured capacitive interactions may be considered to be combined (e.g., according to the law of combining capacitors in series) to result in the capacitance 218. Once again, in various aspects, the value of the capacitance 218 (e.g., measured in farads) may depend on the size, shape, dimensions, and / or material composition of the capacitor pad 108, the capacitor pad 140, and / or the direct capacitive coupler 142.

[0102] FIG. 3 shows a structural diagram of an exemplary and non-limiting qubit lattice 300 that may facilitate the reduction of stray coupling via a multi-junction qubit, according to one or more embodiments described herein. In other words, FIG. 3 shows how the structure / architecture shown in FIG. 1 can be scaled up to form a qubit lattice using a higher-order coupling topology that is not troubled by excessive stray coupling.

[0103] In various embodiments, as shown, the qubit lattice 300 may include a plurality of qubits, namely: qubit 302, qubit 304, qubit 306, qubit 308, qubit 310, qubit 312, qubit 314, qubit 316, qubit 318, qubit 320, qubit 322, qubit 324, qubit 326, qubit 328, qubit 330, qubit 332, qubit 334, qubit 336, qubit 338, qubit 340, qubit 342, qubit 344, qubit 346, and / or qubit 348.

[0104] In various aspects, as shown, some qubits within the qubit lattice 300 can be coupled to two or fewer adjacent qubits, while other qubits within the qubit lattice 300 can be coupled to more than two adjacent qubits. For example, qubit 302, qubit 306, qubit 316, qubit 322, qubit 328, qubit 332, qubit 344, and / or qubit 348 can each be coupled to one adjacent qubit (e.g., directly and / or indirectly capacitively, whether fixed or flux-adjustable). Further, qubit 308, qubit 312, qubit 318, qubit 324, qubit 326, qubit 334, qubit 338, and / or qubit 342 can each be coupled to two adjacent qubits. Still further, qubit 304, qubit 310, qubit 314, qubit 320, qubit 330, qubit 336, qubit 340, and / or qubit 346 can each be coupled to three adjacent qubits. In various cases, as shown, any qubit within the qubit lattice 300 that is coupled to two or fewer neighbors can be a single-junction transmon. However, in various aspects, as further shown, any qubit within the qubit lattice 300 that is coupled to more than two neighbors can be a multi-junction qubit. In fact, in the non-limiting example of FIG. 3, each qubit in the qubit lattice 300 that is coupled to three neighbors can be a two-junction transmon instead of a single-junction transmon. Thus, each of such two-junction transmons can be coupled to three neighbors in the manner shown in FIG. 1. That is, each of such two-junction transmons can be considered to have three capacitor pads, and the neighbors of each of such two-junction transmons can be coupled to different / distinct / unique ones of those three capacitor pads, respectively.

[0105] For example, qubit 304 can be a two-junction transmon having three capacitor pads, where the first of such three capacitor pads can be coupled to qubit 302, where the second of such three capacitor pads can be coupled to qubit 306, and / or where the third of such three capacitor pads can be coupled to qubit 308. Thus, since none of qubit 302, qubit 306, and qubit 308 can be coupled to the same capacitor pad as one another, stray coupling and / or crosstalk among qubit 302, qubit 306, and qubit 308 can be considered to be reduced and / or minimized.

[0106] As another example, qubit 310 can be a two-junction transmon having three capacitor pads, where the first of such three capacitor pads can be coupled to qubit 308, where the second of such three capacitor pads can be coupled to qubit 324, and / or where the third of such three capacitor pads can be coupled to qubit 312. Thus, since none of qubit 308, qubit 324, and qubit 312 can be coupled to the same capacitor pad as one another, stray coupling and / or crosstalk among qubit 308, qubit 324, and qubit 312 can be considered to be reduced and / or minimized.

[0107] As yet another example, qubit 314 can be a two-junction transmon having three capacitor pads, where the first of such three capacitor pads can be coupled to qubit 312, where the second of such three capacitor pads can be coupled to qubit 316, and / or where the third of such three capacitor pads can be coupled to qubit 318. Thus, since none of qubit 312, qubit 316, and qubit 318 can be coupled to the same capacitor pad as one another, stray coupling and / or crosstalk among qubit 312, qubit 316, and qubit 318 can be considered to be reduced and / or minimized.

[0108] As yet another example, qubit 320 can be a two-junction transmon having three capacitor pads, where the first of such three capacitor pads can be coupled to qubit 318, where the second of such three capacitor pads can be coupled to qubit 326, and / or where the third of such three capacitor pads can be coupled to qubit 322. Thus, since none of qubit 318, qubit 326, and qubit 322 can be coupled to the same capacitor pad as one another, stray coupling and / or crosstalk among qubit 318, qubit 326, and qubit 322 can be considered to be reduced and / or minimized.

[0109] As yet another example, qubit 330 can be a two-junction transmon having three capacitor pads, where the first of such three capacitor pads can be coupled to qubit 328, where the second of such three capacitor pads can be coupled to qubit 332, and / or where the third of such three capacitor pads can be coupled to qubit 334. Thus, since none of qubit 328, qubit 332, and qubit 334 can be coupled to the same capacitor pad as one another, stray coupling and / or crosstalk among qubit 328, qubit 332, and qubit 334 can be considered to be reduced and / or minimized.

[0110] As a further example, qubit 336 can be a two-junction transmon having three capacitor pads, where the first of such three capacitor pads can be coupled to qubit 334, where the second of such three capacitor pads can be coupled to qubit 324, and / or where the third of such three capacitor pads can be coupled to qubit 338. Thus, since none of qubit 334, qubit 324, and qubit 338 can be coupled to the same capacitor pad as one another, stray coupling and / or crosstalk among qubit 334, qubit 324, and qubit 338 can be considered to be reduced and / or minimized.

[0111] As yet another example, the qubit 340 can be a two-junction transmon having three capacitor pads, where the first of such three capacitor pads can be coupled to the qubit 338, where the second of such three capacitor pads can be coupled to the qubit 344, and / or where the third of such three capacitor pads can be coupled to the qubit 342. Therefore, since none of the qubit 338, the qubit 344, and the qubit 342 can be coupled to the same capacitor pad as one another, the stray coupling and / or crosstalk among the qubit 338, the qubit 344, and the qubit 342 can be considered to be reduced and / or minimized.

[0112] As yet another example, the qubit 346 can be a two-junction transmon having three capacitor pads, where the first of such three capacitor pads can be coupled to the qubit 342, where the second of such three capacitor pads can be coupled to the qubit 326, and / or where the third of such three capacitor pads can be coupled to the qubit 348. Therefore, since none of the qubit 342, the qubit 326, and the qubit 348 can be coupled to the same capacitor pad as one another, the stray coupling and / or crosstalk among the qubit 342, the qubit 326, and the qubit 348 can be considered to be reduced and / or minimized.

[0113] In this way, the qubit lattice 300 can exhibit a double hexagonal tiling layout such that two qubits within the qubit lattice 300 are not coupled to the same capacitor pad. Thus, since two qubits within the qubit lattice 300 cannot be coupled to the same capacitor pad (e.g., since all qubits in the qubit lattice 300 can be coupled to different / distinct / separate capacitor pads), the qubit lattice 300 can be considered to exhibit no enhanced and / or degraded stray coupling despite showing a double hexagonal topology. In contrast, such enhanced and / or degraded stray coupling occurs in the qubit lattice 300 when each qubit within the qubit lattice 300 that is coupled to three neighbors is a single junction transmon instead of a two - junction transmon. Thus, by replacing each qubit within the qubit lattice that is coupled to more than two neighbors with a multi - junction qubit, the stray coupling can be reduced.

[0114] FIG. 3 shows the qubit lattice 300 as including 24 qubits, which is merely a non - limiting example for ease of illustration. In various cases, the qubit lattice 300 can include any suitable number of qubits.

[0115] FIG. 3 shows the qubit lattice 300 as having a double hexagonal tiling layout / topology, which is merely a non - limiting example for ease of illustration. In various embodiments, the qubit lattice 300 can exhibit any other suitable type of tiling / layout as desired. In fact, any suitable higher - order coupling topology can be achieved without excessive stray coupling as long as any qubit that is coupled to more than two neighbors has a sufficient number of coupling elements rather than being a single - junction transmon.

[0116] The disclosure herein has heretofore described various embodiments primarily as related to the implementation of two-junction transmon qubits for reducing stray coupling in an array / lattice of single-junction transmon qubits. However, this is merely a non-limiting example for ease of illustration / demonstration. In various aspects, the teachings described herein can be applied and / or otherwise extrapolated to any suitable qubit within any suitable qubit lattice / array.

[0117] For example, generally, a multi-junction qubit can be considered to have a plurality of Josephson junctions arranged in series and / or in parallel with a plurality of coupling elements. In various aspects, a coupling element can be any suitable circuit structure (e.g., any suitable physical portion of a multi-junction qubit) by which adjacent qubits can be operably coupled. As mainly described above, a non-limiting example of such a coupling element can be a capacitor pad of a multi-junction qubit. This is because adjacent qubits can capacitively interact with the capacitor pad of the multi-junction qubit, either directly and / or indirectly, in a fixed or flux-adjustable manner. Therefore, a capacitor pad can be considered a non-limiting type of coupling element. However, another non-limiting example of such a coupling element can be an inductive loop of a multi-junction qubit. This is because a multi-junction qubit can be fabricated to have an inductive loop in addition to a capacitor pad, and furthermore, adjacent qubits can inductively interact with the inductive loop of the multi-junction qubit, either directly and / or indirectly, in a fixed or flux-adjustable manner. Therefore, an inductive loop can also be considered a non-limiting type of coupling element. Embodiments regarding such inductive loops are described in more detail with respect to FIGS. 4 through 5.

[0118] FIG. 4 shows a structural diagram of an exemplary and non - limiting system 400 that includes both a capacitive and an inductive coupler that can facilitate the reduction of stray coupling through a multi - junction qubit according to one or more embodiments described herein. In various embodiments, Josephson junction 104, Josephson junction 106, capacitor pad 108, capacitor pad 110, capacitor pad 112, qubit 114, direct capacitive coupler 122, qubit 124, direct capacitive coupler 132, qubit 134, and / or direct capacitive coupler 142 can be as described above.

[0119] In various aspects, as shown, there can be an inductive loop 404 coupled in series with and / or between capacitor pad 108, Josephson junction 104, and capacitor pad 110. In various instances, inductive loop 404 can be any suitable superconducting coil and / or serpentine line that exhibits any suitable inductance value (e.g., measured in henries). In various cases, inductive loop 404 can be fabricated by any suitable microfabrication and / or nanofabrication techniques (e.g., photolithography, deposition, etching, double - angle evaporation), thereby having any suitable size, shape, dimensions, and / or material composition. Similarly, in various instances, there can be an inductive loop 406 coupled in series with and / or between capacitor pad 110, Josephson junction 106, and capacitor pad 112. In various cases, inductive loop 406 can be any suitable superconducting coil and / or serpentine line that exhibits any suitable inductance value (e.g., measured in henries). Just as described above, in various aspects, inductive loop 406 can be fabricated by any suitable microfabrication and / or nanofabrication techniques, thereby having any suitable size, shape, dimensions, and / or material composition.

[0120] FIG. 4 shows induction loops 404 and 406 as identical, which is merely a non-limiting example for ease of illustration. In various aspects, induction loop 404 and / or induction loop 406 can have the same and / or different sizes, shapes, spatial dimensions, and / or material compositions from each other.

[0121] In any case, capacitor pad 108, Josephson junction 104, induction loop 404, capacitor pad 110, Josephson junction 106, induction loop 406, and capacitor pad 112 can be considered together as forming multi-junction qubit 402.

[0122] In various embodiments, as shown, qubit 408 can be present. In various aspects, qubit 408 can include Josephson junction 410, induction loop 412, capacitor pad 414, and / or capacitor pad 416. In various cases, as shown, Josephson junction 410 can be coupled to capacitor pad 414, induction loop 412, capacitor pad 416, such that capacitor pad 414, Josephson junction 410, induction loop 412, capacitor pad 416 can all be considered to be in series with each other. Thus, in various cases, capacitor pad 414 and capacitor pad 416 can be considered together as forming a capacitance that shunts Josephson junction 410, while induction loop 412 can be considered to form an inductance in series with Josephson junction 410.

[0123] In various aspects, any suitable microfabrication and / or nanofabrication techniques can be implemented to fabricate capacitor pad 414, Josephson junction 410, induction loop 412, and / or capacitor pad 416.

[0124] FIG. 4 shows Josephson junction 410 as being the same as the Josephson junction of multi-junction qubit 402, the Josephson junction of qubit 114, the Josephson junction of qubit 124, and / or the Josephson junction of qubit 134, but this is merely a non-limiting example for ease of illustration and / or description. Josephson junction 410 may have the same and / or different sizes, shapes, spatial dimensions, and / or material compositions as the Josephson junction of multi-junction qubit 402, the Josephson junction of qubit 114, the Josephson junction of qubit 124, and / or the Josephson junction of qubit 134 in various aspects.

[0125] Similarly, FIG. 4 shows capacitor pads 414 and 416 as being the same as each other, the same as the capacitor pads of multi-junction qubit 402, the same as the capacitor pads of qubit 114, the same as the capacitor pads of qubit 124, and / or the same as the capacitor pads of qubit 134, but this is merely a non-limiting example for ease of illustration. In fact, in various aspects, capacitor pad 414 and / or capacitor pad 416 may have the same and / or different sizes, shapes, spatial dimensions, and / or material compositions as each other, the capacitor pads of multi-junction qubit 402, the capacitor pads of qubit 114, the capacitor pads of qubit 124, and / or the capacitor pads of qubit 134.

[0126] Still further similarly, FIG. 4 shows inductive loop 412 as being the same as inductive loop 404 and / or inductive loop 406, but this is merely a non-limiting example for ease of illustration. In various cases, inductive loop 412 may have the same and / or different sizes, shapes, spatial dimensions, and / or material compositions as inductive loop 404 and / or inductive loop 406.

[0127] In various embodiments, as shown, the multi-junction qubit 402 can be coupled to the qubit 408 by a direct inductive coupler 418. In particular, the direct inductive coupler 418 can be any suitable wire, cable, and / or circuit structure that can transmit an inductive interaction between the inductive loop 404 of the multi-junction qubit 402 and the inductive loop 412 of the qubit 408. Thus, the direct inductive coupler 418 can be regarded as inductively coupling the inductive loop 404 to the inductive loop 412.

[0128] In various cases, the direct inductive coupler 418 can be fabricated via any suitable microfabrication and / or nanofabrication techniques. In various instances, the direct inductive coupler 418 can have any suitable size, shape, spatial dimension, and / or material composition as desired (e.g., can be made of any suitable superconducting material).

[0129] FIG. 4 shows the inductive loop 404 inductively coupled to the inductive loop 412 by a direct inductive coupler 418, which is merely a non-limiting example for ease of illustration and / or description. In various aspects, any other suitable inductive coupler (e.g., an indirect inductive coupler), whether fixed or flux-adjustable, can be implemented instead of and / or in addition to the direct inductive coupler 418.

[0130] In various embodiments, as shown, a qubit 420 may be present. In various aspects, the qubit 420 may include a Josephson junction 422, an inductive loop 424, a capacitor pad 426, and / or a capacitor pad 428. In various instances, as shown, the Josephson junction 422 may be coupled to the capacitor pad 426, the inductive loop 424, the capacitor pad 428, such that the capacitor pad 426, the Josephson junction 422, the inductive loop 424, and the capacitor pad 428 may all be considered to be in series with each other. Thus, in various cases, the capacitor pad 426 and the capacitor pad 428 may be collectively considered to form a capacitance that shunts the Josephson junction 422, while the inductive loop 424 may be considered to form an inductance in series with the Josephson junction 422.

[0131] Just as described above, in various cases, any suitable microfabrication and / or nanofabrication techniques may be implemented to fabricate the capacitor pad 426, the Josephson junction 422, the inductive loop 424, and / or the capacitor pad 428.

[0132] FIG. 4 shows the Josephson junction 422 as being the same as the Josephson junction of the multi-junction qubit 402, the Josephson junction of the qubit 114, the Josephson junction of the qubit 124, the Josephson junction of the qubit 134, and / or the Josephson junction of the qubit 408, but this is merely a non-limiting example for ease of illustration and / or description. In various aspects, the Josephson junction 422 may have the same and / or different size, shape, spatial dimension, and / or material composition as the Josephson junction of the multi-junction qubit 402, the Josephson junction of the qubit 114, the Josephson junction of the qubit 124, the Josephson junction of the qubit 134, and / or the Josephson junction of the qubit 408 in various aspects.

[0133] Similarly, FIG. 4 shows capacitor pads 426 and 428 as being identical to each other, identical to the capacitor pads of the multi-junction qubit 402, identical to the capacitor pads of qubit 114, identical to the capacitor pads of qubit 124, identical to the capacitor pads of qubit 134, and / or identical to the capacitor pads of qubit 408, but this is merely a non-limiting example for ease of illustration. In fact, in various cases, capacitor pads 426 and / or capacitor pads 428 may have the same and / or different sizes, shapes, spatial dimensions, and / or material compositions from each other, the capacitor pads of the multi-junction qubit 402, the capacitor pads of qubit 114, the capacitor pads of qubit 124, the capacitor pads of qubit 134, and / or the capacitor pads of qubit 408.

[0134] Similarly, FIG. 4 shows induction loop 424 as being identical to induction loops 404, 406, and / or 412, but this is merely a non-limiting example for ease of illustration. In various cases, induction loop 424 may have the same and / or different sizes, shapes, spatial dimensions, and / or material compositions from induction loops 404, 406, and / or 412.

[0135] In various embodiments, as shown, the multi-junction qubit 402 may be coupled to the qubit 420 by a direct inductive coupler 430. In particular, the direct inductive coupler 430 can be any suitable wire, cable, and / or circuit structure that can transmit an inductive interaction between the induction loop 406 of the multi-junction qubit 402 and the induction loop 424 of the qubit 420. Thus, the direct inductive coupler 430 can be regarded as inductively coupling the induction loop 406 to the induction loop 424.

[0136] As described above, in various cases, the direct induction coupler 430 can be manufactured via any suitable microfabrication and / or nanofabrication techniques. In various aspects, the direct induction coupler 430 can have any suitable size, shape, spatial dimension, and / or material composition (e.g., can be made of any suitable superconducting material) as desired (e.g., can have a different size, shape, dimension, and / or composition from the direct induction coupler 418).

[0137] FIG. 4 shows the induction loop 406 inductively coupled by the direct induction coupler 430 to the induction loop 424, which is merely a non-limiting example for ease of illustration and / or description. In various aspects, any other suitable induction coupler (e.g., an indirect induction coupler), whether fixed or flux-adjustable, can be implemented instead of and / or in addition to the direct induction coupler 430.

[0138] In any case, as shown, the multi-junction qubit 402 can be regarded as having five coupling elements (e.g., 108, 110, 112, 404, and 406) through which the multi-junction qubit 402 can be coupled to five adjacent qubits (e.g., 114, 124, 134, 408, and 420). In other words, the multi-junction qubit 402 can be regarded as having one coupling element for each adjacent qubit to which it is coupled. In this way, two adjacent qubits cannot be coupled to the same coupling element, which can help reduce stray coupling (e.g., can help reduce crosstalk of the spectator).

[0139] For example, the qubit 114 can be coupled to the capacitor pad 112 and may not be coupled to any of the capacitor pad 110, the capacitor pad 108, the induction loop 404, and the induction loop 406. Also, qubit 124 can be coupled to capacitor pad 110 and may not be coupled to any of capacitor pad 112, capacitor pad 108, induction loop 404, and induction loop 406. Further, qubit 134 can be coupled to capacitor pad 108 and may not be coupled to any of capacitor pad 110, capacitor pad 112, induction loop 404, and induction loop 406. Additionally, qubit 408 can be coupled to induction loop 404 and may not be coupled to any of capacitor pad 112, capacitor pad 110, capacitor pad 108, and induction loop 406. Also, qubit 420 can be coupled to induction loop 406 and may not be coupled to any of capacitor pad 112, capacitor pad 110, capacitor pad 108, and induction loop 404. Thus, each of qubit 114, qubit 124, qubit 134, qubit 408, and qubit 420 can be considered to be coupled to its own corresponding / unique coupling element, where such a coupling element can be a capacitor pad of multi-junction qubit 402 or an induction loop of multi-junction qubit 402. In any case, the result can be less, reduced, and / or mitigated crosstalk between qubit 114, qubit 124, qubit 134, qubit 408, and / or qubit 420.

[0140] FIG. 4 shows a multi-junction qubit 402 coupled to five neighbors (e.g., 114, 124, 134, 408, and 420) via three capacitor pads (e.g., 108, 110, and 112) and via two inductive loops (e.g., 404 and 406), which is merely a non-limiting example for ease of explanation and / or illustration. More generally, for any suitable positive integer w, it may be desired to capacitively couple the multi-junction qubit 402 to w neighbors, and further, for any suitable positive integer x, it may be desired to inductively couple the multi-junction qubit 402 to x neighbors. In such cases, the multi-junction qubit 402 may be configured / structured to have at least w capacitor pads and at least x inductive loops. Thus, this can help ensure that each of the w neighbors to which the multi-junction qubit 402 is to be capacitively coupled and each of the x neighbors to which the multi-junction qubit 402 is to be inductively coupled can have its own corresponding / unique coupling element. In other words, this can help ensure that two neighbors cannot be coupled to the same coupling element.

[0141] Although not explicitly shown in the figure, the architecture / structure shown in FIG. 4 can be scaled up in various ways to form any suitable higher-order coupling topology / layout / tiling as desired.

[0142] FIG. 5 shows a circuit diagram 500 of an exemplary and non-limiting system that includes both a capacitive and an inductive coupler that can facilitate mitigation of stray coupling via a multi-junction qubit according to one or more embodiments described herein. In particular, FIG. 5 shows a circuit diagram corresponding to the physical structure / architecture shown in FIG. 4. In various cases, Josephson junction 104, Josephson junction 106, inductive loop 404, inductive loop 406, capacitor 202, capacitor 204, capacitor 206, Josephson junction 116, capacitor 208, capacitor 210, Josephson junction 126, capacitor 212, capacitor 214, Josephson junction 136, capacitor 216, capacitor 218, Josephson junction 410, inductive loop 412, direct inductive coupler 418, Josephson junction 422, inductive loop 424, and direct inductive coupler 430 can be as described above.

[0143] In various embodiments, as shown, the circuit diagram of multi-junction qubit 402 can be considered to include Josephson junction 104 shunted by capacitor 204, further include Josephson junction 106 shunted by capacitor 206, and / or further include both Josephson junction 104 and Josephson junction 106 shunted by capacitor 202. As further shown, the circuit diagram of multi-junction qubit 402 can further include inductive loop 404 in series with Josephson junction 104 and can further include inductive loop 406 in series with Josephson junction 106.

[0144] In various aspects, as shown, the circuit diagrams of qubit 114, qubit 124, and qubit 134 can be as described above.

[0145] In various embodiments, as further shown, the circuit diagram of qubit 408 can be considered to include a Josephson junction 410 in series with an inductive loop 412 and shunted by a capacitance 502. In various cases, the capacitance 502 can be considered as the capacitive interaction occurring between capacitor pads 414 and 416. Therefore, in various situations, the value of the capacitance 502 (e.g., measured in farads) can depend on the size, shape, dimensions, and / or material composition of capacitor pad 414 and / or capacitor pad 416. Just as described above, the direct inductive coupler 418 can inductively couple the inductive loop 404 to the inductive loop 412.

[0146] In various cases, as further shown, the circuit diagram of qubit 420 can be considered to include a Josephson junction 422 in series with an inductive loop 424 and shunted by a capacitance 504. In various cases, the capacitance 504 can be considered as the capacitive interaction occurring between capacitor pads 426 and 428. Therefore, in various embodiments, the value of the capacitance 504 (e.g., measured in farads) can depend on the size, shape, dimensions, and / or material composition of capacitor pad 426 and / or capacitor pad 428. Again, just as described above, the direct inductive coupler 430 can inductively couple the inductive loop 406 to the inductive loop 424.

[0147] Figures 6 through 7 show flow diagrams of exemplary and non-limiting methods 600 and 700 that can facilitate reducing stray coupling through a multi-junction qubit according to one or more embodiments described herein.

[0148] First, consider the method 600 shown in FIG. 6. In various embodiments, operation 602 can include providing a first qubit (e.g., 102 and / or 402) having a plurality of Josephson junctions (e.g., 104 and 106) between a plurality of capacitor pads (e.g., 108, 110, and 112).

[0149] In various aspects, operation 604 can include coupling a plurality of second qubits (e.g., 114, 124, and 134) to different ones of a plurality of capacitor pads such that, as a result, no two of the plurality of second qubits are coupled to the same one of the plurality of capacitor pads (e.g., as shown with respect to FIGS. 1 and / or 4).

[0150] Although not explicitly shown in FIG. 6, a plurality of inductive loops (e.g., 404 and 406) can be respectively between a plurality of capacitor pads, and / or method 600 can further include coupling a plurality of third qubits (e.g., 408 and 420) to different ones of the plurality of inductive loops (e.g., as shown in FIG. 4) such that, as a result, no two of the plurality of third qubits can be coupled to the same one of the plurality of inductive loops.

[0151] Although not explicitly shown in FIG. 6, the first qubit can include a first Josephson junction (e.g., 104) between a first capacitor pad (e.g., 108) and a second capacitor pad (e.g., 110), and / or the first qubit can further include a second Josephson junction (e.g., 106) between the second capacitor pad and a third capacitor pad (e.g., 112). In various aspects, a plurality of second qubits (e.g., as shown in FIGS. 1 and / or 4) can include a first transmon qubit (e.g., 134) coupled to the first capacitor pad and not coupled to the second capacitor pad or the third capacitor pad, a second transmon qubit (e.g., 124) coupled to the second capacitor pad and not coupled to the first capacitor pad or the third capacitor pad, and / or a third transmon qubit (e.g., 114) coupled to the third capacitor pad and not coupled to the first capacitor pad or the second capacitor pad.

[0152] Now, consider method 700 of FIG. 7. In various embodiments, operation 702 may include providing a qubit lattice (e.g., 300).

[0153] In various aspects, operation 704 may include coupling at least one qubit (e.g., 102 and / or 402) within the qubit lattice to three or more adjacent qubits (e.g., 114, 124, 134, 408, and / or 420) within the qubit lattice. In various cases, the at least one qubit may have three or more coupling elements (e.g., 108, 110, 112, 404, and / or 406) respectively corresponding to the three or more adjacent qubits. Also, in various cases, two of the three or more adjacent qubits may not be coupled to the same one of the three or more coupling elements (e.g., as shown in FIGS. 1 and 4). Furthermore, in various aspects, the coupling elements may be capacitor pads and / or inductive loops.

[0154] Although not explicitly shown in FIG. 7, at least one qubit may be coupled to three adjacent qubits (e.g., 114, 124, and 134), at least one qubit may have two Josephson junctions (e.g., 104 and 106) in series between three capacitor pads (e.g., 108, 110, and 112), and the three adjacent qubits may be respectively coupled to different ones of the three capacitor pads.

[0155] Although not explicitly shown in FIG. 7, at least one qubit may be coupled to five adjacent qubits (e.g., 114, 124, 134, 408, and 420), at least one qubit may have two Josephson junctions (e.g., 104 and 106) in series between three capacitor pads (e.g., 108, 110, and 112) and two inductive loops (e.g., 404 and 406), and / or the five adjacent qubits may be respectively coupled to different ones of the three capacitor pads and the two inductive loops.

[0156] Accordingly, the various embodiments described herein may contemplate utilizing multi-junction qubits to reduce stray coupling. As described above, the inventor has noticed that existing techniques can generate excessive stray coupling. This is due to the fact that such existing techniques require two or more neighbors to be coupled to the same coupling element (e.g., the same capacitor pad and / or the same inductive loop). Thus, the inventor has realized that whenever it is desired for three or more neighbors to be coupled to a given qubit, such excessive stray coupling can be improved by configuring / structuring the given qubit as a multi-junction qubit. After all, a multi-junction qubit can have more coupling elements than a single-junction qubit. Therefore, the implementation of a multi-junction qubit can help ensure that each of the three or more neighbors is coupled to its own corresponding, unique coupling element, thereby reducing crosstalk of the spectator. Since the various embodiments described herein can address the significant technical problem of stray coupling, such embodiments naturally constitute specific tangible technical solutions to the technical problem.

[0157] The disclosure herein has mainly described the various embodiments as being related to direct / indirect capacitive / inductive couplers, which is merely a non-limiting example for illustrative purposes. In various cases, the teachings described herein can be implemented using any suitable quantum coupler (e.g., a flux-tunable coupler, a mode-selective coupler) as desired.

[0158] The disclosure herein describes non-limiting examples of various embodiments of the innovation of the subject matter. For ease of explanation and / or illustration, various portions of the disclosure herein utilize the term "each" when discussing various embodiments of the innovation of the subject matter. Such use of the term "each" is a non-limiting example. In other words, when the disclosure herein provides a description that applies to "each" of some particular objects and / or components, this should be understood as a non-limiting example of various embodiments of the innovation of the subject matter, and further, in various other embodiments of the innovation of the subject matter, it should be understood that such a description may apply to less than "each" of that particular object and / or component.

[0159] The flowcharts and structures of the figures illustrate the architecture, functionality, and operation of possible implementations, systems, methods, and / or computer program products according to the various embodiments described herein. In this regard, each block in a flowchart may represent a module, segment, or portion of one or more executable instructions for implementing the specified logical function. In some alternative implementations, the functions described in a block may occur in a different order than that depicted in the figure. For example, in fact, two blocks shown consecutively may be executed substantially simultaneously, depending on the functionality involved, or the blocks may, in some cases, be executed in the reverse order. It should also be noted that each block of the flowchart diagrams, and combinations of blocks of the flowchart diagrams, can be implemented by a system based on dedicated hardware that executes the specified function or operation, or a combination of dedicated hardware and computer instructions.

[0160] In addition, the term "or" is intended to mean inclusive "or" rather than exclusive "or". That is, unless otherwise specified or clear from the context, "X adopts A or B" is intended to mean any of the natural and inclusive permutations. That is, when X uses A; X uses B; or X uses both A and B, "X uses A or B" is satisfied under any of the aforementioned cases. Also, the articles "a" and "an" used in this specification and the accompanying drawings should generally be construed to mean "one or more" unless otherwise specified or it is clear from the context that they are directed to the singular form. As used herein, the terms "example" and / or "exemplary" are utilized to mean serving as an example, instance, or illustration. To avoid doubt, the subject matter disclosed herein is not limited to such examples. In addition, any aspect or design described herein as "example" and / or "exemplary" is not necessarily construed as being more preferred or advantageous than other aspects or designs, nor is it intended to exclude equivalent exemplary structures and techniques known to those skilled in the art.

[0161] The foregoing includes only examples of systems and computer-implemented methods. Of course, for the purpose of explaining the present disclosure, it is impossible to describe every possible combination of components or computer-implemented methods, but those skilled in the art will recognize that many more combinations and permutations of the present disclosure are possible. Further, to the extent the terms "comprising", "having", "including", etc. are used in the detailed description, claims, accompanying documents, and drawings, such terms are intended to be inclusive in the same manner as the term "comprising" is construed when employed as a transitional phrase in a claim.

[0162] The descriptions of the various embodiments are presented for illustrative purposes and are not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terms used herein are chosen to best explain the principles of the embodiments, the practical application, or technical improvements made to the technologies found in the marketplace, or to enable other practitioners in the art to understand the embodiments disclosed herein.

Claims

1. A first qubit having a plurality of Josephson junctions respectively between a plurality of capacitor pads; and A plurality of second qubits respectively coupled to different ones of the plurality of capacitor pads A device comprising.

2. The device according to the preceding claim, wherein two of the plurality of second qubits are not coupled to the same one of the plurality of capacitor pads.

3. A plurality of inductive loops respectively between the plurality of capacitor pads; and A plurality of third qubits respectively coupled to different ones of the plurality of inductive loops The device according to the preceding claim, further comprising.

4. The device according to the preceding claim, wherein two of the plurality of third qubits are not coupled to the same one of the plurality of inductive loops.

5. The first qubit has a first Josephson junction between a first capacitor pad and a second capacitor pad, and the first qubit further has a second Josephson junction between the second capacitor pad and a third capacitor pad, according to any one of the preceding claims. The device described.

6. The plurality of second qubits includes a first transmon qubit coupled to the first capacitor pad and not coupled to the second capacitor pad or the third capacitor pad, and a second transmon qubit coupled to the second capacitor pad and not coupled to the first capacitor pad or the third capacitor pad, and a third transmon qubit coupled to the third capacitor pad and not coupled to the first capacitor pad or the second capacitor pad, according to any one of the preceding claims. The device described.

7. The plurality of second qubits are respectively coupled to different ones of the plurality of capacitor pads by flux-adjustable couplers, according to any one of the preceding claims. The device described.

8. The different ones of the plurality of Josephson junctions are sized differently, according to any one of the preceding claims. The device described.

9. Providing a first qubit having a plurality of Josephson junctions respectively between a plurality of capacitor pads; and Respectively coupling a plurality of second qubits to different ones of the plurality of capacitor pads A method comprising.

10. The method according to the preceding claim, wherein two of the plurality of second qubits are not coupled to the same one of the plurality of capacitor pads. **Claim 11** A plurality of inductive loops are each between the plurality of capacitor pads, coupling a plurality of third qubits to different ones of the plurality of inductive loops The method according to the preceding claim, further comprising the step of: **Claim 12** The method according to the preceding claim, wherein two of the plurality of third qubits are not coupled to the same one of the plurality of inductive loops. **Claim 13** The method according to any one of the four preceding claims, wherein the first qubit has a first Josephson junction between a first capacitor pad and a second capacitor pad, and the first qubit further has a second Josephson junction between the second capacitor pad and a third capacitor pad. **Claim 14** The method according to the preceding claim, wherein the plurality of second qubits include a first transmon qubit coupled to the first capacitor pad and not coupled to the second capacitor pad or the third capacitor pad, a second transmon qubit coupled to the second capacitor pad and not coupled to the first capacitor pad or the third capacitor pad, and a third transmon qubit coupled to the third capacitor pad and not coupled to the first capacitor pad or the second capacitor pad. **Claim 15** The method according to any one of the six preceding claims, wherein the plurality of second qubits are each coupled to different ones of the plurality of capacitor pads by flux-adjustable couplers. **Claim 16** The method according to any one of the seven preceding claims, wherein different ones of the plurality of Josephson junctions are sized differently. **Claim 17** A qubit lattice; and at least one qubit within the qubit lattice coupled to three or more adjacent qubits within the qubit lattice A system comprising: The at least one qubit has three or more coupling elements respectively corresponding to the three or more adjacent qubits, two of the three or more adjacent qubits are not coupled to the same one of the three or more coupling elements, and the coupling elements are capacitor pads or inductive loops. System. Claim 18 The at least one qubit is coupled to three adjacent qubits, the at least one qubit has two Josephson junctions in series between three capacitor pads, and the three adjacent qubits are each coupled to a different one of the three capacitor pads, the system according to the preceding claim. Claim 19 The at least one qubit is coupled to five adjacent qubits, the at least one qubit has two Josephson junctions in series between three capacitor pads and two inductive loops, and the five adjacent qubits are each coupled to a different one of the three capacitor pads and the two inductive loops, the system according to any of the two preceding claims. Claim 20 The qubit lattice exhibits a double-hexagonal tiling layout, the system according to any of the three preceding claims.

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