XX coupler for persistent current qubits

Abstract

A system and method for coupling two qubits is provided. A first persistent current qubit is made with a first superconducting loop interrupted by a first Josephson junction separated from a second Josephson junction by a first inductor and a second inductor. A second persistent current qubit is made with a second superconducting loop interrupted by a third Josephson junction separated from a fourth Josephson junction by a third inductor and a fourth inductor. Nodes defined by the Josephson junctions of the first qubit and their adjacent inductors are connected via a first capacitor to corresponding nodes defined by the third Josephson junction and the third inductor, with one pair of connections swapped such that the nodes are not connected to their respective corresponding nodes.

Description

[Technical Field]

[0001] The present invention relates to quantum systems, and more particularly to XX couplers for persistent current qubits. (Government Interests) This invention was made under a government contract and, accordingly, the United States Government has rights in this invention as provided for in that contract. Summary of the Invention

[0002] According to one example, a system includes a first persistent current qubit comprising a first superconducting loop interrupted by a first series of Josephson junctions, the first series of Josephson junctions beginning with a first Josephson junction of the first series and continuing in a first direction around the first superconducting loop, each Josephson junction of the first series being separated from adjacent Josephson junctions by two adjacent inductors of a first plurality of inductors, and having an associated first circuit node between the Josephson junction and a first inductor of the two adjacent inductors of the first plurality of inductors in a first direction on the first superconducting loop and an associated second circuit node between the Josephson junction and a second inductor of the two adjacent inductors in a second direction on the first superconducting loop opposite the first direction.

[0003] The second persistent current qubit includes a second superconducting loop interrupted by a second series of Josephson junctions, the second series of Josephson junctions beginning with a first Josephson junction in the second series and continuing in a first direction around the second superconducting loop, each Josephson junction in the second series separated from an adjacent Josephson junction by two adjacent inductors of the second plurality of inductors, and having an associated first circuit node between the Josephson junction and a first inductor of two adjacent inductors of the second plurality of inductors in the first direction on the second superconducting loop and an associated second circuit node between the Josephson junction and a second inductor of the two adjacent inductors in a second direction opposite the first direction on the second superconducting loop.

[0004] The system also includes a set of capacitive couplings between the circuit node of the first persistent current qubit and the circuit node of the second persistent current qubit. A first capacitive coupling of the set of capacitive couplings connects a first circuit node associated with a first Josephson junction of the first series of Josephson junctions to a first circuit node associated with a first Josephson junction of the second series of Josephson junctions. A second capacitive coupling of the set of capacitive couplings connects a second circuit node associated with a first Josephson junction of the first series of Josephson junctions to a second circuit node associated with a first Josephson junction of the second series of Josephson junctions. A third capacitive coupling of the set of capacitive couplings connects a first circuit node associated with a second Josephson junction of the first series of Josephson junctions to a second circuit node associated with a second Josephson junction of the second series of Josephson junctions. A fourth capacitive coupling of the set of capacitive couplings connects a second circuit node associated with a second Josephson junction of the first series of Josephson junctions to a first circuit node associated with a second Josephson junction of the second series of Josephson junctions.

[0005] According to another example, a method is provided. A first persistent current qubit is fabricated using a first superconducting loop interrupted by a first Josephson junction and a second Josephson junction. The first Josephson junction is separated from the second Josephson junction by a first inductor and a second inductor. A second persistent current qubit is fabricated using a second superconducting loop interrupted by a third Josephson junction and a fourth Josephson junction. The third Josephson junction is separated from the fourth Josephson junction by a third inductor and a fourth inductor. A first node defined by the first Josephson junction and the first inductor is connected via a first capacitor to a second node defined by the third Josephson junction and the third inductor. A third node defined by the first Josephson junction and the second inductor is connected via a second capacitor to a fourth node defined by the third Josephson junction and the fourth inductor. The fifth node defined by the second Josephson junction and the first inductor is connected through a third capacitor to a sixth node defined by the fourth Josephson junction and the fourth inductor. The seventh node defined by the second Josephson junction and the second inductor is connected through a fourth capacitor to an eighth node defined by the fourth Josephson junction and the third inductor.

[0006] According to a further example, a system includes a first persistent current qubit including a first superconducting loop interrupted by a first Josephson junction and a second Josephson junction. The first Josephson junction is separated from the second Josephson junction by a first inductor and a second inductor. The second persistent current qubit includes a second superconducting loop interrupted by a third Josephson junction and a fourth Josephson junction. The third Josephson junction is separated from the fourth Josephson junction by a third inductor and a fourth inductor. A first capacitive coupling connects a first node defined by the first Josephson junction and the first inductor to a second node defined by the third Josephson junction and the third inductor. A second capacitive coupling connects a third node defined by the first Josephson junction and the second inductor to a fourth node defined by the third Josephson junction and the fourth inductor. The third capacitive coupling connects the fifth node defined by the second Josephson junction and the first inductor to the sixth node defined by the fourth Josephson junction and the fourth inductor. The fourth capacitive coupling connects the seventh node defined by the second Josephson junction and the second inductor to the eighth node defined by the fourth Josephson junction and the third inductor. The first capacitive coupling, the second capacitive coupling, the third capacitive coupling, and the fourth capacitive coupling collectively provide XX coupling between the first persistent current qubit and the second persistent current qubit. [Brief explanation of the drawings]

[0007] [Figure 1] FIG. 1 shows an example of a quantum circuit that provides XX coupling between a first persistent current qubit and a second persistent current qubit. [Figure 2] FIG. 1 is a circuit diagram showing a first Josephson junction separated from a second Josephson junction by an inductor. [Figure 3]3 is a heat map showing the energy of the system shown in FIG. 2 as a function of Josephson phase at each of the first and second Josephson junctions. [Figure 4] FIG. 2 is a circuit diagram showing a first flux qubit connected to a second flux qubit via a first capacitor and a second capacitor. [Figure 5] FIG. 1 shows one implementation of a quantum system in which a series of persistent current qubits can be chained together to provide X-X coupling across an array of qubits. [Figure 6] FIG. 1 illustrates a method for fabricating a quantum system with an XX coupling between two persistent current qubits. DETAILED DESCRIPTION OF THE INVENTION

[0008] As used herein, the term "includes" means including, but not limited to, and the term "including" means including, but not limited to. The term "based on" means based at least in part on. Additionally, when this disclosure or claims recite "a," "an," "a first," or "another" element, or equivalents thereof, it should be construed as including one or more such elements, and does not require or exclude more than one such element.

[0009] The systems and methods described herein provide XX coupling between two persistent current qubits. XX coupling between two qubits energetically favors the states of the first and second qubits to be aligned in the same direction along the X axis, either both pointing in the +X direction or both pointing in the -X direction. Each axis corresponds to a specific quantum state defined on the qubit's Bloch sphere. XX interactions have many applications, including generating non-stoquastic Hamiltonians, and are commonly used in quantum annealing machines and various quantum logic gates in combination with ZZ and Z Hamiltonian terms. Quantum circuits can be designed so that there is a nonzero probability that the state of a given qubit can change without the application of energy. Typically, Josephson junctions in a flux qubit loop generate a potential with two or more local minima and barriers through which a multidimensional phase wave function can tunnel. The systems and methods described herein exploit this barrier tunneling to provide XX coupling between two qubits.

[0010] FIG. 1 illustrates an example of a quantum circuit 100 that provides XX coupling between a first persistent current qubit 110 and a second persistent current qubit 120. In one example, each persistent current qubit 110 and 120 is implemented as a flux qubit. A flux qubit, generally speaking, is a superconducting loop interrupted by some number of Josephson junctions. In typical operation, the flux qubit is biased by a magnetic flux of units of a superconducting flux quantum Φ. When the applied bias flux is close to one-half of a flux quantum, for appropriate device parameters, the potential energy of the system exhibits two local minima, one corresponding to clockwise current flow in the superconducting loop and the other corresponding to counterclockwise current flow. The two possible directions of current flow represent the lowest-energy quantum states of the system.

[0011] In the illustrated example, each persistent current qubit 110 and 120 comprises a superconducting loop 111 and 121 interrupted by a first Josephson junction 112 and 122 and a second Josephson junction 113 and 123. The Josephson junctions 112, 113, 122, and 123 within each loop are themselves separated by a first inductor 114 and 124 and a second inductor 115 and 125. Each inductor 114, 115, 124, and 125 is selected to have an inductance large enough to separate the tunneling of phases across the first junctions 114 and 124 from the second junctions 115 and 125. The inductors 114, 115, 124, and 125 may be implemented using, for example, Josephson junction chains, high kinetic inductance superconducting materials, or long lengths of superconducting wire. In one implementation, each inductor 114, 115, 124, and 125 has an inductance of 10 nanohenries to 100 nanohenries, and each Josephson junction 112, 113, 122, and 123 has a critical current of 25 nanoamperes to 100 nanoamperes. The required inductance varies with the critical current of the Josephson junctions 114, 115, 124, and 125; in one example, an inductance of 60 nanohenries can be used for a Josephson junction with a critical current of about 50 nanoamperes.

[0012] An example of the effect that inductors 114, 115, 124, and 125 have on the phase tunneling paths of two Josephson junctions is shown in Figures 2 and 3. Figure 2 is a circuit diagram 200 showing a first Josephson junction 212 isolated from a second Josephson junction 214 by an inductor 216. The circuit is connected to ground through a pair of capacitors 222-224 at a first node 226 between the first Josephson junction 212 and the inductor 216, a second node 227 between the second Josephson junction 214 and the inductor 216, and a third node 228 between the first Josephson junction 212 and the second Josephson junction 214. In the illustrated example, each Josephson junction 212 and 214 has a critical current of 50 nanoamperes, inductor 216 has an inductance of 80 nanohenries, and each capacitor 222-224 has a capacitance of 0.1 femtofarads.

[0013] FIG. 3 is a heat map 300 illustrating the energy of the system shown in FIG. 2 as a function of the Josephson phase at each of the first Josephson junction 212 and the second Josephson junction 214. The phase at the first Josephson junction 212 is shown on the vertical axis 302 in units of radians normalized by dividing by 2π. The phase at the second Josephson junction 214 is shown on the horizontal axis 304 in units of radians normalized by dividing by 2π. The diagram 300 illustrates multiple energy minima 312-315, where the first and second energy minima 312 and 313 represent a first computational state of the system, and the third and fourth energy minima 314 and 315 represent a second computational state of the system. Tunneling paths 316 and 317 represent transitions between the computational states of the system that do not raise the energy of the system beyond the energy of the barrier separating the minima 312-315. As can be seen from heat map 300, the tunneling paths are nearly orthogonal due to the high degree of isolation provided by inductor 216. This allows the tunneling paths to be substantially independent of each other.

[0014] 1, each qubit 110 and 120 can be described in terms of four circuit nodes: first nodes 116 and 126 between the first Josephson junctions 112 and 122 and the first inductors 114 and 124; second nodes 117 and 127 between the first Josephson junctions 112 and 122 and the second inductors 115 and 125; third nodes 118 and 128 between the second Josephson junctions 113 and 123 and the second inductors 115 and 125; and fourth nodes 119 and 129 between the second Josephson junctions 113 and 123 and the first inductors 114 and 124. In the illustrated implementation, each node 116-119 of the first qubit 110 is connected to a selected node 126-129 of the second qubit 120 via a corresponding capacitor 132-135, respectively. In one implementation, capacitors 132-135 have a capacitance of 50 femtofarads to 200 femtofarads. In the illustrated example, each capacitor 132-135 has a capacitance of 150 femtofarads. In the illustrated example, first nodes 116 and 126 and second nodes 117 and 127 are connected to corresponding nodes, while third nodes 118 and 128 of each qubit are connected to fourth nodes 119 and 129 of the other qubit. XX coupling exists because each node 116-119 of first qubit 110 is connected to a corresponding node 126-129 of second qubit 120; however, ZZ coupling and the resulting single-qubit effects can be avoided by reversing the connection order of the nodes associated with one of the Josephson junctions. In one implementation, XX coupling has a coupling strength of 500 megahertz to 2 gigahertz.

[0015] The connections via the multiple capacitors 132-135 create multiple tunneling paths between potential minima associated with multiple states of the first and second flux qubits, resulting in tunneling paths between pairs of basis states with equal bit parity. In other words, the XX coupler allows the system formed by the two qubits to tunnel not only between states |00> and |11>, but also between states |01> and |10>. In effect, the first tunneling path generates a first interaction g1 (|01><10|+|10><01|), where g1 is the strength or tunneling energy of the first interaction, and the second tunneling path generates a second interaction g2 (|00><11|+|11><00|), where g2 is the strength of the second interaction. The interaction strength g for a given tunneling path is i is equal to half the energy splitting between the ground and excited states of the coupling term, along with the height of the tunneling barrier between the two states. The sum of the two interactions is the XX interaction, as described in the standard or Z basis. The example shown provides a binding energy of approximately 0.95 GHz.

[0016] The effect that capacitors have on the phase tunneling paths of two Josephson junctions can be seen in Figure 4, which is a circuit diagram 400 showing a first flux qubit 402 connected to a second flux qubit 404 via a first capacitor 406 and a second capacitor 408. In the example shown, first capacitor 406 and second capacitor 408 have a capacitance of 150 femtofarads, the inductors in each flux qubit 402 and 404 have an inductance of 50 nanohenries, and the critical current of each Josephson junction is 50 nanoamperes. Capacitively coupling the two qubits 402 and 404 in this manner allows for control over the direction of wave function propagation within the multidimensional phase space defined by the Josephson junctions associated with qubits 402 and 404, enabling the selective coupling of wave functions associated with particular potential minima. In this example, states |00> and |11> are coupled to provide a ground state at (|00> + |11>) / √2, as well as degenerate excited states at |01> and |10>, approximately 1.08 GHz above ground, and another excited state at (|00> - |11>) / √2, approximately 1.85 GHz above ground. It will be appreciated that the direction of the wave function spread in phase space, and therefore the particular coupling of the wave function associated with the energy minimum, can be controlled by the selection of the capacitances of capacitors 406 and 408.

[0017] An advantage of the proposed XX coupler is that it can provide XX interactions without coupling qubits along other axes of the Bloch sphere or inducing single-qubit effects such as single-qubit tunneling. The Josephson junctions in the coupler may have slightly different critical currents due to fabrication variations, and in some instances, one or more junctions may be replaced with tunable junctions, such as composite junctions. Furthermore, the proposed coupler can be used for qubits with degenerate energy states (i.e., energy states with the same energy). Flux qubits and fluxonium qubits are examples of qubits that can operate in degenerate ground states. Finally, the coupler can be fabricated with only two loops, limiting the impact of environmental noise on the system 100.

[0018] 5 illustrates one implementation of a quantum system 500 in which a series of persistent current qubits 510, 530, and 560 can be chained together to provide X-X coupling throughout the array of qubits. In the illustrated implementation, each qubit (e.g., 510 and 530) is constructed as a set of four Josephson junctions 511-514 and 531-534 and is isolated from one another via inductors 515-518 and 535-538. Each of the qubits (e.g., 530) is connected to one or more neighboring qubits (e.g., 510 and 560) by a corresponding set of capacitors 521-524 and 541-544, respectively. Each connection between qubits begins at a first circuit node 551-558 between the inductor and Josephson junction on one qubit (e.g., 530) and terminates at a second circuit node 525-528 and 561-564 between a selected inductor and Josephson junction on another qubit (e.g., 510 and 560).

[0019] 1, it may be desirable to connect the qubits such that the connections across the first Josephson junction in a given qubit are made to corresponding locations in the connected qubit, but the connections across the second Josephson junction in a given qubit are reversed relative to the connections of the first Josephson junction. To simplify the fabrication of the connections, every other qubit, in this case qubit 503, may be fabricated such that the shape of the superconducting loop is altered to allow Josephson junctions at the same physical location between qubits 502 and 503 to be connected differently. For example, the superconducting loop may be substantially planar within a defined plane, such that the projection onto the defined plane of the superconducting loops associated with some qubits (e.g., 510 and 560) forms a single closed loop, and the projection onto the defined plane of the superconducting loops associated with other qubits (e.g., 530) forms two connected loops. As a result, the qubits (510, 530, and 560) can be connected in a standardized manner while still maintaining the inverse or staggered connection described in FIG.

[0020] With the structural and functional features described above in mind, an exemplary method will be better understood with reference to Figure 6. For ease of explanation, the exemplary method of Figure 6 is shown and described as being performed sequentially, however, it should be understood and appreciated that the present example is not limited by the order shown, as in other examples, some operations may be performed multiple times and / or simultaneously in a different order than shown and described herein. Moreover, not all illustrated operations need to be performed to implement the method.

[0021] FIG. 6 illustrates a method 600 for fabricating a quantum system with an XX coupling between two persistent current qubits, such as flux qubits. In 602, a first persistent current qubit is fabricated. The first persistent current qubit includes a first superconducting loop interrupted by a first Josephson junction and a second Josephson junction. The first Josephson junction is separated from the second Josephson junction by a first inductor and a second inductor. The inductors may be fabricated, for example, as a Josephson junction chain and made from a high-kinetic-inductance superconducting material or as a long superconducting wire. In one example, each Josephson junction has an inductance of 10 nanohenries to 100 nanohenries, and each Josephson junction can have a critical current of 25 nanoamperes to 100 nanoamperes.

[0022] In 604, a second persistent current qubit is fabricated. The second persistent current qubit includes a second superconducting loop interrupted by a third Josephson junction and a fourth Josephson junction. The third Josephson junction is separated from the fourth Josephson junction by a third inductor and a fourth inductor. The inductors may be fabricated, for example, as a Josephson junction chain and made from a high kinetic inductance superconducting material or as a long superconducting wire. In one example, each Josephson junction has an inductance of 10 nanohenries to 100 nanohenries, and each Josephson junction can have a critical current of 25 nanoamperes to 100 nanoamperes. In one example, each of the first superconducting loop and the second superconducting loop is substantially planar within a defined plane, and a projection of the first superconducting loop onto the defined plane forms a single closed loop, and a projection of the second superconducting loop onto the defined plane forms two connected loops.

[0023] At 606, a first node defined by the first Josephson junction and the first inductor is connected via a first capacitor to a second node defined by the third Josephson junction and the third inductor. At 608, a third node defined by the first Josephson junction and the second inductor is connected via a second capacitor to a fourth node defined by the third Josephson junction and the fourth inductor. At 610, a fifth node defined by the second Josephson junction and the first inductor is connected via a third capacitor to a sixth node defined by the fourth Josephson junction and the fourth inductor. At 612, a seventh node defined by the second Josephson junction and the second inductor is connected via a fourth capacitor to an eighth node defined by the fourth Josephson junction and the third inductor. In one example, the first capacitor, the second capacitor, the third capacitor, and the fourth capacitor each have a capacitance of 50 femtofarads to 200 femtofarads. The capacitive connections between the nodes by 606, 608, 610, and 612 collectively provide an X-X coupling between the first persistent current qubit and the second persistent current qubit. In one example, the X-X coupling has a coupling strength of 500 megahertz to 2 gigahertz.

[0024] In the foregoing description, specific details are set forth to provide a thorough understanding of exemplary implementations of the invention described in this disclosure. However, it will be apparent that various implementations may be practiced without these specific details. For example, circuits, systems, networks, processes, and other components may be shown as components in block diagram form so as not to obscure the exemplary implementations in unnecessary detail. In other instances, well-known circuits, processes, algorithms, structures, and techniques may be shown without unnecessary detail so as to avoid obscuring the examples. While the description of the exemplary implementations provides those skilled in the art with an enabling description for practicing examples of the invention, it should be understood that various changes can be made in the function and arrangement of elements without departing from the spirit and scope of the invention. Accordingly, it is intended that the present invention encompass all such changes, modifications, and variations that fall within the scope of the appended claims. The technical concepts that can be understood from the above-described embodiment will be described below as supplementary notes. [Appendix 1] 1. A system comprising: a first persistent current qubit comprising a first superconducting loop interrupted by a first series of Josephson junctions, the first series of Josephson junctions beginning with a first Josephson junction of the first series and continuing in a first direction around the first superconducting loop, each Josephson junction of the first series separated from an adjacent Josephson junction by two adjacent inductors of a first plurality of inductors, the first Josephson junction having an associated first circuit node between the Josephson junction and a first inductor of the two adjacent inductors of the first plurality of inductors in the first direction on the first superconducting loop and an associated second circuit node between the Josephson junction and a second inductor of the two adjacent inductors in a second direction on the first superconducting loop opposite the first direction; a second persistent current qubit comprising a second superconducting loop interrupted by a second series of Josephson junctions, the second series of Josephson junctions beginning with a first Josephson junction of the second series and continuing in a first direction around the second superconducting loop, each Josephson junction of the second series separated from adjacent Josephson junctions by two adjacent inductors of a second plurality of inductors, the second persistent current qubit having an associated first circuit node between a Josephson junction and a first inductor of the two adjacent inductors of the second plurality of inductors in the first direction on the second superconducting loop and an associated second circuit node between a Josephson junction and a second inductor of the two adjacent inductors in a second direction on the second superconducting loop opposite the first direction; a set of capacitive couplings between circuit nodes of the first persistent current qubit and the second persistent current qubit, a first capacitive coupling of the set of capacitive couplings connecting the first circuit node associated with the first Josephson junction of the first series of Josephson junctions to the first circuit node associated with the first Josephson junction of the second series of Josephson junctions, and a second capacitive coupling of the set of capacitive couplings connecting the second circuit node associated with the first Josephson junction of the first series of Josephson junctions to the second circuit node associated with the first Josephson junction of the second series of Josephson junctions; a third capacitive coupling of the set of capacitive couplings connects the first circuit node associated with a second Josephson junction of the first series to the second circuit node associated with a second Josephson junction of the second series, and a fourth capacitive coupling of the set of capacitive couplings connects the second circuit node associated with the second Josephson junction of the first series to the first circuit node associated with the second Josephson junction of the second series. [Appendix 2] a third persistent current qubit comprising a third superconducting loop interrupted by a third series of Josephson junctions, the third series of Josephson junctions beginning with a first Josephson junction in the third series and continuing in a first direction around the third superconducting loop, each Josephson junction in the third series being separated from an adjacent Josephson junction by an inductor of a third plurality of inductors, the Josephson junction having an associated first circuit node between the Josephson junction and a first inductor of the two adjacent inductors in the first direction on the third superconducting loop and an associated second circuit node between the Josephson junction and a second inductor of the two adjacent inductors in a second direction on the third superconducting loop opposite the first direction, the set of capacitive couplings being the first Josephson junction associated with a second Josephson junction in the third series of Josephson junctions; 10. The system of claim 1, further comprising: a fifth capacitive coupling of the set of capacitive couplings connecting a first circuit node to the first circuit node associated with a third Josephson junction of the second series of Josephson junctions; a sixth capacitive coupling of the set of capacitive couplings connecting the second circuit node associated with the second Josephson junction of the third series of Josephson junctions to the second circuit node associated with the third Josephson junction of the second series of Josephson junctions; a seventh capacitive coupling of the set of capacitive couplings connecting the first circuit node associated with the first Josephson junction of the third series of Josephson junctions to the second circuit node associated with a fourth Josephson junction of the second series of Josephson junctions; and an eighth capacitive coupling of the set of capacitive couplings connecting the second circuit node associated with the first Josephson junction of the third series of Josephson junctions to the first circuit node associated with the fourth Josephson junction of the second series of Josephson junctions. [Appendix 3] 10. The system of claim 1, wherein each of the first superconducting loop and the second superconducting loop is substantially planar within a defined plane, wherein a projection of the first superconducting loop onto the defined plane forms a single closed loop and a projection of the second superconducting loop onto the defined plane forms two connected loops. [Appendix 4] 2. The system of claim 1, wherein each of the pair of capacitive couplings has a capacitance of 10 femtofarads to 200 femtofarads. [Appendix 5] 10. The system of claim 1, wherein each inductor of the first plurality of inductors and the second plurality of inductors has an inductance between 1 nanohenry and 100 nanohenry. [Appendix 6] 10. The system of claim 1, wherein the set of capacitive couplings provides an X-X coupling between the first persistent current qubit and the second persistent current qubit. [Appendix 7] 7. The system of claim 6, wherein the XX coupling has a coupling strength of 500 megahertz to 10 gigahertz. [Appendix 8] 2. The system of claim 1, wherein each inductor of the first plurality of inductors and the second plurality of inductors is implemented using one of a Josephson junction chain, a high kinetic inductance superconducting material, and a long superconducting wire. [Appendix 9] 10. The system of claim 1, wherein each of the first persistent current qubit and the second persistent current qubit is a flux qubit. [Appendix 10] 2. The system of claim 1, wherein the first series of Josephson junctions and the second series of Josephson junctions each have a critical current of 25 nanoamperes to 500 nanoamperes. [Appendix 11] 1. A method comprising: fabricating a first persistent current qubit comprising a first superconducting loop interrupted by a first Josephson junction and a second Josephson junction, the first Josephson junction being separated from the second Josephson junction by a first inductor and a second inductor; fabricating a second persistent current qubit comprising a second superconducting loop interrupted by a third Josephson junction and a fourth Josephson junction, the third Josephson junction being separated from the fourth Josephson junction by a third inductor and a fourth inductor; connecting a first node defined by the first Josephson junction and the first inductor through a first capacitor to a second node defined by the third Josephson junction and the third inductor; connecting a third node defined by the first Josephson junction and the second inductor through a second capacitor to a fourth node defined by the third Josephson junction and the fourth inductor; connecting a fifth node defined by the second Josephson junction and the first inductor through a third capacitor to a sixth node defined by the fourth Josephson junction and the fourth inductor; and connecting a seventh node defined by the second Josephson junction and the second inductor through a fourth capacitor to an eighth node defined by the fourth Josephson junction and the third inductor. [Appendix 12] 12. The method of claim 11, wherein each of the first superconducting loop and the second superconducting loop is substantially planar in a defined plane, wherein a projection of the first superconducting loop onto the defined plane forms a single closed loop and a projection of the second superconducting loop onto the defined plane forms two connected loops. [Appendix 13] 12. The method of claim 11, wherein the first capacitor, the second capacitor, the third capacitor, and the fourth capacitor each have a capacitance of 10 femtofarads to 200 femtofarads. [Appendix 14] 12. The method of claim 11, wherein the first inductor, the second inductor, the third inductor, and the fourth inductor each have an inductance between 1 nanohenry and 100 nanohenry. [Appendix 15] 12. The method of claim 11, wherein a set of capacitive couplings provides XX coupling between the first persistent current qubit and the second persistent current qubit. [Appendix 16] 12. The method of claim 11, wherein each inductor of the first plurality of inductors and the second plurality of inductors is fabricated as one of a Josephson junction chain, a high kinetic inductance superconducting material, and a long superconducting wire. [Appendix 17] 12. The method of claim 11, wherein each of the first persistent current qubit and the second persistent current qubit is a flux qubit. [Appendix 18] 12. The system of claim 11, wherein each of the first Josephson junction, the second Josephson junction, the third Josephson junction, and the fourth Josephson junction has a critical current between 25 nanoamperes and 500 nanoamperes. [Appendix 19] 1. A system comprising: a first persistent current qubit comprising a first superconducting loop interrupted by a first Josephson junction and a second Josephson junction, the first Josephson junction separated from the second Josephson junction by a first inductor and a second inductor; a second persistent current qubit comprising a second superconducting loop interrupted by a third Josephson junction and a fourth Josephson junction, the third Josephson junction separated from the fourth Josephson junction by a third inductor and a fourth inductor; a first capacitive coupling connecting a first node defined by the first Josephson junction and the first inductor to a second node defined by the third Josephson junction and the third inductor; a second capacitive coupling connecting a third node defined by the first Josephson junction and the second inductor to a fourth node defined by the third Josephson junction and the fourth inductor; a third capacitive coupling connecting a fifth node defined by the second Josephson junction and the first inductor to a sixth node defined by the fourth Josephson junction and the fourth inductor; a fourth capacitive coupling connecting a seventh node defined by the second Josephson junction and the second inductor to an eighth node defined by the fourth Josephson junction and the third inductor; the first capacitive coupling, the second capacitive coupling, the third capacitive coupling, and the fourth capacitive coupling collectively provide an X-X coupling between the first persistent current qubit and the second persistent current qubit. [Appendix 20] 20. The system of claim 19, wherein the XX coupling has a coupling strength of 500 megahertz to 10 gigahertz.

Claims

1. 1. A system comprising: a first persistent current qubit comprising a first superconducting loop interrupted by a first series of Josephson junctions, the first series of Josephson junctions beginning with a first Josephson junction of the first series and continuing in a first direction around the first superconducting loop, each Josephson junction of the first series separated from an adjacent Josephson junction by two adjacent inductors of a first plurality of inductors, the first Josephson junction having an associated first circuit node between the Josephson junction and a first inductor of the two adjacent inductors of the first plurality of inductors in the first direction on the first superconducting loop and an associated second circuit node between the Josephson junction and a second inductor of the two adjacent inductors in a second direction on the first superconducting loop opposite the first direction; a second persistent current qubit comprising a second superconducting loop interrupted by a second series of Josephson junctions, the second series of Josephson junctions beginning with a first Josephson junction of the second series and continuing in a first direction around the second superconducting loop, each Josephson junction of the second series separated from adjacent Josephson junctions by two adjacent inductors of a second plurality of inductors, the second persistent current qubit having an associated first circuit node between a Josephson junction and a first inductor of the two adjacent inductors of the second plurality of inductors in the first direction on the second superconducting loop and an associated second circuit node between a Josephson junction and a second inductor of the two adjacent inductors in a second direction on the second superconducting loop opposite the first direction; a set of capacitive couplings between circuit nodes of the first persistent current qubit and the second persistent current qubit, a first capacitive coupling of the set of capacitive couplings connecting the first circuit node associated with the first Josephson junction of the first series of Josephson junctions to the first circuit node associated with the first Josephson junction of the second series of Josephson junctions, and a second capacitive coupling of the set of capacitive couplings connecting the second circuit node associated with the first Josephson junction of the first series of Josephson junctions to the second circuit node associated with the first Josephson junction of the second series of Josephson junctions; a third capacitive coupling of the set of capacitive couplings connects the first circuit node associated with a second Josephson junction of the first series to the second circuit node associated with a second Josephson junction of the second series, and a fourth capacitive coupling of the set of capacitive couplings connects the second circuit node associated with the second Josephson junction of the first series to the first circuit node associated with the second Josephson junction of the second series.

2. a third persistent current qubit comprising a third superconducting loop interrupted by a third series of Josephson junctions, the third series of Josephson junctions beginning with a first Josephson junction of the third series of Josephson junctions and continuing in a first direction around the third superconducting loop, each Josephson junction of the third series being separated from an adjacent Josephson junction by an inductor of a third plurality of inductors, the Josephson junction having an associated first circuit node between the Josephson junction and a first inductor of the two adjacent inductors in the first direction on the third superconducting loop and an associated second circuit node between the Josephson junction and a second inductor of the two adjacent inductors in a second direction on the third superconducting loop opposite the first direction; 2. The system of claim 1, further comprising: a fifth capacitive coupling of the set of capacitive couplings connecting a first circuit node to the first circuit node associated with a third Josephson junction of the second series of Josephson junctions; a sixth capacitive coupling of the set of capacitive couplings connecting the second circuit node associated with the second Josephson junction of the third series of Josephson junctions to the second circuit node associated with the third Josephson junction of the second series of Josephson junctions; a seventh capacitive coupling of the set of capacitive couplings connecting the first circuit node associated with the first Josephson junction of the third series of Josephson junctions to the second circuit node associated with a fourth Josephson junction of the second series of Josephson junctions; and an eighth capacitive coupling of the set of capacitive couplings connecting the second circuit node associated with the first Josephson junction of the third series of Josephson junctions to the first circuit node associated with the fourth Josephson junction of the second series of Josephson junctions.

3. 2. The system of claim 1, wherein each of the first superconducting loop and the second superconducting loop is substantially planar in a defined plane, a projection of the first superconducting loop onto the defined plane forms a single closed loop, and a projection of the second superconducting loop onto the defined plane forms two connected loops.

4. 10. The system of claim 1, wherein each of the pair of capacitive couplings has a capacitance between 10 femtofarads and 200 femtofarads.

5. 10. The system of claim 1, wherein each inductor of the first plurality of inductors and the second plurality of inductors has an inductance between 1 nanohenry and 100 nanohenry.

6. 2. The system of claim 1, wherein the set of capacitive couplings provides XX coupling between the first persistent current qubit and the second persistent current qubit.

7. The system of claim 6 , wherein the XX coupling has a coupling strength of 500 megahertz to 10 gigahertz.

8. 10. The system of claim 1, wherein each inductor of the first plurality of inductors and the second plurality of inductors is implemented using one of a Josephson junction chain, a high kinetic inductance superconducting material, and a long length of superconducting wire.

9. 10. The system of claim 1, wherein each of the first persistent current qubit and the second persistent current qubit is a flux qubit.

10. 10. The system of claim 1, wherein the first series of Josephson junctions and the second series of Josephson junctions each have a critical current of 25 nanoamperes to 500 nanoamperes.

11. 1. A method comprising: fabricating a first persistent current qubit comprising a first superconducting loop interrupted by a first Josephson junction and a second Josephson junction, the first Josephson junction being separated from the second Josephson junction by a first inductor and a second inductor; fabricating a second persistent current qubit comprising a second superconducting loop interrupted by a third Josephson junction and a fourth Josephson junction, the third Josephson junction being separated from the fourth Josephson junction by a third inductor and a fourth inductor; connecting a first node defined by the first Josephson junction and the first inductor through a first capacitor to a second node defined by the third Josephson junction and the third inductor; connecting a third node defined by the first Josephson junction and the second inductor through a second capacitor to a fourth node defined by the third Josephson junction and the fourth inductor; connecting a fifth node defined by the second Josephson junction and the first inductor through a third capacitor to a sixth node defined by the fourth Josephson junction and the fourth inductor; and connecting a seventh node defined by the second Josephson junction and the second inductor through a fourth capacitor to an eighth node defined by the fourth Josephson junction and the third inductor.

12. 12. The method of claim 11 , wherein each of the first superconducting loop and the second superconducting loop is substantially planar in a defined plane, a projection of the first superconducting loop onto the defined plane forms a single closed loop, and a projection of the second superconducting loop onto the defined plane forms two connected loops.

13. 12. The method of claim 11, wherein the first capacitor, the second capacitor, the third capacitor, and the fourth capacitor each have a capacitance between 10 femtofarads and 200 femtofarads.

14. 12. The method of claim 11 , wherein a set of capacitive couplings provides XX coupling between the first persistent current qubit and the second persistent current qubit.

15. 12. The method of claim 11, wherein the first Josephson junction, the second Josephson junction, the third Josephson junction, and the fourth Josephson junction each have a critical current between 25 nanoamperes and 500 nanoamperes.

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