**SYSTEMS, DEVICES, AND METHODS FOR CONTROLLABLY COUPLING QUBITS**

JOHNSON, Mark W. (3979 West 18th Avenue, Vancouver, British Columbia V6S 1B6, CA)

BUNYK, Paul (#7 - 2222 Alma Street, Vancouver, British Columbia V6R 3R3, CA)

JOHNSON, Mark W. (3979 West 18th Avenue, Vancouver, British Columbia V6S 1B6, CA)

*;*

**H01L39/22**

**G06N99/00**US20040016918A1 | ||||

US6838694B2 | ||||

US6984846B2 |

CLAIMS
We claim:
1. A coupling system to couple a first qubit and a second qubit, the coupling system comprising: a first loop of superconducting material; a second loop of superconducting material; a first Josephson junction interrupting the first and the second loops of superconducting material; a second Josephson junction interrupting the second loop of superconducting material; a first magnetic flux inductor that forms at least a portion of a first mutual inductance interface to inductively couple the first loop of superconducting material with the first qubit; a second magnetic flux inductor that forms at least a portion of a second mutual inductance interface to inductively couple the first and the second loops of superconducting material with the second qubit; a third magnetic flux inductor forming a third mutual inductance interface to inductively couple the first loop to a first coupling state control structure; and a fourth magnetic flux inductor forming a fourth mutual inductance interface to inductively couple the second loop to a second coupling state structure.
2. The coupling system of claim 1 wherein at least one of the first qubit and the second qubit is a superconducting flux qubit.
3. The coupling system of claim 1 wherein a flux provided to the third magnetic flux inductor by the first coupling state structure at least partially controls a coupling state of the coupling system.
4. The coupling system of claim 3 wherein the coupling state is produced and there exists a persistent current within the loop of superconducting material with a magnitude of about zero.
5. The coupling system of claim 3 wherein the coupling state of the coupling system is selected from a group consisting of anti-ferromagnetic coupling, ferromagnetic coupling and zero coupling.
6. The coupling system of claim 1 wherein a flux provided to the fourth magnetic flux inductor by the second coupling state structure at least partially controls a coupling state of the coupling system.
7. The coupling system of claim 3 wherein the coupling state is produced and there exists a persistent current within the loop of superconducting material with a magnitude of about zero.
8. The coupling system of claim 3 wherein the coupling state of the coupling system is selected from a group consisting of anti-ferromagnetic coupling, ferromagnetic coupling and zero coupling.
9. The coupling system of claim 1 wherein the first coupling state control structure includes a fifth magnetic flux inductor positioned to inductively couple with the third magnetic flux inductor, the third and the fifth magnetic flux inductors forming a first magnetic flux transformer.
10. The coupling system of claim 9 wherein the second coupling state control structure includes a sixth magnetic flux inductor positioned to inductively couple with the fourth magnetic flux inductor, the fourth and the sixth magnetic flux inductors forming a second magnetic flux transformer.
11. A method of controllably coupling a first qubit and a second qubit with a coupling system, the method comprising: coupling the first qubit to the coupling system through a first mutual inductance interface; coupling the second qubit to the coupling system through a second mutual inductance interface; applying a first amount of flux to the coupling system through a third mutual inductance interface; and applying a second amount of flux to the coupling system through a fourth mutual inductance interface; and wherein the first qubit and the second qubit are essentially magnetically isolated from each other when the first amount of flux is zero and the second amount of flux is approximately zero.
12. The method of claim 11 wherein the first qubit and the second qubit are anti-ferromagnetically coupled to each other when at least one of the first amount of flux or the second amount of flux is non-zero.
13. The method of claim 11 wherein the first qubit and the second qubit are ferromagnetically coupled to each other when at least one of the first amount of flux or the second amount of flux is non-zero.
14. The method of claim 11 wherein the first qubit and the second qubit are essentially magnetically isolated from each other when the first amount of flux is zero and the second amount of flux is non-zero.
15. The method of claim 11 wherein the coupling system is comprised of: a first loop of superconducting material; a second loop of superconducting material; a first Josephson junction interrupting the first and the second loops of superconducting material; a second Josephson junction interrupting the second loop of superconducting material; a first magnetic flux inductor forming the first mutual inductance interface to inductively couple the first loop of superconducting material to the first qubit; a second magnetic flux inductor forming the second mutual inductance interface to inductively couple the first and second loops of superconducting material to the second qubit; a third magnetic flux inductor forming the third mutual inductance interface to inductively couple the first loop to a first coupling state control structure; and a fourth magnetic flux inductor forming the fourth mutual inductance interface to inductively couple the second loop to a second coupling state control structure.
16. The method of claim 11 wherein at least one of the first qubit and the second qubit is a superconducting flux qubit.
17. The method of claim 11 , further comprising: adjusting the first amount of flux applied to the coupling system.
18. The method of claim 17 wherein adjusting the first amount of flux applied causes a change in coupling between the first qubit and the second qubit.
19. The method of claim 11 , further comprising: adjusting the second amount of flux applied to the coupling system.
20. The method of claim 19 wherein adjusting the second amount of flux applied causes a change in coupling between the first qubit and the second qubit. |

SYSTEMS, DEVICES, AND METHODS FOR CONTROLLABLY COUPLING QUBITS

BACKGROUND

Field The present disclosure generally relates to superconducting computing, for example analog or quantum computing employing processors that operate at superconducting temperatures.

Description of the Related Art

A Turing machine is a theoretical computing system, described in 1936 by Alan Turing. A Turing machine that can efficiently simulate any other Turing machine is called a Universal Turing Machine (UTM). The Church- Turing thesis states that any practical computing model has either the equivalent or a subset of the capabilities of a UTM.

A quantum computer is any physical system that harnesses one or more quantum effects to perform a computation. A quantum computer that can efficiently simulate any other quantum computer is called a Universal Quantum Computer (UQC).

In 1981 Richard P. Feynman proposed that quantum computers could be used to solve certain computational problems more efficiently than a UTM and therefore invalidate the Church-Turing thesis. See e.g., Feynman R. P., 'Simulating Physics with Computers", International Journal of Theoretical Physics, Vol. 21 (1982) pp. 467-488. For example, Feynman noted that a quantum computer could be used to simulate certain other quantum systems, allowing exponentially faster calculation of certain properties of the simulated quantum system than is possible using a UTM.

Approaches to Quantum Computation

There are several general approaches to the design and operation of quantum computers. One such approach is the "circuit model" of quantum computation. In this approach, qubits are acted upon by sequences of logical gates that are the compiled representation of an algorithm. Circuit model quantum computers have several serious barriers to practical implementation. In the circuit model, it is required that qubits remain coherent over time periods much longer than the single-gate time. This requirement arises because circuit model quantum computers require operations that are collectively called quantum error correction in order to operate. Quantum error correction cannot be performed without the circuit model quantum computer's qubits being capable of maintaining quantum coherence over time periods on the order of 1 ,000 times the single-gate time. Much research has been focused on developing qubits with coherence sufficient to form the basic information units of circuit model quantum computers. See e.g., Shor, P. W. "Introduction to Quantum Algorithms", arXiv.org:quant-ph/0005003 (2001 ), pp. 1-27. The art is still hampered by an inability to increase the coherence of qubits to acceptable levels for designing and operating practical circuit model quantum computers. Another approach to quantum computation, involves using the natural physical evolution of a system of coupled quantum systems as a computational system. This approach does not make critical use of quantum gates and circuits. Instead, starting from a known initial Hamiltonian, it relies upon the guided physical evolution of a system of coupled quantum systems wherein the problem to be solved has been encoded in the terms of the system's Hamiltonian, so that the final state of the system of coupled quantum systems contains information relating to the answer to the problem to be solved. This approach does not require long qubit coherence times. Examples of this type of approach include adiabatic quantum computation, cluster-state quantum computation, one-way quantum computation, quantum annealing and classical annealing, and are described, for example, in Farhi, E. et al.,

"Quantum Adiabatic Evolution Algorithms versus Simulated Annealing" arXiv.org:quant-ph/0201031 (2002), pp 1-24.

Qubits

As mentioned previously, qubits can be used as fundamental units of information for a quantum computer. As with bits in UTMs, qubits can refer to at least two distinct quantities; a qubit can refer to the actual physical device in which information is stored, and it can also refer to the unit of information itself, abstracted away from its physical device.

Qubits generalize the concept of a classical digital bit. A classical information storage device can encode two discrete states, typically labeled "0" and "1". Physically these two discrete states are represented by two different and distinguishable physical states of the classical information storage device, such as direction or magnitude of magnetic field, current, or voltage, where the quantity encoding the bit state behaves according to the laws of classical physics. A qubit also contains two discrete physical states, which can also be labeled "0" and "1". Physically these two discrete states are represented by two different and distinguishable physical states of the quantum information storage device, such as direction or magnitude of magnetic field, current, or voltage, where the quantity encoding the bit state behaves according to the laws of quantum physics. If the physical quantity that stores these states behaves quantum mechanically, the device can additionally be placed in a superposition of 0 and 1. That is, the qubit can exist in both a "0" and "1" state at the same time, and so can perform a computation on both states simultaneously. In general, N qubits can be in a superposition of 2 ^{N }
states. Quantum algorithms make use of the superposition property to speed up some computations.

In standard notation, the basis states of a qubit are referred to as the |0> and |1> states. During quantum computation, the state of a qubit, in general, is a superposition of basis states so that the qubit has a nonzero probability of occupying the |0) basis state and a simultaneous nonzero probability of occupying the |1> basis state. Mathematically, a superposition of

basis states means that the overall state of the qubit, which is denoted |ψ>, has the form |ψ) = α|θ) + Z>|l) , where a and b are coefficients corresponding to the probabilities \a\ ^{2 }
and |jb| ^{2 }
, respectively. The coefficients a and b each have real and imaginary components, which allows the phase of the qubit to be characterized. The quantum nature of a qubit is largely derived from its ability to exist in a coherent superposition of basis states and for the state of the qubit to have a phase. A qubit will retain this ability to exist as a coherent superposition of basis states when the qubit is sufficiently isolated from sources of decoherence. To complete a computation using a qubit, the state of the qubit is measured (i.e., read out). Typically, when a measurement of the qubit is performed, the quantum nature of the qubit is temporarily lost and the superposition of basis states collapses to either the |0) basis state or the |1> basis state and thus regaining its similarity to a conventional bit. The actual state of the qubit after it has collapsed depends on the probabilities \a\ ^{2 }
and \b\ ^{2 }
immediately prior to the readout operation.

Superconducting Qubits

There are many different hardware and software approaches under consideration for use in quantum computers. One hardware approach uses integrated circuits formed of superconducting materials, such as aluminum or niobium. The technologies and processes involved in designing and fabricating superconducting integrated circuits are similar to those used for conventional integrated circuits.

Superconducting qubits are a type of superconducting device that can be included in a superconducting integrated circuit. Superconducting qubits can be separated into several categories depending on the physical property used to encode information. For example, they may be separated into charge, flux and phase devices, as discussed in, for example Makhlin et al., 2001 , Reviews of Modern Physics 73, pp. 357-400. Charge devices store and manipulate information in the charge states of the device, where elementary

charges consist of pairs of electrons called Cooper pairs. A Cooper pair has a charge of 2e and consists of two electrons bound together by, for example, a phonon interaction. See e.g., Nielsen and Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge (2000), pp. 343- 345. Flux devices store information in a variable related to the magnetic flux through some part of the device. Phase devices store information in a variable related to the difference in superconducting phase between two regions of the phase device. Recently, hybrid devices using two or more of charge, flux and phase degrees of freedom have been developed. For practical superconducting quantum computing systems, superconducting qubits are coupled together. See e.g., U.S. Patent No. 6,838,694 and U.S. Patent Application No. 2005-0082519.

Persistent Current Coupler

In Figure 1A shows schematic diagram of a controllable coupler 100. This coupler is a loop of superconducting material 101 interrupted by a single Josephson junction 102 and is used to couple a first qubit 110 and a second qubit 120 for use in an analog computer. The first qubit 110 is comprised of a loop of superconducting material 111 interrupted by a compound Josephson junction 112 and is coupled to the controllable coupler 100 through the exchange of flux 103 between the coupler 100 and the first qubit 110. The second qubit 120 is comprised of a loop of superconducting material 121 interrupted by a compound Josephson junction 122 and is coupled to the controllable coupler 100 through the exchange of flux 104 between the coupler 100 and the second qubit 120. Flux 105 created by electrical current flowing through a magnetic flux transformer 130 is applied to the loop of superconducting material 101.

Flux 105 produced by the magnetic flux transformer 130 is applied to the loop of superconducting material 101 and controls the state of the controllable coupler 100. The controllable coupler 100 is capable of producing a zero coupling between the first qubit 110 and the second qubit 120, an anti-

ferromagnetic coupling between the first qubit 110 and the second qubit 120, and a ferromagnetic coupling between the first qubit 110 and the second qubit 120.

Figure 1 B shows an exemplary two-pi-periodic graph 150B giving the relationship between the persistent current (I) flowing within the loop of superconducting material 101 of the controllable coupler 100 (Y-axis) as a function of the flux (φ _{x }
) 105 from the magnetic flux transformer 130 applied to the loop of superconducting material 101 and scaled with the superconducting flux quantum φ _{o }
(X-axis). Zero coupling exists between the first qubit 110 and the second qubit 120 when the coupler 100 is set to point 16OB or any other point along the graph 150B with a similar slope of about zero of point 160B. Anti-ferromagnetic coupling exists between the first qubit 110 and the second qubit 120 when the coupler 100 is set to the point 170B or any other point along the graph 150 with a similar positive slope of point 17OB. Ferromagnetic coupling exists between the first qubit 110 and the second qubit 120 when the coupler 100 is set to the point 180B or any other point along the graph 150 with a similar negative slope of point 180B.

The coupler is set to states 160B, 170B and 180B by adjusting the amount of flux 105 coupled between the magnetic flux transformer 130 and the loop of superconducting material 101. The state of the coupler is dependant upon the slope of the graph 150B. For dI/dφ _{κ }
equal to zero, the coupler is said to produce a zero coupling or non-coupling state where the quantum state of the first qubit 110 does not interact with the state of the second qubit 120. For dI/dφ _{x }
greater than zero, the coupler is said to produce an anti- ferromagnetic coupling where the state of the first qubit 110 and the state of the second qubit 120 will be dissimilar in their lowest energy state. For dI/dφ _{x }
less than zero, the coupler is said to produce a ferromagnetic coupling where the state of the first qubit 110 and the state of the second qubit 120 will be similar in their lowest energy state. Those of skill in the art would appreciate that depending upon the configuration of the coupler; anti-ferromagnetic coupling

may be associated with dI/dφ _{x }
less than zero whereas ferromagnetic coupling may be associated with dI/dφ _{x }
greater than zero. From the zero coupling state with corresponding flux level 161 , the amount of flux (φ _{x }
) 105 produced by the magnetic flux transformer 130 applied to the loop of superconducting material 101 can be decreased to a flux level 171 to produce an anti-ferromagnetic coupling between the first qubit 110 and the second qubit 120 or increased to a flux level 181 to produce a ferromagnetic coupling between the first qubit 110 and the second qubit 120.

Examining the persistent current 162 that exists at the zero coupling point 160B, with corresponding zero coupling applied flux 161 , shows a large persistent current is coupled into the first qubit 110 and the second qubit 120. This is not ideal as there may be unintended interactions between this persistent current flowing through the controllable coupler 100 and other components within the analog processor in which the controllable coupler 100 exists. Both anti-ferromagnetic coupling persistent current level 172 and ferromagnetic coupling persistent current level 182 may be of similar magnitudes as compared to zero coupling persistent current level 162 thereby causing similar unintended interactions between the persistent current of the coupler 100 and other components within the analog processor in which the controllable coupler 100 exists. Anti-ferromagnetic coupling persistent current level 172 and ferromagnetic coupling persistent current level 182 may be minimized such that the persistent current levels 172 and 182 are about zero during regular operations.

Figure 1C shows a graph 150C giving the relationship between the coupling strength (of arbitrary units) between the first qubit 110 and the second qubit 120 (Y-axis) as a function of the flux bias 105 from the magnetic flux transformer 130 applied to the loop of superconducting material 101 and scaled by the superconducting flux quantum φ _{o }
(X-axis).

Zero coupling exists between the first qubit 110 and the second qubit 120 when the coupler 100 is set to point 16OC or any other point along the graph 15OC with a similar coupling strength of zero as is exhibited by point

160C. Anti-ferromagnetic coupling exists between the first qubit 110 and the second qubit 120 when the coupler 100 is set to the point 170C or any other point along the graph 150C with a coupling strength greater than zero as is exhibited by point 17OC. Ferromagnetic coupling exists between the first qubit 110 and the second qubit 120 when the coupler 100 is set to the point 180B or any other point along the graph 15OC with a coupling strength less than zero as is exhibited by point 180C.

The coupling response of the controllable coupler 100 to an applied flux bias 105 is very non-symmetric in nature in relation to anti- ferromagnetic and ferromagnetic responses. When anti-ferromagnetic coupling is created, adjustments to the amount of flux bias 105 applied to the loop of superconducting material 101 can be conducted over a large region of applied flux 105 while affecting the anti-ferromagnetic coupling very little. For example, applying a flux 105 of approximately -0.5φ _{0 }
to 0.5φ _{0 }
to the loop of superconducting material 101 results in anti-ferromagnetic coupling produced by the controllable coupler 100 between the first qubit 110 and the second qubit 120. When ferromagnetic coupling is created, adjustments to the amount of flux bias 105 applied to the loop of superconducting material 101 can be conducted over only a very small region of applied flux 105 while maintaining the ferromagnetic coupling state. For example, applying a flux 105 of approximately 0.95φ _{0 }
to 1.05φ _{0 }
to the loop of superconducting material 101 results in ferromagnetic coupling produced by the controllable coupler 100 between the first qubit 110 and the second qubit 120. Therefore it can be seen that while one form of coupling is attainable with limited precision with regards to control over the amount of flux bias 105 being applied to the loop of superconducting material 101 , a coupling requires much greater precision. Also, zero coupling requires a very precise amount of flux bias 105 to be applied to the superconducting loop 101 to be achieved. Without very accurate control over the flux bias 105 being applied to the controllable coupler 100, the coupling produced by the controllable coupler 100 may not, in practice be what is desired.

For further discussion of the persistent current couplers, see e.g., Harris, R., "Sign and Magnitude Tunable Coupler for Superconducting Flux Qubits", arXiv.org: cond-mat/0608253 (2006), pp. 1-5, and van der Brink, A. M. et al., "Mediated tunable coupling of flux qubits," New Journal of Physics 7 (2005) 230.

BRIEF SUMMARY

One aspect may be summarized as a coupling system to couple a first qubit and a second qubit, that includes a first loop of superconducting material; a second loop of superconducting material; a first Josephson junction interrupting the first and the second loops of superconducting material; a second Josephson junction interrupting the second loop of superconducting material; a first magnetic flux inductor that forms at least a portion of a first mutual inductance interface to inductively couple the first loop of superconducting material with the first qubit; a second magnetic flux inductor that forms at least a portion of a second mutual inductance interface to inductively couple the first and the second loops of superconducting material with the second qubit; a third magnetic flux inductor forming a third mutual inductance interface to inductively couple the first loop to a first coupling state control structure; and a fourth magnetic flux inductor forming a fourth mutual inductance interface to inductively couple the second loop to a second coupling state structure.

Another aspect may be summarized as a method of controllably coupling a first qubit and a second qubit with a coupling system that includes coupling the first qubit to the coupling system through a first mutual inductance interface; coupling the second qubit to the coupling system through a second mutual inductance interface; applying a first amount of flux to the coupling system through a third mutual inductance interface; applying a second amount of flux to the coupling system through a fourth mutual inductance interface; and wherein the first qubit and the second qubit are essentially magnetically isolated

from each other when the first amount of flux is zero and the second amount of flux is approximately zero.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

In the drawings, identical reference numbers identify similar elements or acts. The sizes and relative positions of elements in the drawings are not necessarily drawn to scale. For example, the shapes of various elements and angles are not drawn to scale, and some of these elements are arbitrarily enlarged and positioned to improve drawing legibility. Further, the particular shapes of the elements as drawn are not intended to convey any information regarding the actual shape of the particular elements, and have been solely selected for ease of recognition in the drawings.

Figure 1 A is a schematic diagram of a controllable coupler according to the prior art.

Figure 1 B is a graph of persistent current versus magnetic flux applied to a loop of superconducting material of a controllable coupler according to the prior art.

Figure 1C is a graph of coupling strength versus magnetic flux applied to a loop of superconducting material of a controllable coupler according to the prior art. Figure 2A is a schematic diagram of an embodiment of a superconducting controllable coupler system.

Figure 2B is a graph of coupling strength versus magnetic flux applied to a loop of superconducting material of a controllable coupler.

Figure 2C is a graph of coupling strength versus magnetic flux applied to a loop of superconducting material of a controllable coupler.

Figure 2D is a graph of coupling strength versus magnetic flux applied to a loop of superconducting material of a controllable coupler.

Figure 3 is a topographical plot of the coupling strength of a controllable coupler.

DETAILED DESCRIPTION

Figure 2A shows schematic diagram of a controllable coupler 200 according to one illustrated embodiment. Controllable coupler 200 includes two loops of inter-woven superconducting material, a first loop 201 A and a second loop 201 B. First loop 201 A is interrupted by a single Josephson junction 202A and second loop 201 B is interrupted by two Josephson junctions 202A and 202B, where 202A is a part of both first loop 201 A and second loop 201 B. Controllable coupler 200 is used to couple a first qubit 210 and a second qubit 220 for use in an analog computer. First qubit 210 is coupled to controllable coupler 200 through the exchange of flux 203 between coupler 200 and first qubit 210. Second qubit 220 is coupled to controllable coupler 200 through the exchange of flux 204 between coupler 200 and second qubit 220. Qubit 210 and qubit 220 are, in some embodiments, superconducting flux qubits. A state of the controllable coupler 200 is controlled by signals received via a first and a second state control structures 229A, 229B, respectively. Flux 205A created by electrical current flowing through first state control structure 229A is applied to first loop of superconducting material 201 A. First state control structure 229A may, for example, take the form of a magnetic flux inductor, which along with a counterpart inductor 231 A in first loop of superconductor material 201 A forms a magnetic flux transformer 230A. Flux 205B-1 and flux 205B-2 created by electrical current flowing through second state control structure 229B is applied to second loop of superconducting material 201 B. Second state control structure 229B may, for example, take the form of one or more inductors, which along with counterpart inductors 231 B-1 , 231 B-2 in the second loop of superconducting material 201 A, 201 B forms a magnetic flux transformers 230B-1 , 230B-2 (collectively 230B).

Flux 205A produced by the magnetic flux transformer 230A, which is applied to the first loop 201 A, together with flux 205B-1 and flux 205B-2 produced by magnetic flux transformers 230B-1 , 230B-2, which is effectively applied to second loop 201 B, controls the state of controllable coupler 200.

Controllable coupler 200 is capable of producing a zero coupling between first qubit 210 and second qubit 220, an anti-ferromagnetic coupling between first qubit 210 and second qubit 220, and a ferromagnetic coupling between first qubit 210 and second qubit 220. Depending upon the ratio and magnitude of flux produced by magnetic flux transformers 230A and 230B, controllable coupler 200 can be capable of only producing a zero coupling between first qubit 210 and second qubit 220 and an anti-ferromagnetic coupling between first qubit 210 and second qubit 220. Depending upon the ratio and magnitude of flux produced by magnetic flux transformers 230A and 230B, controllable coupler 200 can be capable of only producing a zero coupling between first qubit 210 and second qubit 220 and a ferromagnetic coupling between first qubit 210 and second qubit 220.

Figure 2B shows an exemplary graph 250B giving the relationship between the coupling strength (of arbitrary units) between first qubit 210 and second qubit 220 (Y-axis) as a function of flux bias 205A from the magnetic flux transformer 230A applied to first loop of superconducting material 201 A and scaled by the superconducting flux quantum φ _{o }
(X-axis). Note that flux 205B (the sum of flux 205B-1 and 205B-2) created by electrical current flowing through magnetic flux transformers 230B-1 , 230B-2 is produced with a magnitude of approximately O.25φo.

Zero coupling exists between first qubit 210 and second qubit 220 when coupler 200 is set to point 260B or any other point along the graph 250B with a similar coupling strength of zero as is exhibited by point 260B. Anti- ferromagnetic coupling exists between first qubit 210 and second qubit 220 when coupler 200 is set to point 270B or any other point along graph 250B with a coupling strength greater than zero as is exhibited by point 270B. Ferromagnetic coupling exists between first qubit 210 and second qubit 220 when coupler 200 is set to point 280B or any other point along graph 250B with a coupling strength less than zero as is exhibited by point 280B. There may exist direct magnetic coupling interactions between first qubit 210 and second qubit 220 wherein an inherent coupling exists between first qubit 210 and

second qubit 220 when no flux 205A or 205B (the sum of flux 205B-1 and 205B-2) created by electrical current flowing through magnetic flux transformers 230B-1 , 230B-2 is produced.

The symmetric nature of the coupling response of graph 250B is very desirable. It allows for predictable operations of controllable coupler 200 without undue testing and analysis to precisely quantify the response of controllable coupler 200 as flux bias 205A is manipulated. Also, there exists a well defined zero coupling state 260B attainable when about zero flux bias 205A applied to the controllable coupler 200. Figure 2C shows an exemplary graph 250C giving the relationship between the coupling strength (of arbitrary units) between first qubit 210 and second qubit 220 (Y-axis) as a function of flux bias 205A from magnetic flux transformer 230A applied to first loop of superconducting material 201 A scaled by the superconducting flux quantum φ _{o }
(X-axis). Note that flux 205B (the sum of flux 205B-1 and 205B-2) created by electrical current flowing through magnetic flux transformers 230B-1 , 230B-2 is produced with about equal magnitude and direction as that produced by flux bias 205A from magnetic flux transformer 230A.

Zero coupling exists between first qubit 210 and second qubit 220 when coupler 200 is set to point 260C or any other point along the graph 250C with a similar coupling strength of zero as is exhibited by point 260C. Anti- ferromagnetic coupling exists between first qubit 210 and second qubit 220 when coupler 200 is set to point 270C or any other point along graph 250C with a coupling strength greater than zero as is exhibited by point 270C. There may exist direct magnetic coupling interactions between first qubit 210 and second qubit 220 wherein an inherent coupling exists between first qubit 210 and second qubit 220 when no flux 205A or 205B (the sum of flux 205B-1 and 205B-2) created by electrical current flowing through magnetic flux transformers 230B-1 , 230B-2 is produced. A well defined zero coupling state 260C is attainable with about zero flux bias 205A and 205B applied to the controllable coupler 200 in this

embodiment of controllable coupler 200. Having a zero-coupling state as the "off' state of the controllable coupler 200 is a desirable characteristic of any coupler within a analog or quantum system. Since persistent current couplers' "off' state does not produce zero coupling, an iterative process is required during calibration of analog or quantum systems which incorporate persistent current couplers 100. This is a very difficult and time consuming process as before a qubit can be calibrated, the zero coupling state of couplers surrounding the qubit must be found. Couplers having an "off' state which produces zero-coupling allows for calibration of the analog or quantum system in a much more straight-forward and less-iterative approach.

Figure 2D shows an exemplary graph 250D giving the relationship between the coupling strength (of arbitrary units) between first qubit 210 and second qubit 220 (Y-axis) as a function of flux bias 205A from magnetic flux transformer 230A being applied to first loop of superconducting material 201 A scaled by the superconducting flux quantum φ _{o }
(X-axis). Note that flux bias 205B (the sum of flux 205B-1 and 205B-2) created by electrical current flowing through magnetic flux transformers 230B-1 , 230B-2 is produced with about equal magnitude but opposite direction as that produced by flux bias 205A from magnetic flux transformer 230A. Zero coupling exists between first qubit 210 and second qubit 220 when coupler 200 is set to point 260D or any other point along graph 250D with a similar coupling strength of zero as is exhibited by point 260D. Ferromagnetic coupling exists between first qubit 210 and second qubit 220 when coupler 200 is set to point 280D or any other point along graph 250D with a coupling strength greater than zero as is exhibited by point 270D. There may exist direct magnetic coupling interactions between first qubit 210 and second qubit 220 wherein an inherent coupling exists between first qubit 210 and second qubit 220 when no flux 205A or 205B (the sum of flux 205B-1 and 205B-2) created by electrical current flowing through magnetic flux transformers 230B-1 , 230B-2 is produced.

A well defined zero coupling state 260D is attainable with no flux bias 205A or flux bias 205B applied to controllable coupler 200 in this embodiment of a controllable coupler 200. Having a zero-coupling state as the "off' state of controllable coupler 200 is a desirable characteristic of any coupler within an analog or quantum system. Since persistent current couplers' "off' state does not produce zero coupling, an iterative process is required during calibration of analog or quantum systems which incorporate persistent current couplers 100. This is a very difficult and time consuming process as before a qubit can be calibrated, the zero coupling state of couplers surrounding the qubit must be found. Couplers having an "off' state which produces zero- coupling allows for calibration of the analog or quantum system in a much more strait-forward and less-iterative approach.

Figure 3 shows a topographical plot 300 of the coupling strength of controllable coupler 200. Plot 300 depicts how the coupling strength created by controllable coupler 200 is dependant upon both flux 205A from flux bias 230A (x-axis) and flux 205B (the sum of flux 205B-1 and 205B-2) from flux bias 230B (y-axis).

Line 350B denotes the contour used in the exemplary embodiment of Figure 2B where zero coupling, anti-ferromagnetic couple and ferromagnetic coupling was producible by varying the amount of flux 205A being applied to coupler 200 by magnetic flux transformer 230A. Curve 250B was found by following the contour of line 350B.

Line 350C denotes the contour used in the exemplary embodiment of Figure 2C where zero coupling and anti-ferromagnetic coupling was producible by varying flux 205A and flux 205B applied to coupler 200 in a proportional fashion by the respective magnetic flux transformers 230A and 230B. Curve 250C was found by following the contour of line 350C. When controllable coupler 200 is operated along line 350C, ferromagnetic coupling cannot be produced between first qubit 210 and second qubit 220. Line 350D denotes the contour used in the exemplary embodiment of Figure 2D where zero coupling and anti-ferromagnetic coupling

was producible by varying flux 205A and flux 205B applied to the coupler 200 in a proportional but opposite fashion by the respective magnetic flux transformers 230A and 230B. Curve 250D was found by following the contour of line 350D. When the controllable coupler 200 is along line 350D, anti-ferromagnetic coupling cannot be produced between the first qubit 210 and the second qubit 220.

Further embodiments of the controllable coupler 200 may be realized by applying flux though magnetic flux transformers 230A and 230B in a predetermined fashion to map out further contours on the plot 300.

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