Patent Document

CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Patent Application No. 60/886,253 filed Jan. 23, 2007, this provisional application is incorporated herein by reference in their entirety. 
     
    
     BACKGROUND 
       [0002]    1. Field 
         [0003]    The present disclosure generally relates to superconducting computing, for example analog or quantum computing employing processors that operate at temperatures at which materials superconduct. 
         [0004]    2. Description of the Related Art 
         [0005]    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. 
         [0006]    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). 
         [0007]    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 
       [0008]    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&#39;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 sufficient coherence to form the basic elements 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. 
         [0009]    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 use of quantum gates and circuits. Instead, the computational system starts from a known initial Hamiltonian with an easily accessible ground state and is controllably guided to a final Hamiltonian whose ground state represents the answer to a problem. 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 
       [0010]    As mentioned previously, qubits can be used as fundamental elements in 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. 
         [0011]    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. 
         [0012]    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&gt;), has the form |&gt;=a|0&gt;+b|1, where a and b are coefficients corresponding to the probabilities |a| 2  and |b| 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. 
         [0013]    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&gt; basis state or the |1&gt; 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 
       [0014]    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. 
         [0015]    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. See e.g., U.S. Pat. No. 6,838,694 and U.S. Patent Application No. 2005-0082519. 
       Computational Complexity Theory 
       [0016]    In computer science, computational complexity theory is the branch of the theory of computation that studies the resources, or cost, of the computation required to solve a given computational problem. This cost is usually measured in terms of abstract parameters such as time and space, called computational resources. Time represents the number of steps required to solve a problem and space represents the quantity of information storage required or how much memory is required. 
         [0017]    Computational complexity theory classifies computational problems into complexity classes. The number of complexity classes is ever changing, as new ones are defined and existing ones merge through the contributions of computer scientists. The complexity classes of decision problems include: 
         [0018]    1. P—The complexity class containing decision problems that can be solved by a deterministic UTM using a polynomial amount of computation time; 
         [0019]    2. NP (“Non-deterministic Polynomial time”)—The set of decision problems solvable in polynomial time on a non-deterministic UTM. Equivalently, it is the set of problems that can be “verified” by a deterministic UTM in polynomial time; 
         [0020]    3. NP-hard (Nondeterministic Polynomial-time hard)—A problem H is in the class NP-hard if and only if there is an NP-complete problem L that is polynomial time Turing-reducible to H. That is to say, L can be solved in polynomial time by an oracle machine with an oracle for H; 
         [0021]    4. NP-complete—A decision problem C is NP-complete if it is complete for NP, meaning that:
       (a) it is in NP and   (b) it is NP-hard,
 
i.e., every other problem in NP is reducible to it. “Reducible” means that for every problem L, there is a polynomial-time reduction, a deterministic algorithm which transforms instances I ε L into instances c ε C, such that the answer to c is YES if and only if the answer to I is YES. To prove that an NP problem A is in fact an NP-complete problem it is sufficient to show that an already known NP-complete problem reduces to A.
       
 
         [0024]    Decision problems have binary outcomes. Problems in NP are computation problems for which there exists a polynomial time verification. That is, it takes no more than polynomial time (class P) in the size of the problem to verify a potential solution. It may take more than polynomial time, however, to find a potential solution. NP-hard problems are at least as hard as any problem in NP. 
         [0025]    Optimization problems are problems for which one or more objective functions are minimized or maximized over a set of variables, sometimes subject to a set of constraints. For example, the Traveling Salesman Problem (“TSP”) is an optimization problem where an objective function representing, for example, distance or cost, must be optimized to find an itinerary, which is encoded in a set of variables representing the optimized solution to the problem. For example, given a list of locations, the problem may consist of finding the shortest route that visits all locations exactly once. Other examples of optimization problems include Maximum Independent Set, integer programming, constraint optimization, factoring, prediction modeling, and k-SAT. These problems are abstractions of many real-world optimization problems, such as operations research, financial portfolio selection, scheduling, supply management, circuit design, and travel route optimization. Many large-scale decision-based optimization problems are NP-hard. See e.g., “A High-Level Look at Optimization: Past, Present, and Future” e-Optimization.com, 2000. 
         [0026]    Simulation problems typically deal with the simulation of one system by another system, usually over a period of time. For example, computer simulations can be made of business processes, ecological habitats, protein folding, molecular ground states, quantum systems, and the like. Such problems often include many different entities with complex inter-relationships and behavioral rules. In Feynman it was suggested that a quantum system could be used to simulate some physical systems more efficiently than a UTM. 
         [0027]    Many optimization and simulation problems are not solvable using UTMs. Because of this limitation, there is need in the art for computational devices capable of solving computational problems beyond the scope of UTMs. In the field of protein folding, for example, grid computing systems and supercomputers have been used to try to simulate large protein systems. See Shirts et al., 2000,  Science  290, pp. 1903-1904, and Allen et al., 2001 , IBM Systems Journal  40, p. 310. The NEOS solver is an online network solver for optimization problems, where a user submits an optimization problem, selects an algorithm to solve it, and then a central server directs the problem to a computer in the network capable of running the selected algorithm. See e.g., Dolan et al., 2002 , SIAM News Vol.  35, p. 6. Other digital computer-based systems and methods for solving optimization problems can be found, for example, in Fourer et al., 2001 , Interfaces  31, pp. 130-150. All these methods are limited, however, by the fact they utilize digital computers, which are UTMs, and accordingly, are subject to the limits of classical computing that inherently possess unfavorable scaling of solution time as a function of problem size. 
       Persistent Current Coupler 
       [0028]      FIG. 1A  shows a 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. First qubit  110  is comprised of a loop of superconducting material  111  interrupted by a compound Josephson junction  112  and is coupled to controllable coupler  100  through the exchange of flux  103  between coupler  100  and first qubit  110 . Second qubit  120  is comprised of a loop of superconducting material  121  interrupted by a compound Josephson junction  122  and is coupled to controllable coupler  100  through the exchange of flux  104  between coupler  100  and second qubit  120 . Loop of superconducting material  101  is threaded by flux  105  created by electrical current flowing through a magnetic flux inductor  130 . 
         [0029]    Flux  105  produced by magnetic flux inductor  130  threads loop of superconducting material  101  and controls the state of controllable coupler  100 . Controllable coupler  100  is capable of producing a zero coupling between first qubit  110  and second qubit  120 , an anti-ferromagnetic coupling between first qubit  110  and second qubit  120 , and a ferromagnetic coupling between first qubit  110  and second qubit  120 . 
         [0030]      FIG. 1  B shows an exemplary two-pi-periodic graph  150  giving the relationship between the persistent current (I) flowing within loop of superconducting material  101  of controllable coupler  100  (Y-axis) as a function of flux (Φ X )  105  from magnetic flux inductor  130  threading loop of superconducting material  101  and scaled with the superconducting flux quantum Φ 0  (X-axis). 
         [0031]    Zero coupling exists between first qubit  110  and second qubit  120  when coupler  100  is set to point  160  or any other point along graph  150  with a similar slope of about zero of point  160 . Anti-ferromagnetic coupling exists between first qubit  110  and second qubit  120  when coupler  100  is set to the point  170  or any other point along graph  150  with a similar positive slope of point  170 . Ferromagnetic coupling exists between first qubit  110  and second qubit  120  when coupler  100  is set to point  180  or any other point along graph  150  with a similar negative slope of point  180 . 
         [0032]    Coupler  100  is set to states  160 , 170  and  180  by adjusting amount of flux  105  coupled between magnetic flux inductor  130  and loop of superconducting material  101 . The state of coupler  100  is dependant upon the slope of graph  150 . For dI/dΦ x  equal to approximately zero, coupler  100  is said to produce a zero coupling or non-coupling state where the quantum state of first qubit  110  does not interact with the state of second qubit  120 . For dI/dΦ x  greater than zero, the coupler is said to produce an anti-ferromagnetic coupling where the state of first qubit  110  and the state of 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 first state  110  and the state of second qubit  120  will be similar in their lowest energy state. From the zero coupling state with corresponding flux level  161 , flux (Φ X )  105  produced by magnetic flux inductor  130  threading loop of superconducting material  101  can be decreased to a flux level  171  to produce an anti-ferromagnetic coupling between first qubit  110  and second qubit  120  or increased to a flux level  181  to produce a ferromagnetic coupling between first qubit  110  and second qubit  120 . 
         [0033]    Examining persistent current  162  that exists at zero coupling point  160 , with corresponding zero coupling applied flux  161 , shows a large persistent current is coupled into first qubit  110  and second qubit  120 . This is not ideal as there may be unintended interactions between this persistent current flowing through controllable coupler  100  and other components within the analog processor in which 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 coupler  100  and other components within the analog processor in which controllable coupler  100  exists. Anti-ferromagnetic coupling persistent current level  172  and ferromagnetic coupling persistent current level  182  may be minimized such that persistent current levels  172  and  182  are about zero during regular operations. 
         [0034]    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 Maassen van der Brink, A. et al., “Mediated tunable coupling of flux qubits,” New Journal of Physics 7 (2005) 230. 
       BRIEF SUMMARY 
       [0035]    In at least one embodiment, a coupling system includes an rf-SQUID having a loop of superconducting material interrupted by a compound Josephson junction; a magnetic flux inductor; a first mutual inductance coupling the rf-SQUID to a first qubit; a second mutual inductance coupling the rf-SQUID to a second qubit; and a third mutual inductance coupling the compound Josephson junction to the magnetic flux inductor. 
         [0036]    In at least one embodiment, a method of controllably coupling a first qubit to a second qubit by an rf-SQUID having a loop of superconducting material interrupted by a compound Josephson junction includes coupling the first qubit to the rf-SQUID; coupling the second qubit to the rf-SQUID; coupling a magnetic flux inductor to the compound Josephson junction; and adjusting an amount of flux, produced by the magnetic flux inductor, threading the compound Josephson junction. 
         [0037]    In at least one embodiment, a coupling system includes an rf-SQUID having a loop of superconducting material interrupted by a compound Josephson junction; and a first magnetic flux inductor configured to selectively provide a first magnetic flux inductor mutual inductance coupling the first magnetic flux inductor to the compound Josephson junction, wherein the loop of superconducting material positioned with respect to a first qubit to provide a first mutual inductance coupling the rf-SQUID to the first qubit and wherein the loop of superconducting material positioned with respect to a second qubit to provide a second mutual inductance coupling rf-SQUID to the second qubit. The coupling system may further include a second magnetic flux inductor configured to selectively provide a second magnetic flux inductor mutual inductance coupling the second magnetic flux inductor to the compound Josephson junction. 
         [0038]    In at least one embodiment, a superconducting processor includes a first qubit; a second qubit; an rf-SQUID having a loop of superconducting material interrupted by a compound Josephson junction; and magnetic flux means for selectively providing inductance coupling the magnetic flux means to the compound Josephson junction, wherein the loop of superconducting material is configured to provide a first mutual inductance coupling the rf-SQUID to the first qubit and to provide a second mutual inductance coupling rf-SQUID to the second qubit. The magnetic flux means may take the form of a first magnetic flux inductor configured to provide a third mutual inductance selectively coupling the magnetic flux inductor to the compound Josephson junction. The magnetic flux means may further take the form of a second magnetic flux inductor configured to provide a fourth mutual inductance selectively coupling the second magnetic flux inductor to the compound Josephson junction. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0039]    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. 
           [0040]      FIG. 1A  is a schematic diagram of a controllable coupler according to the prior art. 
           [0041]      FIG. 1B  is a graph of persistent current versus magnetic flux threading a loop of superconducting material of a controllable coupler according to the prior art. 
           [0042]      FIG. 2A  is a schematic diagram of an embodiment of a superconducting controllable coupler system. 
           [0043]      FIG. 2B  is a graph of persistent current versus magnetic flux threading a loop of superconducting material of a controllable coupler system. 
           [0044]      FIG. 2C  is a graph of persistent current versus magnetic flux threading a loop of superconducting material of a controllable coupler system. 
           [0045]      FIG. 2D  is a graph of persistent current versus magnetic flux threading a loop of superconducting material of a controllable coupler system. 
           [0046]      FIG. 3  is a schematic diagram of a superconducting controllable coupler system according to one illustrated embodiment. 
           [0047]      FIG. 4  is a schematic diagram of a superconducting controllable coupler system according to another illustrated embodiment. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0048]    A coupler  100  produces a non-zero persistent current when producing a zero coupling state  160  between a first qubit  110  and a second qubit  120 . This non-zero persistent current generates flux offsets in qubits  110  and  120  which may be compensated for. Persistent current  162  generates a flux within the coupler which may thereby be unintentionally coupled into qubits  110  and  120 . Qubits  110  and  120  must therefore be biased such that the unintentional flux does not effect the state of qubits  110  and  120 . Also, while dI/dΦ x  is near zero, higher order derivatives may cause higher-order, non-negligible interactions which may be undesirable between first qubit  110  and second qubit  120 . 
         [0049]    One embodiment of the present system, devices and methods is shown in the schematic diagram of  FIG. 2A . A controllable coupler  200 , (i.e., a loop of superconducting material  201  interrupted by a compound Josephson junction  202 ) is used to inductively couple a first qubit  210  and a second qubit  220  for use in an analog computer. In one embodiment, first qubit  210  is comprised of a loop of superconducting material  211  interrupted by a compound Josephson junction  212  and is coupled to controllable coupler  200  through the exchange of flux  203  between coupler  200  and first qubit  210 . Second qubit  220  is comprised of a loop of superconducting material  221  interrupted by a compound Josephson junction  222  and is coupled to controllable coupler  200  through the exchange of flux  204  between coupler  200  and second qubit  220 . Those of skill in the art appreciate other superconducting flux qubit designs may be chosen. Those of skill in the art appreciate that the qubit design of first qubit  210  may be of a different design than that of second qubit  220 . Compound Josephson junction  202  is threaded by flux  205  created by current flowing through a magnetic flux inductor  230 . Flux  205  produced by magnetic flux inductor  230  threads compound Josephson junction  202  of controllable coupler  200  and controls the state of controllable coupler  200 . 
         [0050]    In one embodiment, controllable coupler  200  is capable of producing a zero coupling between first qubit  210  and second qubit  220 . To produce the zero coupling between first qubit  210  and second qubit  220 , amount of flux  205  threading compound Josephson junction  202  is adjusted to be about (n+½)Φ 0 , wherein n is an integer and (Do is the magnetic flux quantum. In one embodiment, controllable coupler  200  is capable of producing an anti-ferromagnetic coupling between first qubit  210  and second qubit  220 . To produce the anti-ferromagnetic coupling between first qubit  210  and second qubit  220 , amount of flux  205  threading compound Josephson junction  202  is adjusted to be about (2n)Φ 0 , wherein n is an integer. In one embodiment, controllable coupler  200  is capable of producing a ferromagnetic coupling between first qubit  210  and second qubit  220 . To produce the ferromagnetic coupling between first qubit  210  and second qubit  220 , amount of flux  205  threading compound Josephson junction  202  is adjusted to be about (2n+1)Φ 0 , wherein n is an integer. Those of skill in the art would appreciate amount of flux  205  threading compound Josephson junction  202  is a rough value and amounts of flux  205  threading compound Josephson junction  202  of comparable amounts will produce similar coupling states. 
         [0051]    One of skill in the art would appreciate that a twist in loop of superconducting material  201  results in controllable coupler  200  producing an anti-ferromagnetic coupling between first qubit  210  and second qubit  220  when amount of flux  205  threading compound Josephson junction  202  is adjusted to be about (2n+1)Φ 0 , wherein n is an integer and a ferromagnetic coupling between first qubit  210  and second qubit  220  when amount of flux  205  threading compound Josephson junction  202  is adjusted to be about (2n)Φ 0 , wherein n is an integer. 
         [0052]      FIG. 2B  shows an exemplary two-pi-periodic graph  250 B giving the relationship between the persistent current (I) flowing within loop of superconducting material  201  of controllable coupler  200  (Y-axis) and the amount of flux (Φ X ) threading loop of superconducting material  201  divided by Φ 0  (X-axis) wherein amount of flux  205  threading compound Josephson junction  202  is adjusted to be about (n+½)Φ 0 , wherein n is an integer, such that zero coupling is produced by controllable coupler  200  between first qubit  210  and second qubit  220 . 
         [0053]    Point  260 A identifies one possible operating point of controllable coupler  200  where there is no flux (Φ X ) threading loop of superconducting material  201  and a zero coupling is produced. Point  260 B shows a second possible operating point of controllable coupler  200  where there is a non-zero amount of flux threading loop of superconducting material  201  and a zero coupling state is produced. The amount of flux may be from an external magnetic field that threads through loop of superconducting material  201 , or the amount may be from the flux  205  intentionally or unintentionally produced by the magnetic flux inductor that threads loop of superconducting material  201  rather than compound Josephson junction  205 . By applying an amount of flux  205  threading compound Josephson junction  202  of about (2n+1)Φ 0 , graph  250 B exhibits the zero coupling state that controllable coupler  200  produces between first qubit  210  and second qubit  220  for all values of flux threading loop of superconducting material  201 . Little or no persistent current exists within loop of superconducting material  201  as seen by how closely graph  250 B is to the zero persistent current value for all values of flux threading loop of superconducting material  201 . This gives an improvement over controllable coupler  100  where a large persistent current  162  is present when the zero-coupling state is produced, as seen in  FIG. 1B . 
         [0054]      FIG. 2C  shows an exemplary two-pi-periodic graph  250 C giving the relationship between the persistent current (I) flowing within loop of superconducting material  201  of controllable coupler  200  (Y-axis) and the amount of flux (Φ X ) threading loop of superconducting material  201  divided by Φ 0  (X-axis) wherein amount of flux  205  threading compound Josephson junction  202  is adjusted to be about (2n)Φ 0 , wherein n is an integer, such that an anti-ferromagnetic coupling is produced by controllable coupler  200  between first qubit  210  and second qubit  220 . 
         [0055]    Point  270 A identifies one possible operating point of controllable coupler  200  where there is no flux (Φ X ) threading loop of superconducting material  201  and an anti-ferromagnetic coupling is produced. Point  270 B shows a second possible operating point of controllable coupler  200  where an amount of flux  271 B threading loop of superconducting material  201  and an anti-ferromagnetic coupling is produced. Flux  271 B may be from an external magnetic field that threads through loop of superconducting material  201 , or flux  271 B may be from flux  205  produced by the magnetic flux inductor threads loop of superconducting material  201  rather than compound Josephson junction  205 . By applying an amount of flux  205  threading compound Josephson junction  202  of about (2n)Φ 0  graph  250 C exhibits the anti-ferromagnetic coupling state produced by controllable coupler  200  between first qubit  210  and second qubit  220  for all values of flux threading loop of superconducting material  201  where the slope of graph  250 C is similar to that at points  270 A and  270 B. Persistent current  272 B associated with operating point  270 B is small. 
         [0056]      FIG. 2D  shows an exemplary two-pi-periodic graph  250 D giving the relationship between the persistent current (I) flowing within loop of superconducting material  201  of controllable coupler  200  (Y-axis) and the amount of flux (Φ X ) threading loop of superconducting material  201  divided by Φ 0  (X-axis) wherein amount of flux  205  threading compound Josephson junction  202  is adjusted to be about (2n+1)Φ 0 , wherein n is an integer, such that a ferromagnetic coupling is produced by controllable coupler  200  between first qubit  210  and second qubit  220 . 
         [0057]    Point  280 A identifies one possible operating point of controllable coupler  200  where there is no flux (Φ X ) threading loop of superconducting material  201  and a ferromagnetic coupling is produced. Point  280 B shows a second possible operating point of controllable coupler  200  where an amount of flux  281 B threading loop of superconducting material  201  and a ferromagnetic coupling is produced. Amount of flux  281 B may be from an external magnetic field that threads through loop of superconducting material  201 , or the amount  281 B may be from the flux  205  produced by the magnetic flux inductor threads loop of superconducting material  201  rather than compound Josephson junction  205 . By applying an amount of flux  205  threading compound Josephson junction  202  of about (2n+1)Φ 0  graph  250 D exhibits the ferromagnetic coupling state produced by controllable coupler  200  between first qubit  210  and second qubit  220  for all values of flux threading loop of superconducting material  201  where the slope of the graph  250 D is similar to that at points  280 A and  280 B. Persistent current amount  282 B associated with operating point  280 B is small. 
         [0058]      FIG. 3  shows a further embodiment of the present systems, devices, and devices. A controllable coupler  300 , (i.e., a loop of superconducting material  301  interrupted by a compound Josephson junction  302 ) is used to inductively couple a first qubit  310  and a second qubit  320  for use in an analog computer. In this embodiment, first qubit  310  is comprised of a loop of superconducting material  311  interrupted by a compound Josephson junction  312  and is coupled to controllable coupler  300  through the exchange of flux  303  between coupler  300  and first qubit  310 . Second qubit  320  is comprised of a loop of superconducting material  321  interrupted by a compound Josephson junction  322  and is coupled to controllable coupler  300  through the exchange of flux  304  between coupler  300  and second qubit  320 . Those of skill in the art appreciate other qubit superconducting flux qubit designs may be chosen. Those of skill in the art appreciate that the qubit design of first qubit  310  may be of a different design than that of second qubit  320 . Compound Josephson junction  302  is threaded by flux  305  created by current flowing through a magnetic flux inductor  330 . Flux  305  produced by magnetic flux inductor  330  threads compound Josephson junction  302  of controllable coupler  300  and controls the state of controllable coupler  300 . Loop of superconducting material  301  is threaded by flux  306  created by current flowing through a magnetic flux inductor  340 . Flux  306  produced by the magnetic flux inductor  340  threads loop of superconducting material  301  of controllable coupler  320  and ensures that the net value of flux threading loop of superconducting material  301  is about zero. By ensuring the net value of flux threading loop of superconducting material  301  is about zero, a minimum amount of persistent current will be present within loop of superconducting material  301  during all states produced by controllable coupler  300 . 
         [0059]    In one embodiment, controllable coupler  300  is capable of producing a zero coupling between first qubit  310  and second qubit  320 . To produce the zero coupling between first qubit  310  and second qubit  320 , amount of flux  305  threading compound Josephson junction  302  is adjusted to be about (n+½)Φ 0 , wherein n is an integer. In one embodiment, controllable coupler  300  is capable of producing an anti-ferromagnetic coupling between first qubit  310  and second qubit  320 . To produce the anti-ferromagnetic coupling between first qubit  310  and second qubit  320 , amount of flux  305  threading compound Josephson junction  302  is adjusted to be about (2n)Φ 0 , wherein n is an integer. In one embodiment, controllable coupler  300  is capable of producing a ferromagnetic coupling between first qubit  310  and second qubit  320 . To produce the ferromagnetic coupling between first qubit  310  and second qubit  320 , amount of flux  305  threading compound Josephson junction  302  is adjusted to be about (2n+1)Φ 0 , wherein n is an integer. Those of skill in the art would appreciate amount of flux  305  threading compound Josephson junction  302  is a rough value and amounts of flux  205  threading compound Josephson junction  302  of comparable amounts will produce similar coupling states. 
         [0060]    As was seen by the design of controllable coupler  200 , there may be a net flux threading loop of superconducting material  201  thereby producing coupling states  260 B,  270 B and  280 B. With the use of magnetic flux inductor  340 , flux  306  is controllably coupled into loop of superconducting material  301  of controllable coupler  300  to ensure that the net value of flux threading loop of superconducting material  301  is minimized such that coupling states  260 A,  270 A and  280 A are produced by controllable coupler  300 , thereby minimizing persistent current in loop of superconducting material  301  and thereby keeping the bias operations point in the centre of the linear regime of graphs  250 C and  250 D in order to minimize higher order derivatives which can cause unintended interactions between a first qubit  310  and a second qubit  320 . 
         [0061]    One embodiment of the present system, devices and methods is shown in the schematic diagram of  FIG. 4 . A controllable coupler  400 , (i.e., a loop of superconducting material  401  interrupted by a compound Josephson junction  402 ) is used to inductively couple a first qubit  410  and a second qubit  420  for use in an analog computer. In one embodiment, first qubit  410  is comprised of a loop of superconducting material  411  interrupted by a compound Josephson junction  412  and is coupled to controllable coupler  400  through the exchange of flux  403  between coupler  400  and first qubit  410 . Second qubit  420  is comprised of a loop of superconducting material  421  interrupted by a compound Josephson junction  422  and is coupled to controllable coupler  400  through the exchange of flux  404  between coupler  400  and second qubit  420 . Those of skill in the art appreciate other superconducting flux qubit designs may be chosen. Those of skill in the art appreciate that the qubit design of first qubit  410  may be of a different design than that of second qubit  420 . Compound Josephson junction  402  is threaded by flux  405   a  created by current flowing through a magnetic flux inductor  430   a  and flux  405   b  created by current flowing through a magnetic flux inductor  430   b . Flux  405   a  produced by magnetic flux inductor  430   a  and flux  405   b  produced by magnetic flux inductor  430   b  thread compound Josephson junction  402  of controllable coupler  400  and the sum of flux  405   a  and flux  405   b  controls the state of controllable coupler  400 .

Technology Category: 7