Abstract:
Multiple substrates that carry quantum devices are coupled to provide quantum mechanical communicators therebetween, for example, using superconducting interconnects, vias, solder and/or magnetic flux. Such may advantageously reduce a footprint of a device such as a quantum processor.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims benefit under 35 U.S.C. 119(e) of U.S. Provisional Patent Application Ser. No. 61/018,820, filed Jan. 3, 2008 and entitled “Quantum Processor,” which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     1. Field 
     This disclosure generally relates to quantum computing and quantum processors, for example, multiple chip substrate quantum processors. 
     2. 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&#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 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&#39;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 1-16. 
     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. Examples of qubits include quantum particles, atoms, electrons, photons, ions, and the like. 
     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&gt; and |1&gt; 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&gt; basis state and a simultaneous nonzero probability of occupying the |1&gt; basis state. Mathematically, a superposition of basis states means that the overall state of the qubit, which is denoted |Ψ&gt;, has the form |Ψ&gt;=a|0&gt;+b|1&gt;, 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. 
     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 
     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 in some respects to those used for conventional integrated circuits. 
     Superconducting qubits are a type of superconducting device that can be included in a superconducting integrated circuit. Typical superconducting qubits, for example, have the advantage of scalability and are generally classified depending on the physical properties used to encode information including, for example, charge and phase devices, phase or flux devices, hybrid devices, and the like. 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. 
     Examples of flux qubits that may be used include rf-SQUIDs, which include a superconducting loop interrupted by one Josephson junction, or a compound junction (where a single Josephson junction is replaced by two parallel Josephson junctions), or persistent current qubits, which include a superconducting loop interrupted by three Josephson junctions, and the like. See e.g., Mooij et al, 1999,  Science  285, 1036; and Orlando et al., 1999,  Phys. Rev . B 60, 15398. Other examples of superconducting qubits can be found, for example, in II&#39;ichev et al., 2003,  Phys. Rev. Lett.  91, 097906; Blatter et al., 2001,  Phys. Rev.  B 63, 174511, and Friedman et al., 2000,  Nature  406, 43. In addition, hybrid charge-phase qubits may also be used. 
     The qubits may include a corresponding local bias device. The local bias devices may include a metal loop in proximity to a superconducting qubit that provides an external flux bias to the qubit. The local bias device may also include a plurality of Josephson junctions. Each superconducting qubit in the quantum processor may have a corresponding local bias device or there may be fewer local bias devices than qubits. In some embodiments, charge-based readout and local bias devices may be used. The readout device(s) may include a plurality of dc-SQUID magnetometers, each inductively connected to a different qubit within a topology. The readout device may provide a voltage or current. The dc-SQUID magnetometers including a loop of superconducting material interrupted by at least one Josephson junctions are well known in the art. 
     Quantum Processor 
     A computer processor may take the form of an analog processor, for instance a quantum processor such as a superconducting quantum processor. A superconducting quantum processor may include a number of qubits and associated local bias devices, for instance two or more superconducting qubits. Further detail and embodiments of exemplary quantum processors that may be used in conjunction with the present systems, methods, and apparatus are described in US Patent Publication No. 2006-0225165 and US Provisional Patent Application Ser. No. 60/872,414 filed Jan. 12, 2007 and entitled “System, Devices and Methods for Interconnected Processor Topology.” 
     A superconducting quantum processor may include a number of coupling devices operable to selectively couple respective pairs of qubits. Examples of superconducting coupling devices include rf-SQUIDs and dc-SQUIDs, which couple qubits together by flux. SQUIDs include a superconducting loop interrupted by one Josephson junction (an rf-SQUID) or two Josephson junctions (a dc-SQUID). The coupling devices may be capable of both ferromagnetic and anti-ferromagnetic coupling, depending on how the coupling device is being utilized within the interconnected topology. In the case of flux coupling, ferromagnetic coupling implies that parallel fluxes are energetically favorable and anti-ferromagnetic coupling implies that anti-parallel fluxes are energetically favorable. Alternatively, charge-based coupling devices may also be used. Other coupling devices can be found, for example, in US Patent Publication No. 2006-0147154 and U.S. Provisional Patent Application 60/886,253 filed Jan. 23, 2007, entitled “SYSTEMS, DEVICES, AND METHODS FOR CONTROLLABLY COUPLING QUBITS.” Respective coupling strengths of the coupling devices may be tuned between zero and a maximum value, for example, to provide ferromagnetic or anti-ferromagnetic coupling between qubits. 
     BRIEF SUMMARY 
     At least one embodiment may be summarized as a multi-chip processor including a first plurality of quantum devices carried by a first substrate; a second plurality of quantum devices carried by a second substrate; and a multi-substrate couplable quantum device coupled to a first quantum device of the first plurality of quantum devices and a second quantum device of the second plurality of quantum devices. At least one of a quantum device from the first plurality of quantum devices, a quantum device from the second plurality of quantum devices and the multi-substrate couplable quantum device may be a loop of superconducting material interrupted by at least one Josephson junction. The multi-substrate couplable quantum device may be configured to entangle the first quantum device of the first plurality of quantum devices with the second quantum device of the second plurality of quantum devices. 
     The multi-substrate couplable quantum device may include a first portion, a second portion and a third portion, the first portion of the multi-substrate couplable quantum device carried by the first substrate; the second portion of the multi-substrate couplable quantum device carried by the second substrate; and the third portion of the multi-substrate couplable quantum device that superconductingly connects the first portion to the second portion. The third portion may include at least two superconducting solder bumps situated between the first substrate and the second substrate. The third portion may further include at least two superconducting vias situated within the second substrate. The third portion may include superconducting wires within a multi-chip module. The first portion may be coupled to the first quantum device of the first plurality of qubits and the second portion is coupled to the second quantum device of the second plurality of qubits. 
     The multi-substrate couplable quantum device may be carried by the first substrate and wherein a first magnetic flux inductor is configured to couple flux from the multi-substrate couplable quantum device to a second magnetic flux inductor from the second quantum device of the second plurality of quantum devices. Each quantum device in at least one of the first plurality of quantum devices and the second plurality of quantum devices may be selected from the group consisting of: a qubit and a qubit coupler. The multi-substrate couplable quantum device may be a qubit. The qubit may be a superconducting flux qubit comprising a loop of superconducting material interrupted by at least one Josephson junction. The multi-substrate couplable quantum device may be a qubit coupler. The qubit coupler may be a superconducting flux qubit coupler comprising a loop of superconducting material interrupted by at least one Josephson junction. 
     The first substrate and the second substrate may be packaged within a multi-chip module. The first substrate may be packaged within a first multi-chip module and the second substrate is packaged within a second multi-chip module. The first multi-chip module may be stacked on the second multi-chip module. 
     The multi-chip processor may further include a second multi-substrate couplable quantum device coupled to a third quantum device of the first plurality of quantum devices and a fourth quantum device of the second plurality of quantum devices. 
     At least one embodiment may be summarized as a method of exchanging quantum information between a first plurality of quantum devices and a second plurality of quantum devices including coupling a multi-substrate couplable quantum device to the first quantum device from a first plurality of quantum devices carried by a first substrate; and coupling the multi-substrate couplable quantum device to the second quantum device from a second plurality of quantum devices carried by a second substrate. Coupling a multi-substrate couplable quantum device to the first quantum device from a first plurality of quantum devices carried by a first substrate may include threading the first quantum device with magnetic flux produced by current flowing within the multi-substrate couplable quantum device and threading the multi-substrate couplable quantum device with magnetic flux produced by current flowing within the first quantum device. Coupling a multi-substrate couplable quantum device to the second quantum device from a second plurality of quantum devices carried by a second substrate may include threading the second quantum device with magnetic flux produced by current flowing within the multi-substrate couplable quantum device and threading the multi-substrate couplable quantum device with magnetic flux produced by current flowing within the second quantum device. Coupling a multi-substrate couplable quantum device to the first quantum device may include coupling the multi-substrate couplable quantum device to one of a first qubit or a first qubit coupler and coupling the multi-substrate couplable quantum device to the second quantum device includes coupling the multi-substrate couplable quantum device to one of a second qubit or a second qubit coupler. 
     The multi-substrate couplable quantum device may be a multi-substrate coupler qubit further including entangling the first and second qubits via the multi-substrate couplable qubit. The multi-substrate couplable qubit may be a superconducting flux qubit comprising a loop of superconducting material interrupted by at least one Josephson junction. 
     The multi-substrate couplable quantum device may a multi-substrate couplable qubit coupler further including entangling the first and the second quantum devices via the multi-substrate couplable qubit coupler. The multi-substrate couplable qubit coupler is a superconducting flux qubit coupler may include a loop of superconducting material interrupted by at least one Josephson junction. At least one of the first quantum device from the first plurality of quantum devices, a quantum device from the second plurality of quantum devices and the multi-substrate couplable quantum device may be a loop of superconducting material interrupted by at least one Josephson junction. 
     The method may further include entangling the first quantum device of the first plurality of quantum devices and the second quantum device of the second plurality of quantum devices via the multi-substrate couplable quantum device. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S) 
       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. 
         FIG. 1A  is a schematic diagram of a quantum processor according to one illustrated embodiment. 
         FIG. 1B  is a cross-sectional view of a portion of the quantum processor of  FIG. 1A  taken along a section line  1 B- 1 B. 
         FIG. 2A  is a schematic diagram of a quantum processor according to another illustrated embodiment. 
         FIG. 2B  is a cross-sectional view of a portion of a quantum processor of  FIG. 2A  taken along section line  2 B- 2 B. 
         FIG. 2C  is a cross-sectional view of a portion of a quantum processor of  FIG. 2A  taken along section line  2 B- 2 B according to yet another illustrated embodiment. 
         FIG. 2D  is a cross-sectional view of a portion of a quantum processor of  FIG. 2A  taken along section line  2 B- 2 B according to a further illustrated embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     For quantum computers to be scalable, coupling of qubits over more than one substrate may be required. Chip substrates of approximately 2 cm×2 cm may hold approximately 4000 physical qubits. If more than 4000 physical qubits are required to encode a problem, multiple chip substrates may be placed in close proximity to each other to facilitate the coupling of qubits carried by the multiple chip substrates. When two qubits from different respective chip substrates are coupled together, quantum information may pass from each coupled qubit, despite being carried by two different chip substrates. 
     Miyazaki et al., IEEE Transactions on Applied Superconductivity, Vol. 17, No. 2, 2007 discusses separating SFQ circuitry, carried by a first substrate, from superconducting quantum bits comprising Josephson junctions, carried by a second substrate, due to relatively high heat production inherent to SFQ circuits. If heat is present while the quantum bits of Miyazaki et al. operate, the decoherence time of the quantum bits will reduce thereby reducing the amount of time available to compute with the quantum bits. The superconducting quantum bits of Miyazaki et al. are all carried by a single substrate. No quantum information is passed between chip substrates; only classical information is transmitted from the SFQ circuitry to the superconducting quantum bits. 
     Passing quantum information between substrates opens up new scaling possibilities to quantum processor designers. Quantum information, however, is very susceptible to noise or decoherence. Decoherence occurs when a system interacts with its environment, or any complex external system, in such a thermodynamically irreversible way that ensures different elements in the quantum superposition is lost thereby losing quantum information. Proper shielding must be used to isolate the quantum processor from external magnetic fields of its environment. While superconducting shielding incorporated into the printed circuit board or substrate of a quantum processor chip, as discussed by U.S. Ser. No. 11/948,817, may limit magnetic field interactions on-chip, such superconducting shielding may not effectively shield the devices which pass quantum information between chip substrates. External magnetic shielding, as is described in, e.g., U.S. Ser. No. 60/981,763 and U.S. Ser. No. 60/984,321, may be used to limit magnetic field strengths in the vicinity of the quantum processor. 
     Heat is also a consideration when dealing with decoherence of quantum bits and quantum and classical information the quantum bits hold. The presence of heat may cause decoherence in quantum processors. While the programming of the quantum processor is likely to produce heat, such as with the use of SFQ circuitry or other types of programmable devices as is described in, e.g., U.S. Ser. No. 11/950,276, depending upon how the quantum processor is operated the quantum processor may be able to allow the heat produced during programming to dissipate and not affect the information held by the quantum bits. 
     Interconnected processor topologies have been described in, e.g., U.S. Publication No. 2006/0225165, U.S. Ser. No. 60/956,104 and U.S. Ser. No. 60/986,554. Each of the interconnected processor topologies allows for scalability of an interconnected topology upon one chip substrate. If about 4000 qubits can be carried by one substrate, for a quantum processor to incorporate more than 4000 qubits, multiple chip substrates may be coupled together. While it may be possible to employ larger chip substrates, the probability of defect may increase as a function of the number of individual qubits increases. A single defect may, in some situations, render the entire chip substrate or a portion of the entire chip defective. Thus, the use of multiple chip substrates of a relatively smaller size may be preferred to the use of a single, larger chip substrate. 
       FIG. 1A  depicts a quantum processor  100  according to one illustrated embodiment. A multichip module (MCM)  110  has sixteen discrete substrates  120   a - 120   p  (collectively  120 ) packaged in such a way as to facilitate substrates  120  use as a single quantum processor  100 . MCM  110  may be stacked in a vertical configuration with additional MCMs of similar configurations, making the stacked MCM footprint smaller than would have been required for a given number of substrates  120  packaged carried by a single MCM  110  (albeit at the cost of a thicker or taller quantum processor  100 ). This may allow for large numbers of substrates  120  to exist within a small footprint. While sixteen substrates  120  are shown in  FIG. 1A , any number of substrates  120  may be designed into a MCM  110 . 
       FIG. 1B  shows substrates  120   a - 120   d  carried by MCM  110 . An interconnect  130   ab  is used to transmit quantum information between at least one device from substrate  120   a  and at least one device from substrate  120   b . An interconnect  130   bc  is used to transmit quantum information between at least one device from substrate  120   b  and at least one device from substrate  120   c . An interconnect  130   cd  is used to transmit quantum information between at least one device from substrate  120   c  and at least one device from substrate  120   d.    
     Interconnect  130   ab ,  130   bc ,  130   cd  may be a quantum device or a portion of a quantum device. A quantum devices may be a qubit, such as superconducting qubit which may be a loop of superconducting material interrupted by at least one Josephson junction or compound Josephson junction, or a qubit coupler, such as a superconducting qubit coupler which may be loops of superconducting material interrupted by at lest one Josephson junction or compound Josephson junction. For discussions of coupling devices, see, e.g., U.S. Publication No. 2006/0147154, U.S. Patent Ser. No. 60/886,253, U.S. Patent Ser. No. 60/915,657, U.S. Ser. No. 60/975,083 and Maassen van den Brink et al.,  New J. Phys.  7 (November 2005) 230. 
     Interconnect  130   ab  may be two superconducting wires which connect two sections of a multi-substrate quantum device to form a loop, wherein a first section of the multi-substrate quantum device carried by substrate  120   a  has a magnetic flux inductor coupled to a first quantum device carried by substrate  120   a  and a second section of the multi-substrate quantum device carried by substrate  120   b  has a second magnetic flux inductor coupled to a second quantum device carried by substrate  120   b . At least one Josephson junction or compound Josephson junction may interrupt the loop of superconducting material comprising the first section of the multi-substrate quantum device, the two wires of interconnect  130   ab  and the second section of the multi-substrate quantum device. 
     Interconnect  130   bc  may be two superconducting wires which connect two sections of a multi-substrate quantum device to form a loop, wherein a first section of the multi-substrate quantum device carried by substrate  120   b  has a magnetic flux inductor coupled to a first quantum device carried by substrate  120   b,  and a second section of the multi-substrate quantum device carried by substrate  120   c  has a second magnetic flux inductor coupled to a second quantum device carried by substrate  120   c . At least one Josephson junction or compound Josephson junction may interrupt the loop of superconducting material comprising the first section of the multi-substrate quantum device, the two wires of interconnect  130   bc  and the second section of the multi-substrate quantum device. 
     Interconnect  130   cd  may be two superconducting wires which connect two sections of a multi-substrate quantum device to form a loop, wherein a first section of the multi-substrate quantum device carried by substrate  120   c  has a magnetic flux inductor coupled to a first quantum device carried by substrate  120   c,  and a second section of the multi-substrate quantum device carried by substrate  120   d  has a second magnetic flux inductor coupled to a second quantum device carried by substrate  120   d . At least one Josephson junction or compound Josephson junction may interrupt the loop of superconducting material comprising the first section of the multi-substrate quantum device, the two wires of interconnect  130   cd  and the second section of the multi-substrate quantum device. 
     There may be an interconnect between each pair of substrates in quantum processor  100  such that each substrate  120  is connected to every other substrate  120  carried by MCM  110 . There may be an interconnect between each pair of adjacent substrates (i.e., nearest and next-nearest neighbors) in quantum processor  100 , such that, for example, substrate  120   m  is connected to substrate  120   i , substrate  120   j , and substrate  120   n . There may be an interconnect between each pair of substrates in a quantum processor which share a side (i.e., nearest neighbors), such that, for example, substrate  120   m  is coupled to substrate  120   i  and substrate  120   n.    
       FIG. 2A  depicts a quantum processor  200  according to another illustrated embodiment. The stacked multi-chip arrangement depicted in  FIG. 2A  has five substrates  210   a - 210   e  (collectively  210 ) arranged in two levels, where the first level has substrates  210   a - 210   d  and the second level has substrate  210   e , to facilitate use of substrates  210  as a single quantum processor  200 . Additional levels may be stacked vertically. This may allow for large numbers of substrates  210  to exist within a fairly small footprint with a tighter packing than is available with a MCM. While four substrates  210   a - 210   d  are shown in the first level and one substrate  210   e  is shown in the second level of  FIG. 1A , any number of substrates  210  may be designed into the first level and/or the second level. Quantum devices  220   a - 1  and  220   a - 2  are carried by substrate  210   a . Quantum devices  220   b - 1  and  220   b - 2  are carried by substrate  210   b . Each substrate  210  may carry a respective plurality of quantum devices  220 . 
       FIG. 2B  shows the quantum processor  200  of  FIG. 2A  with substrate  210   a , substrate  210   b  and substrate  210   e  coupled such that quantum information may be transferred from substrate  210   a  to substrate  210   e , from substrate  210   e  to substrate  210   a , from substrate  210   b  to substrate  210   e , and from substrate  210   e  to substrate  210   b . Quantum device  220   a - 2  is coupled to quantum device  220   a - 1  such that the state of quantum device  220   a - 2  may affect the state of quantum device  220   a - 1  and the state of quantum device  220   a - 1  may affect the state of quantum device  220   a - 2 . Quantum device  220   a - 1  and quantum device  220   a - 2  are both carried by substrate  210   a . Quantum device  220   b - 1  and quantum device  220   b - 2  are both carried by substrate  210   b . Quantum device  220   b - 2  is coupled to quantum device  220   b - 1  such that the state of quantum device  220   b - 2  may affect the state of quantum device  220   b - 1  and the state of quantum device  220   b - 1  may affect the state of quantum device  220   b - 2 . Quantum device  220   e - 1  and quantum device  220   e - 2  are both carried by substrate  210   e . Quantum device  220   e - 2  is coupled to quantum device  220   e - 1  such that the state of quantum device  220   e - 2  may affect the state of quantum device  220   e - 1  and the state of quantum device  220   e - 1  may affect the state of quantum device  220   e - 2 . Superconducting solder bumps  240   ae - 1  and  240   ae - 2  (collectively  240   ae ) may be used to connect quantum device  220   a - 1  with quantum device  220   e - 1  such that quantum device  220   a - 1 , solder bumps  240   ae , and quantum device  220   e - 1  collectively form a loop of superconducting material interrupted by at least one Josephson junction. Quantum device  220   a - 2  and quantum device  220   e - 2  may be quantum mechanically coupled to and entangled with each other, wherein quantum information passes between quantum device  220   a - 2  and quantum device  220   e - 2  though quantum device  220   a - 1 , solder bumps  240   ae  and quantum device  220   e - 1 . Superconducting solder bumps  240   be - 1  and  240   be - 2  (collectively  240   be ) may be used to connect quantum device  220   b - 1  with quantum device  220   e - 2  such that quantum device  220   b - 1 , solder bumps  240   be , and quantum device  220   e - 2  collectively form a loop of superconducting material interrupted by at least one Josephson junction. Quantum device  220   b - 2  and quantum device  220   e - 1  may be quantum mechanically coupled to and entangled with each other, wherein quantum information passes between quantum device  220   b - 2  and quantum device  220   e - 1  though quantum device  220   b - 1 , solder bumps  240   be  and quantum device  220   e - 2 . For a description of the transmission of single flux quantum (digital information) between superconducting chips, see, e.g., U.S. Pat. No. 6,678,540. 
     Quantum devices may be qubits, such as superconducting qubits which may be loops of superconducting material interrupted by at least one Josephson junction or compound Josephson junction, or qubit couplers, such as superconducting qubit couplers which may be loops of superconducting material interrupted by at lest one Josephson junction or compound Josephson junction. There may be many superconducting solder bumps  240   ae  coupling the quantum devices carried by substrate  210   a  and substrate  210   e , such that quantum information may transmit between quantum devices carried by substrate  210   a  and quantum devices carried by substrate  210   e . There may be many superconducting solder bumps  240   be  coupling the quantum devices carried by substrate  210   b  and substrate  210   e , such that quantum information may transmit between quantum devices carried by substrate  210   b  and quantum devices carried by substrate  210   e.    
     Superconducting solder bumps  240   ae - 1  and  240   ae - 2  may connect two sections of a multi-substrate quantum device together to form a loop, wherein a first section of the multi-substrate quantum device is carried by substrate  210   a  and has a magnetic flux inductor coupled to a first quantum device carried by substrate  210   a  and a second section of the multi-substrate quantum device carried by substrate  210   e  and has a magnetic flux inductor coupled to a second quantum device carried by substrate  210   e . At least one Josephson junction, such as a compound Josephson junction, may interrupt the loop of superconducting material comprising the first section of the multi-substrate quantum device, the superconducting solder bumps  240   ae - 1  and  240   ae - 2  and the second section of the multi-substrate quantum device. 
     Superconducting solder bumps  240   be - 1  and  240   be - 2  may connect two sections of a multi-substrate quantum device together to form a loop, wherein a first section of the multi-substrate quantum device is carried by substrate  210   b  and has a magnetic flux inductor coupled to a first quantum device carried by substrate  210   b  and a second section of the multi-substrate quantum device carried by substrate  210   e  and has a magnetic flux inductor coupled to a second quantum device carried by substrate  210   e . At least one Josephson junction, such as a compound Josephson junction, may interrupt the loop of superconducting material comprising the first section of the multi-substrate quantum device, the superconducting solder bumps  240   be - 1  and  240   be - 2  and the second section of the multi-substrate quantum device. 
       FIG. 2C  shows a portion of a quantum processor according to another illustrated embodiment where substrate  210   a , substrate  210   b  and substrate  210   e  are coupled such that quantum information may be transferred from substrate  210   a  to substrate  210   e , from substrate  210   e  to substrate  210   a,  from substrate  210   b  to substrate  210   e , and from substrate  210   e  to substrate  210   b.  A quantum device  220   a - 2  is coupled to a quantum device  220   a - 1 , and both quantum device  220   a - 1  and quantum device  220   a - 2  are carried by substrate  210   a.  Quantum device  220   a - 2  is coupled to quantum device  220   a - 1  such that the state of quantum device  220   b - 2  may affect the state of quantum device  220   a - 1  and the state of quantum device  220   b - 1  may affect the state of quantum device  220   b - 2 . A quantum device  220   b - 2  is coupled to a quantum device  220   b - 1 , and both quantum device  220   b - 1  and quantum device  220   b - 2  are carried by substrate  210   b.  Quantum device  220   b - 2  is coupled to quantum device  220   b - 1  such that the state of quantum device  220   b - 2  may affect the state of quantum device  220   b - 1  and the state of quantum device  220   b - 1  may affect the state of quantum device  220   b - 2 . A quantum device  220   e - 2  is coupled to a quantum device  220   e - 1 , and both quantum device  220   e - 1  and quantum device  220   e - 2  are carried by substrate  210   e.  Quantum device  220   e - 2  is coupled to quantum device  220   e - 1  such that the state of quantum device  220   e - 2  may affect the state of quantum device  220   e - 1  and the state of quantum device  220   e - 1  may affect the state of quantum device  220   e - 2 . Magnetic flux  250   ae  may be used to couple quantum device  220   a - 1  and quantum device  220   e - 1  such that quantum device  220   a - 1  and quantum device  220   e - 1  may be quantum mechanically coupled to and entangled with each other, and wherein quantum information may pass between quantum device  220   a - 1  and quantum device  220   e - 1 . A magnetic flux inductor from each quantum device  220   e - 1  and quantum device  220   a - 1  may be coupled together to allow for flux from quantum device  220   a  to thread into quantum device  220   e  and flux from quantum device  220   e  to thread into quantum device  220   a . Magnetic flux  250   be  may be used to couple quantum device  220   b - 1  and quantum device  220   e - 2  such that quantum device  220   b - 1  and quantum device  220   e - 2  may be quantum mechanically coupled to and entangled with each other, and wherein quantum information may pass between quantum device  220   b - 1  and quantum device  220   e - 2 . A magnetic flux inductor from each quantum device  220   e - 2  and quantum device  220   b - 1  may be coupled together to allow for flux from quantum device  220   b  to thread into quantum device  220   e  and flux from quantum device  220   e  to thread into quantum device  220   b.    
     Quantum devices may be qubits, such as superconducting qubits which may be loops of superconducting material interrupted by at least one Josephson junction or compound Josephson junction, or qubit couplers, such as superconducting qubit couplers which may be loops of superconducting material interrupted by at lest one Josephson junction or compound Josephson junction. 
       FIG. 2D  shows a portion of a quantum processor according to a further illustrated embodiment where substrate  210   a , substrate  210   b  and substrate  210   e  are coupled such that quantum information may be transferred from substrate  210   a  to substrate  210   e , from substrate  210   e  to substrate  210   a , from substrate  210   b  to substrate  210   e , and from substrate  210   e  to substrate  210   b.  Superconducting vias  230   e - 1  to  230   e - 4  may be used to transfer quantum information from substrate  210   a  to substrate  210   e , from substrate  210   e  to substrate  210   a , from substrate  210   b  to substrate  210   e , and from substrate  210   e  to substrate  210   b . A quantum device  220   a - 2  is coupled to a quantum device  220   a - 1 , and both quantum device  220   a - 1  and quantum device  220   a - 2  are carried by substrate  210   a . Quantum device  220   a - 2  is coupled to quantum device  220   a - 1  such that the state of quantum device  220   b - 2  may affect the state of quantum device  220   a - 1  and the state of quantum device  220   b - 1  may affect the state of quantum device  220   b - 2 . A quantum device  220   b - 2  is coupled to a quantum device  220   b - 1 , and both quantum device  220   b - 1  and quantum device  220   b - 2  are carried by substrate  210   b . Quantum device  220   b - 2  is coupled to quantum device  220   b - 1  such that the state of quantum device  220   b - 2  may affect the state of quantum device  220   b - 1  and the state of quantum device  220   b - 1  may affect the state of quantum device  220   b - 2 . Superconducting solder bumps  240   ae - 1  and  240   ae - 2  (collectively  240   ae ) may be used to connect quantum device  220   a - 1  with quantum device  220   e - 1  such that quantum device  220   a - 2  and quantum device  220   e - 2  may be quantum mechanically coupled to and entangled with each other, wherein quantum information passes between quantum device  220   a - 2  and quantum device  220   e - 2  though quantum device  220   a - 1 , solder bumps  240   ae  and quantum device  220   e - 1 . Superconducting solder bumps  240   be - 1  and  240   be - 2  (collectively  240   be ) may be used to connect quantum device  220   b - 1  with quantum device  220   e - 2  such that quantum device  220   b - 2  and quantum device  220   e - 1  may be quantum mechanically coupled to and entangled with each other, wherein quantum information passes between quantum device  220   b - 2  and quantum device  220   e - 1  though quantum device  220   b - 1 , solder bumps  240   be  and quantum device  220   e - 2 . Superconducting solder bumps  240   ae - 1  and  240   ae - 2  (collectively  240   ae ) may be used to connect quantum device  220   a - 1  and quantum device  220   e - 1 , through superconducting backside vias  230   e - 1  and  230   e - 2 , such that quantum device  220   a - 2  and quantum device  220   e - 2  may be quantum mechanically coupled to and entangled with each other, wherein quantum information passes between quantum device  220   a - 2  and quantum device  220   e - 2 . Superconducting solder bumps  240   be - 1  and  240   be - 2  (collectively  240   be ) may be used to connect quantum device  220   b - 1  and quantum device  220   e - 1 , through superconducting backside vias  230   e - 3  and  230   e - 4 , such that quantum device  220   b - 1 , solder bumps  240   be , superconducting backside vias  230   e - 3  and  230   e - 4 , and quantum device  220   e - 2  collectively form a loop of superconducting material interrupted by at least one Josephson junction. Quantum device  220   b - 2  and quantum device  220   e - 1  may be quantum mechanically coupled to and entangled with each other, wherein quantum information passes between quantum device  220   b - 2  and quantum device  220   e - 1 . For a description of the transmission of single flux quantum (digital information) between superconducting chips, see, e.g., U.S. Pat. No. 6,678,540. 
     Quantum devices may be qubits, such as superconducting qubits which may be loops of superconducting material interrupted by at least one Josephson junction or compound Josephson junction, or qubit couplers, such as superconducting qubit couplers which may be loops of superconducting material interrupted by at lest one Josephson junction or compound Josephson junction. There may be many superconducting solder bumps  240   ae  coupling the quantum devices carried by substrate  210   a  and substrate  210   e  and/or superconducting backside vias  230   e - 1  and  230   e - 2  within substrate  210   e  such that quantum information may transmit between quantum devices carried by substrate  210   a  and quantum devices carried by substrate  210   e . There may be many superconducting solder bumps  240   be  coupling the quantum devices carried by substrate  210   b  and substrate  210   e  and/or superconducting backside vias  230   e - 3  and  230   e - 4  within substrate  210   e  such that quantum information may transmit between quantum devices carried by substrate  210   b  and quantum devices carried by substrate  210   e.    
     Superconducting solder bumps  240   ae - 1  and  240   ae - 2  may connect two sections of a multi-substrate quantum device together to form a loop, wherein a first section of the multi-substrate quantum device is carried by substrate  210   a  and has a magnetic flux inductor coupled to a first quantum device carried by substrate  210   a  and a second section of the multi-substrate quantum device is carried by substrate  210   e  and has a magnetic flux inductor coupled to a second quantum device carried by substrate  210   e . Superconducting backside vias  230   e - 1  and  230   e - 2  connect the second section of the multi-substrate quantum device to the superconducting solder bumps  240   ae . At least one Josephson junction, such as a compound Josephson junction, may interrupt the loop of superconducting material comprising the first section of the multi-substrate quantum device, the superconducting backside vias  230   e - 1  and  230   e - 2 , the superconducting solder bumps  240   ae - 1  and  240   ae - 2  and the second section of the multi-substrate quantum device. 
     Superconducting solder bumps  240   be - 1  and  240   be - 2  may connect two sections of a multi-substrate quantum device together to form a loop, wherein a first section of the multi-substrate quantum device is carried by substrate  210   b  and has a magnetic flux inductor coupled to a first quantum device carried by substrate  210   b  and a second section of the multi-substrate quantum device is carried by substrate  210   e  and has a magnetic flux inductor coupled to a second quantum device carried by substrate  210   e . Superconducting backside vias  230   e - 3  and  230   e - 4  connect the second section of the multi-substrate quantum device to the superconducting solder bumps  240   be . At least one Josephson junction, such as a compound Josephson junction, may interrupt the loop of superconducting material comprising the first section of the multi-substrate quantum device, the superconducting backside vias  230   e - 3  and  230   e - 4 , the superconducting solder bumps  240   be - 1  and  240   be - 2  and the second section of the multi-substrate quantum device. 
     As used herein, the term “carried by” and variations thereof such as “carries” or “carrying” means that the quantum device is supported on, in or formed as part of the substrate. 
     The above description of illustrated embodiments, including what is described in the Abstract, is not intended to be exhaustive or to limit the embodiments to the precise forms disclosed. Although specific embodiments of and examples are described herein for illustrative purposes, various equivalent modifications can be made without departing from the spirit and scope of the disclosure, as will be recognized by those skilled in the relevant art. The teachings provided herein of the various embodiments can be applied to other quantum processors and systems, not necessarily the exemplary quantum processors and systems generally described above. 
     For instance, the foregoing detailed description has set forth various embodiments of the devices and/or processes via the use of block diagrams, schematics, and examples. Insofar as such block diagrams, schematics, and examples contain one or more functions and/or operations, it will be understood by those skilled in the art that each function and/or operation within such block diagrams, flowcharts, or examples can be implemented, individually and/or collectively, by a wide range of hardware, software, firmware, or virtually any combination thereof. The present subject matter may, for example, be implemented via Application Specific Integrated Circuits (ASICs). 
     The various embodiments described above can be combined to provide further embodiments. All of the U.S. patents, U.S. patent application publications, U.S. patent applications, foreign patents, foreign patent applications and non-patent publications referred to in this specification and/or listed in the Application Data Sheet, including but not limited to U.S. Pat. No. 6,838,694, U.S. Patent Publication No. 2005-0082519, US Patent Publication Number 2006-0225165, U.S. Provisional Patent Application Ser. No. 60/872,414 filed Jan. 12, 2007, entitled “System, Devices and Methods for Interconnected Processor Topology”, U.S. Provisional Patent Application Ser. No. 60/956,104 filed Aug. 15, 2007 and entitled “Systems, Devices, and Methods for Interconnected Processor Topology”, U.S. Patent Publication Number 2006-0147154, U.S. Provisional Patent Application Ser. No. 60/886,253 filed Jan. 23, 2007 and entitled “Systems, Devices, and Methods for Controllably Coupling Qubits”, U.S. Provisional Patent Application Ser. No. 60/981,764, filed Oct. 22, 2007, entitled “Systems, Methods and Apparatus for Electronic Filters,” U.S. Provisional Patent Application Ser. No. 60/979,031, filed Oct. 10, 2007, entitled “Systems, Methods and Apparatus for Multilayer Superconducting Printed Circuit Boards,” and U.S. Provisional Patent Application Ser. No. 60/881,358 filed Jan. 18, 2007 and entitled “Input/Output System and Devices for Use with Superconducting Based Computing Systems,” are incorporated herein by reference, in their entirety. Aspects of the embodiments can be modified, if necessary, to employ systems, circuits and concepts of the various patents, applications and publications to provide yet further embodiments. 
     These and other changes can be made to the embodiments in light of the above-detailed description. In general, in the following claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and the claims, but should be construed to include all possible embodiments along with the full scope of equivalents to which such claims are entitled. Accordingly, the claims are not limited by the disclosure.