RELATED APPLICATIONS

[00Q1J This application claims priority from U.S. Patent Application Serial

No. 16/012543, filed 19 June 2018, which is incorporated herein in its entirety.

GOVERNMENT LICENSE RIGHTS

[0002] This invention was made with Government support under Contract No. 30059298.

The government has certain rights in this invention.

TECHNICAL FIELD

[0003] The present invention relates generally to quantum and classical digital superconducting circuits, and specifically to reconfigurahle quantum routing.

BACKGROUND

[0004] A fundamental challenge for quantum computation and simulation is to construct a large-scale syste of highly connected coherent qubits to perform various operations.

Superconducting qubits utilize macroscopic circuits to process quantum information and are a promising candidate towards this end. Recently, materials research and circuit optimization has led to significant progress in qubit coherence. Superconducting qubits can now perform hundreds of operations within their coherence times, allowing for research into complex algorithms such as error correction. In many applications, it is desirable to combine these high- coherence qubits with tunable inter-qubit coupling, since it would allow for both coherent local operations and dynamically varying qubit interactions. For quantum computation, this would provide isolation for single-qubit gates while at the same time enabling fast two-qubit gates that minimize errors from decoherence. SUMMARY

[0005] One example includes a reconfigurable quantum router system The system includes first, second, and third quantum objects respectively connected to first, second, and third ports of a quantum router. The quantum router includes two variable-inductance coupling elements each in an RF-SQUID, at least two of the variable-inductance coupling elements being connected to at least one shared inductor such that their respective RF-SQUIDs share the inductor in common. The quantum router further includes first and second control flux lines, wherein one of the flux control lines is configured to inductively provide a static current to at least two of the variable-inductance coupling elements and the other of the control flux lines is configured to provide a dynamic current to at least two of the variable-inductance coupling elements The quantum router further includes first, second, and third resonators by which the first, second, and third quantum objects are respectively each connected to at least one of the RF- SQUIDs, such that each quantum object can be placed arbitrarily distantly from the RF-SQUIDs on a chip. Actuation of the direction of the dynamic current couples at least the first quantum object to only one of the first or second quantum objects based on the dynamic current direction to provide reconfigurable quantum routing.

[0006] Another example includes a method of reconfigurable quantum routing. A static control signal is provided to one of a first flux line that is inductively coupled to two

RF-SQUIDs via at least one common inductor to induce a current split between variable inductance coupling elements in respective ones of the RF-SQUIDs, or a second flux line that is inductively coupled to at least two RF-SQUIDs via other inductors in each of them. A dynamic control signal is provided to the other of the first flux line or the second flux line, such that the difference between induced common flux current and induced dynamic flux current places at least one of the variable inductance coupling elements in one of a high or low inductance state and places at least another of the variable inductance coupling elements in the other of the high or low inductance state. The direction of the dynamic control signal is actuated to couple at least a first quantum object (e.g , a qubit) to only one of at least two other quantum objects, based on the dynamic control signal direction. [0007] Yet another example includes a reconfigurable quantu router. The quantum router includes first, second, and third ports each coupleable to a respective qubit, and first, second, and third resonators each respectively connected between the first, second, and third ports and an RF-SQUID bridge. The RF-SQUID bridge includes a first Josephson junction connected between the first resonator and the second resonator, and a second Josephson junction connected between the first resonator and the third resonator. First and second flux lines are arranged to switch the inductance of the Josephson junctions between high and low inductance states to selectively couple or uncouple qubits connected to the ports.

BRIEF DESCRIPTION OF THE DRAWINGS

[0008] FIG. 1 A is a block diagram of an example reconfigurable quantum router system.

[0009] FIG. IB is a diagram showing both of two alternate routing states of a first example reconfigurable quantum router.

[0010] FIG. 1C is a diagram showing a first of two alternate routing states of a second example reconfigurable quantum router (a“bar” state).

[0011] FIG. ID is a diagram showing a second of two alternate routing states of the second example reconfigurable quantum router (a“cross” state).

[0012] FIG. 2 is a circuit diagram of an example reconfigurable quantum router.

[0013] FIG. 3 is a diagram showing hybridized resonators producing frequency-split even and odd modes.

[0014] FIG. 4 is a logical-level quantum circuit illustration for a parity check operation between two logical qubits.

[0015] FIG. 5 is a quantum circuit segment illustration for the operation of FIG. 4.

[0016] FIG. 6 is a circuit diagram of an example reconfigurable quantum router.

[0017] FIG. 7 is an annotated logical-level quantum circuit illustration for Toffoli distillation.

[0018] FIGS. 8A, 8B, and 8C are flow charts illustrating example methods of reconfigurable quantum routing. DETAILED DESCRIPTION

[0019] Performing quantum algorithms on a physical quantum processor can present a challenge when different circuit blocks, which can be remotely located on the chip, need to interact sequentially with another circuit block. This situation may arise, for example, in performing parity check operations on a logical level, or in state distillation routines on both physical and logical levels. One challenge of routing of quantum information is that“signal path” (i.e., the connectivity) of quantum objects must be reconfigurable in real time,

[0020] A 2-port, tunable bus-mediated coupling that uses a radio frequency

superconducting quantum interference device (RF-SQUID) as a tunable coupling element embedded in the center point of a half-wave bus resonator is described in U.S. patent application publication No 2017/0212860 Al, which disclosure is herein incorporated by reference. The effecti ve coupling between a qubit connected to the Port 1 of the bus and a qubit connected to Port 2 of the bus is observable as a balance between two contributions (even and odd modes of the bus) having opposite signs and variable strengths. This coupling does not permit routing of quantum information between quantum objects, or for more than two quantum objects to be connected together to exchange information. Thus, even with such a coupling, connectivity between qubits is fixed in the design of the chip: although the strength of the coupling can be field- tunable, the topology of the circuit cannot be changed. As described herein, the sought- after real-time reconfigurability of quantum object connectivity can be provided with either or both of a single-pole double-throw switch and a cross-point switch.

[0021] Thus, this disclosure relates generally to reconfigurable quantum routing in superconducting circuits, for example, to provide reconfigurable connectivity between qubits or other quantum objects. This disclosure particularly provides both a single-pole double-throw switch and a cross-point switch for the connectivity configuration of a quantum circuit. In various examples, one or more variable inductance coupling elements are placed between qubits or other quantum objects that may reside in separate remote superconducting systems. The variable inductance coupling elements can each be adjusted between a strongly coupled state and a decoupled (or isolation) state between quantum objects in addition to various states of intermediate coupling strengths in between. In this manner, manipulation can be performed on state information of isolated qubits in a decoupled state, while this state information can be exchanged between qubits during a strongly coupled state, for example. Furthermore, state information can be manipulated and passed between qubits without destroying the state information of the originating qubit in an intermediate coupling strength state between qubits. In some examples, the variable inductance coupling elements can be Josephson junctions. Each variable inductance coupling element can be arranged as a single Josephson junction or a series array of N Josephson junctions, each having a critical current N times larger than the original (single) Josephson junction.

[0022] Some example reconfigurabie quantum routers can include one or more

Josephson junctions embedded at a dovetail node of a split half-wave resonator bus. The RF-SQUID facilitates bus-mediated dispersive interaction between connected qubits or other quantum objects for coupling. The advantage of bus-mediated coupling, as opposed to direct inductive coupling, is that the quantum objects can be physically placed remotely from each other, for example, in separate circuit blocks on the quantum processor chip. The advantage of a reconfigurabie quantum router is that it permits signals to be routed between quantum objects as desired and at the coupling or interaction strengths desired. Thus, for example, interaction strengths can be calibrated and trimmed in the field to compensate for variability in

manufacturing processes, and can be controlled in real time as part of a computation protocol.

[0023] FIG. 1 A illustrates an example superconducting system 100 with reconfigurabie quantum routing. The superconducting system 100 includes three or four quantum objects (e.g., qubits) 114, 116, 118, 120. As illustrated, one pair of quantum objects is connected on each side of router 102, but one side of router 102 may be connected to only one quantum object. Each quantum object can, for example, be part of a qubit system that belongs to a logical block that can perform different logical operations such as different gate operations, error correction operations, memory operations, or any of a variety of other superconducting operations.

Connections between the quantum objects 114, 116, 118, 120 can be bus-mediated, allowing the quantum objects 114, 1 16, 118, 120 to reside at arbitrarily distant parts of a chip on which they are fabricated, for example. Router 102 thus couples or uncouples the quantum objects via a reconfigurable RF-SQUID bridge 104 (consisting for example, of two or four RF-SQUIDs) and further via resonators (e.g., transmission lines) 106, 108, 110, 112. Router can thereby couple one quantum object (e.g., 114) to one of two other quantum objects (e.g., either of 118 or 120), as shown in FIG. I B, or can couple two quantum objects (e.g., 114, 1 16) to two other quantum objects (e.g., 118, 120) in bar or cross fashions, as shown in FIGS. 1C and ID, respectively. (In FIG. IB, the two broken lines in router 102 indicate alternate couplings, whereas those in FIG. 1C indicate simultaneous couplings, as do those in FIG. ID.)

[0024] Quantum router 102 can thus, for example, constitute a compound bus composed of three resonators (e.g., 106, 110, 112) and a two- Joseph son-junction coupler 104, or of four resonators (106, 108, 110, 112) and a four-Josephson-junction coupler 104, in either case having bias elements 122 (e.g., a static flux bias and a control flux) to activate the switching

functionality of the router 102. The system 100 can be implemented in any of a variety of superconducting circuit systems to provide coupling and decoupling between quantum objects. The signals between the coupled objects can be, for example, microwave signals that are implemented in a control scheme for a quantum circuit, such as performing a gate or a readout operation on a qubit, or to perform one of a variety of algorithms, such as those discussed herein. As another example, the signals can be a signal pulse, a communication signal, or a control command signal. The system 100 can operate at cryogenic temperatures, can dissipate substantially no power, and can be controlled with single flux quantum (SFQ) compatible signals.

[0025] System 100 can include a switch controller 124 and bias elements 122. The

RF-SQUID bridge 104 can employ variable inductance coupling elements controlled by magnetic flux via the bias elements 122 and the s which controller 124 to couple and decouple connected quantum objects based on a selected mode (i.e., between either of the modes depicted in FIG. I B, or between the modes separately depicted in FIGS. 1C and ID, depending on the configuration of the router 102). The variable inductance coupling elements can each include, for example, one or more Josephson junctions. The one or more Josephson junctions can have a first inductance when no current or a low current is induced in the respective RF-SQUID, and a second inductance when a current or a higher current is induced in the respective RF-SQUID that is at a predetermined threshold that generates or induces a flux, for example, greater than about 0.1 Fo and less than about 0.45 Fo, where Fo is equal to a flux quantum. The first such inductance (e.g., h!lelc, where h is Planck’s constant divided by 2p, e is electron charge and Ic is the critical current of the Josephson junction) can provide coupling between quantum objects, while the second such inductance (e.g., a large inductance value) can provide decoupling between the quantum objects.

[0026] FIG. 2 illustrates an example reconfigurable quantum router 200 arranged as a single-pole double-throw (SPOT) reconfigurable bus coupler, which can function, for example, as a one-to-two multiplexer. Resonators TL , TL ₂ , and TLa are coupleable via respective capacitors Ci, C ₂ and C ₃ to quantum objects (e.g., qubits) that can be connected at Ports 1-3 respectively. Each resonator can support coupling to a plurality of qubits, either capacitively, as illustrated in FIG. 2, or inductively, or combination of both, as described in U.S. patent

No. 9,501 748 which is herein incorporated by reference. Each of the resonators TL , TL ₂ , and TL ₃ can be, for example, a quarter-wave shorted transmission line resonator, configured such that resonator TLi and TL ₂ are both connected via RF-SQUID couplers to resonator TL ₃ . In the illustrated example, a first RF-SQUID is composed of Josephson junction Ji connected to inductors Li and L ₃ to form a first superconducting loop, and a second RF-SQUID is composed of Josephson junction J ₂ connected to inductors L ₂ and L ₃ to form a second superconducting loop, where both loops share a common inductor L ₃ . The Josephson inductance of each of the josephson junctions J and J ₂ is greater than the total linear inductance of the respective loops (i.e., L _{JI V'} Li l· L ₃ and L _J2 ^ L ₂ H- L3).

[0027] In circuit 200, Josephson junctions Ji and J ₂ function as variable inductance elements, as determined by the magnetic flux enclosed in each respective RF-SQUID loop.

When an RF-SQUID encloses a flux F _ON that is substantially zero, the inductance of the junction in the RF-SQUID has a value equal to h/2cl _c, where h is Planck’s constant divided by 2p, e is the electron charge, and I _c is the junction critical current. When the RF-SQUID encloses a flux ±F _ORR that is a significant fraction of ±Fo/2, e.g., greater than about 0.1 Fo and less than about 0.45 Fo, the inductance of the junction diverges. Therefore, when the RF-SQUID formed by Ji, Li, and U ₃ , encloses a flux F _ORR , the coupling between resonators TL _t and TL ₃ is essentially zero, and the qubits connected to the respective resonators do not interact (e.g. they do not exchange information). However when the same RF-SQUID encloses a flux Foc, the resonators TLi and TL ₃ become coupled with a coupling strength g _c , and hybridize to support two oscillation modes as shown in diagram 300 FIG. 3. The qubits that are connected to the respective resonators experience a non·· zero effective coupling, g _eff in FIG. 3. Similarly, the coupling between resonators TL ₂ and TL ₃ can be turned on or off based on a flux F _ON or F _ORR enclosed by the RF-SQUID formed by junction J ₂ and inductors L ₂ and L ₃ , and similarly the effective coupling between the qubits that connect to the respective resonators can be turned on or off.

[0028] The fluxes applied to the two RF-SQUIDs can be controlled via two flux-bias lines, indicated in FIG. 2 by differential flux line 202 (between nodes DF+ and DF-) and common flux line 204 (between nodes CF+ and CF-). A current flowing in the differential flux control line 202 induces a current in inductors Li and L ₂ through respective mutual inductances Mi and M ₂ . A current flowing in the common flux control line 204 induces a current in inductor L ₃ through mutual inductance M ₃ . The current induced in inductor L ₃ splits to flow through inductors L and L ₂ such that in one of the inductors the current adds to that induced by the differential flux control line, and in the other it subtracts. In other words, the two control currents can combine to produce any flux configuration in the two RF-SQUIDs. In particular, the common flux can be static and set at (F _ORR + F _ON ) /2 and the differential flux can be toggled between (F _ORT - F _ON ) /2 and -(O _OFF - F _ON ) /2, so that in a first configuration the first RF-SQUID encloses a total flux F _ON and the second RF-SQUID encloses a flux F _OGR , whereas in a second configuration the first RF-SQUID encloses a flux F _ORR while the second RF-SQUID encloses a flux F _ON . Therefore, in the first configuration qubits connected to TL ₃ have an effective coupling to qubits connected to TLi (but not to qubits connected to TL _2), whereas in the second configuration the qubits connected to TL ₃ have an effective coupling to those connected to TL ₂ (but not to qubits connected to TLi). The functionalities of common flux line 204 and differential flux line 202 can be interchanged, with differential line 202 being held static and common line 204 being toggled, to result in a circuit that functions similarly. In either case, because no net power is delivered between the ports, the functioning of circuit 200 differs from the actuation of a SPDT microwave switch to control deli very of microwave power in that circuit 200 can control an effective dispersive bus-mediated coupling between quantum objects without power delivery between ports.

[0029] Thus in an example functioning of circuit 200, two RF-SQUIDs commonly coupled by inductor L ₃ can be provided common flux via line 204 that yields an induced current coming out of inductor L ₃ that in turn is shared in opposite directions between Josephson junctions Ji and J ₂ . Such current is therefore either contributorily added or subtracted from the current induced by differential flux line 202, which flows in the same direction through each of inductors Li and L ₂ . Thus, one of Josephson junctions Ji, J ₂ is in a high inductance state while the other is in a low inductance state, the inductance states of the respective Josephson junctions being based entirely on the direction of the current flowing through differential flux line 202 in this example. Common flux current through line 204 stays steady, while differential flux current through line 202 is actuated in each of two directions, depending on the intended configuration of switch 202 to change the coupling between one of the qubits (for example) on one of Port 1 or Port 2 with the qubit (for example) on Port 3. However, as already noted, the roles of lines 202 and 204 are interchangeable.

[0030] FIGS. 4 and 5 together show an example of a logical-level quantum circuit that can use circuit 200 to provide reconfigurable quantum routing. Quantum circuit segment 500 in FIG. 5 performs a parity check operation between two logical qubits 502, 504, using a logical ancilla 506. Each of the logical qubits 502, 504 may be composed of an error- corrected collection of physical qubits, and as such may be located at a separate physical circuit block on a quantum processor chip. Circuit 200, with its dual RF-SQUID construction represented by circuit portion 508 in FIG. 5, allows for a remote connection (i.e., over a mm-scale distances) between the circuit blocks. The circuit 400 of FIG. 4 illustrates the sequence of connections. The first logical CNOT gate 402 corresponds to the control fluxes being configured such that the anci!!a 506, whose physical qubits axe connected to TL ₃ , is coupled via the RF-SQUIDs 508 to the second logical data qubit 504, whose physical qubits axe connected to TL _2. After the function of the first CNOT gate 402 is performed, the control fluxes can be switched so that the first logical data qubit 502, whose physical qubits axe connected to TLi, is coupled to the ancilla 506 and the function of the second logical CNOT gate 404 can thereby be performed [0031 ] FIG. 6 illustrates another example reconfigurable quantum router 600 arranged as a cross-point reconfigurable bus coupler. Similar to reconfigurable quantum router 200 of FIG. 2, circuit 600 also uses RF-SQUIDs to couple resonators, in this case resonators TLj, TL ₂ , TL ₃ , TL , which can be, for example, short-terminated quarter-wave resonators. In the illustrated example, a first RF-SQUID is composed of Josephson junction Ji connected to inductors Li and L ₃ to form a first superconducting loop, a second RF-SQUID is composed of Josephson junction J ₂ connected to inductors L ₂ and L ₄ to form a second superconducting loop, a third RF-SQUID is composed of Josephson junction J ₃ connected to inductors Li and L ₄ to form a third

superconducting loop, and a fourth RF-SQUID is composed of Josephson junction J ₄ connected to inductors L ₂ and L ₃ to form a fourth superconducting loop, where the first and third loops share a common inductor Li, the second and fourth loops share a common inductor L _2, the first and fourth loops share a common inductor L ₃ , the second and third loops share a common inductor L ₄ . Circuit 600 is also control led by two flux lines, fluxl 602 and flux2 604, one of which can be configured as a static DC flux offset while the other is configured to be controlled in real time. Thus, for example, flu l 602 can serve as a common flux line while flux2 604 serves as a differential flux line, or vice versa

[0032] Under the condition that equal magnitude currents flow in flux control lines 602, 604 in the same direction, the currents induced through josephson junctions Ji and J ₂ cancel, while the currents through Josephson junctions J ₃ and J ₄ sum. The total currents induced through josephson junctions J ₃ and J ₄ put these Josephson junctions in a high inductance state, causing the effective coupling between resonators TL ₄ and TLi, as well as between resonators TL ₃ and TL ₂ , to vanish. Under such condition, since the currents in Josephson junctions Ji and J ₄ cancel, these Josephson junctions exhibit a low inductance state and there exists an appreciable effective coupling between resonators TL ₃ and TLj, as well as between resonators TL ₄ and TL ₂ . This condition, wherein Ports 1 and 3 are coupled, Ports 2 and 4 are coupled, Ports 1 and 4 are uncoupled, and Ports 2 and 3 are uncoupled, may be referred to as a bar state.

[0033] Under the condition that equal magnitude currents flow in flux control lines 602, 604 in opposite directions, the induced currents will, by contrast, add on Josephson junctions Ji and J ₂ and cancel on Josephson junctions J ₃ and J ₄ . In this configuration there exists an effective coupling between resonators TL ₃ and TL ₂ as well as between resonators TL and TLi, while the coupling between resonators TL ₃ and TLi, as well as between resonators TL and TL ₂ , vanishes. This condition, wherein Ports 1 and 4 are coupled, Ports 2 and 3 are coupled, Ports 1 and 3 are uncoupled, and Ports 2 and 4 are uncoupled, may be referred to as a cross state.

[0034] Reconfigurable quantum router 600 in FIG. 6 therefore functions as a cross point reconfigurable bus that can selectively connect pairs of qubits (or groups of qubits) in response to two control currents having the same or opposite sign. Thus in an example of the functioning of circuit 600, when flux is provided in the same direction through lines 602, 604, pairs of RF- SQUIDs exhibit respective high or low inductance states to place the switch 600 in a bar configuration (as shown in FIG. 1C), while changing the polarity of one of the flux lines relative to the other alters the respective inductance states to place the switch 600 in a cross configuration (as shown in FIG. ID). Thus, the josephson junctions in the RF-SQUIDs of router 600 are switched in pairwise fashion.

[0035] FIG. 7 illustrates an example quantum algorithm for which cross-point reconfigurable bus 600 may be applied. /7-to-Tofloli distillation circuit 700 is shown in terms of the |F/)-slate implementation of Margolus-Toffoli gates. The algorithm uses pairwise CNOT gates 708/710, 712/714, 716/718 with alternating operands, where the circuit 600 facilitates the swapping of the operands as shown in FIG. 7. CNOT gates 708, 710 are achieved by bar state 702; CNOT gates 712, 714 are achieved by cross state 704; and CNOT gates 716, 718 are achieved by bar state 706. The last CNOT gate 720 in the algorithm can be achieved using a fixed coupling between member qubits. Performing the algorithm using circuit 600 alleviates complications that arise due to frequency crowding of the qubits and errors that may occur when qubit frequencies are swept across each other. Any algorithm that requires similar operand swapping can similarly benefit from the use of circuit 600.

[0036] Multiple of the switches 100, 200, 600 can be concatenated to create higher- connectivity configurations. For example, two“Port 3”s of second and third instances of router 200 could be connected, respectively, to Port 1 and Port two of a first instance of router 200 to result in a one-to-four multiplexer. As another example, multiple switches 600 could be connected to each other, or one or more routers 200 could be connected to one or more routers 600, extending the number of“input” and“output” ports and creating a greater variety of switching solutions. In such concatenated examples a single switch controller 124 could be configured to control the multiple bias elements 122 for multiple or all concatenated routers.

[0037] FIG. 8A shows an example method 800 of reconfigurable quantum routing. A static control signal is provided 802 to one of a common flux line that is inductively coupled to two RF-SQUIDs via a common inductor to induce a current split between first and second variable inductance coupling elements in the respective RF-SQUIDs, or a differential flux line that is inductively coupled to the two RF-SQUIDs via other inductors in each of the RF-SQUIDs to induce a current flowing unsplit through the first and second variable inductance coupling elements. A dynamic control signal is provided 804 to the other of the common flux line or the differential flux line, such that the difference between induced common flux current and induced dynamic flux current places 806 the first variable inductance coupling element (e.g., a first Josephson junction in the first RF-SQUID) in one of a high or low inductance state and places 806 the second variable inductance coupling element (e.g., a second josephson junction in the second RF-SQUID) in the other of the high or low inductance state. The differential and common flux lines can be configured, for example, like lines 202 and 204 of circuit 200 shown in FIG. 2. The direction of the dynamic control signal (provided to one of the common flux line or the differential flux line) is actuated 808 to couple a first quantum object (e.g., a qubit) to either a second quantum object or a third quantum object, based on the dynamic control signal direction. Reconfigurable quantum routing is thereby achieved between the quantum objects. [0038] FIG. 8B shows another example method 850 of reconfigurable quantum routing.

A static control signal is provided 852 to one of a first flux line that is inductively coupled to first and second RF-SQUIDs via a common first inductor and third and fourth RF-SQUIDS via a common second inductor to induce currents split between first and second variable inductance coupling elements in the respective first and second RF-SQUIDs and between third and fourth variable inductance coupling elements in the respective third and fourth RF-SQUIDs, or a second flux line that is inductively coupled to the first and fourth RF SQUIDs via a common third inductor and the second and third RF-SQUIDs via a common fourth inductor to induce currents split between the first and fourth variable inductance coupling elements and between the second and third variable inductance coupling elements. A dynamic control signal is provided 854 to the other of the first flux line or the second flux line, such that the difference between induced first flux current and induced second flux current in each of the RF-SQUIDs places 856 two of the variable inductance coupling elements in one of a high or low inductance state and places 856 the other two variable inductance coupling elements in the other of the high or low- inductance state. The first and second flux lines can be configured, for example, like lines 602 and 604 of circuit 600 shown in FIG. 6. The direction of the dynamic control signal is actuated 858 to couple a first quantum object (e.g., a qubit) to one of a second quantum object or a third quantum object and to couple a fourth quantum object to the other of the second quantum object or the third quantum object, based on the dynamic control signal direction.

Reconfigurable quantum routing (in either“bar” or“cross” states) is thereby achieved between the quantum objects.

[0039] FIG. 8C shows an example method 870 of reconfigurable quantum routing. A static control signal is provided 872 to one of a first flux line that is inductively coupled to at least two RF-SQUIDs via at least one common inductor to induce at least one current split between variable inductance coupling elements in respective ones of the RF-SQUIDs, or a second flux line that is inductively coupled to the or another at least two RF-SQUIDs via other inductors in each of the RF-SQUIDs. A dynamic control signal is provided 874 to the other of the first flux line or the second flux line, such that the difference between induced common flux current and induced dynamic flux current places 876 at least one of the variable inductance coupling elements in one of a high or low inductance state and places 876 at least another of the variable inductance coupling elements in the other of the high or low inductance state. The first and second flux lines can be configured, for example, like lines 204 and 202 of circuit 200 shown in FIG. 2 or like lines 602 and 604 of circuit 600 shown in FIG. 6. The direction of the dynamic control signal is actuated 878 to couple at least a first quantum object (e.g , a qubit) to only one of at least two other quantum objects, based on the dynamic control signal direction. Reconfigurable quantum routing is thereby achieved between the quantum objects.

[0040] What have been described above are examples of the invention. It is, of course, not possible to describe every conceivable combination of components or methodologies for purposes of describing the invention, but one of ordinary skill in the art will recognize that many further combinations and permutations of the invention are possible. Accordingly, the invention is intended to embrace all such alterations, modifications, and variations that fall within the scope of this application, including the appended claims. Additionally, where the disclosure or claims recite“a,”“an,”“a first,” or“another” element, or the equivalent thereof, it should be interpreted to include one or more than one such element, neither requiring nor excluding two or more such elements. As used herein, the term“includes” means includes but not limited to, and the term“including” means including but not limited to. The term“based on” means based at least in part on.