Josephson crossbar switch fabric

Abstract

A Josephson junction based crossbar device (200) includes a plurality of superconducting loops (202a-202d). Each superconducting loop includes at least one Josephson junction (204). Each loop of the plurality of superconducting loops are electrically coupled and is configured to shift or annihilate magnetic flux quanta in one or more of the superconducting loops in response to a combination of signals and single flux quantum, SFQ, pulses. A readout line (230) is additionally coupled to the plurality of superconducting loops. A plurality of data and control lines (212, 214, 216) are coupled to the plurality of superconducting loops. Each line of the plurality of data and control lines is configured to provide at least one of a plurality of signals to at least a portion of the plurality of superconducting loops. The plurality of signals includes a data signal (212), a mirrored enable control signal (214), and a strobe control signal (216).

Description

JOSEPHSON CROSSBAR SWITCH FABRIC FIELD OF THE DISCLOSURE

[0001] This application relates to superconducting circuits. In particular, this application discloses a crossbar circuit implemented using a plurality of superconducting Josephson junctions and related circuitry. In such scenarios, the implementations may use single-flux quantum (SFQ) pulses to store information. BACKGROUND

[0002] Conventional digital circuits make use of complementary metal-oxide semiconductor (CMOS) technology to provide digital logic functionality. Recent developments have provided a more power efficient, higher-bandwidth, and denser solution: superconducting digital (SCD) technology, including pulse conservative logic (PCL), which makes use of Josephson single flux quantum (SFQ) pulses, while retaining compatibility with existing electronic design automation (EDA) tools.

[0003] A major computational cost and source of latency within high-performance computers and machine learning accelerators is efficient communication of data and instructions between different computational units on a chip and across the system. SUMMARY

[0004] Network on Chip (NoC) addresses the above and other challenges by using a network-based interconnect architecture to route packets between cores, memories, and peripherals. NoC can offer advantages such as scalability, modularity, parallelism, fault- tolerance, and reduced power consumption over traditional bus-based or point-to-point interconnects.

[0005] A key component of NoC design is the crossbar circuit, which is a switch that connects multiple input ports to multiple output ports. The crossbar determines how signals (e.g., data packets) are routed from source to destination, and affects the performance, reliability, and power consumption of the network. A well-designed crossbar can improve the bandwidth, latency, and throughput of the NoC, as well as reduce the contention and congestion among competing packets.

[0006] The embodiments herein efficiently utilize Josephson junctions by using specialized gates in a crossbar implementation. Since each router in the NoC contains a crossbar,reducing the size of the crossbar significantly lowers the NoC resource and area utilization, and improves latency.

[0007] The embodiments herein relate to an implementation of a crossbar circuit in PCL- based SCD circuits, specifically making use of superconducting Josephson junctions and related circuitry as well as single-flux quantum (SFQ) pulses stored in loops to retain state information.

[0008] In a first aspect, a Josephson junction based crossbar device is provided. The Josephson junction based crossbar device may be configured to multiplex digital signals. The Josephson junction based crossbar device includes a plurality of superconducting loops. Each loop of the plurality of superconducting loops includes at least one Josephson junction. Each loop of plurality of superconducting loops is electrically coupled. Each loop of the plurality of superconducting loops is configured to shift or annihilate magnetic flux quanta in one or more of the superconducting loops in response to a combination of signals and single flux quantum (SFQ) pulses. The Josephson junction based crossbar device also includes a readout line coupled to the plurality of superconducting loops. The Josephson junction based crossbar device also includes a plurality of data and control lines coupled to the plurality of superconducting loops. Each line of the plurality of data and control lines is configured to provide at least one of a plurality of signals to at least a portion of the plurality of superconducting loops. The plurality of signals includes a data signal, a mirrored enable control signal, and a strobe control signal.

[0009] In a second aspect, a method for multiplexing digital signals in a Josephson junction based crossbar device is provided. The method includes providing, to a plurality of superconducting loops, a combination of a plurality of signals and single flux quantum (SFQ) pulses. Each superconducting loop comprises at least one Josephson junction. The plurality of superconducting loops are electrically coupled. The plurality of signals includes a data signal, a mirrored enable control signal, and a strobe control signal. A plurality of data and control lines are coupled to the plurality of superconducting loops. Each line of the plurality of data and control lines is configured to provide at least one of the plurality of signals to at least a portion of the plurality of superconducting loops. The method also includes, in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops. The method further includes transmitting, via a readout line coupled to the plurality of superconducting loops, an output signal.

[0010] In a third aspect, a crossbar fabric system is provided. The crossbar fabric system may comprise a plurality of nodes arranged in a grid pattern. Each node may comprise a plurality of input and output connections and a plurality of connections between neighboring nodes within the grid pattern. The connections are an intersection of an output-to-input connection and an input-to-output connection between two nodes. The crossbar fabric system may also comprise a Josephson junction based crossbar device coupled to each connection. The Josephson junction based crossbar device may include a plurality of superconducting loops. Each superconducting loop includes at least one Josephson junction. Each loop of plurality of superconducting loops is electrically coupled, and is configured to shift or annihilate magnetic flux quanta in one or more of the superconducting loops in response to a combination of signals and single flux quantum (SFQ) pulses. The Josephson junction based crossbar device may also include a readout line coupled to the plurality of superconducting loops. The Josephson junction based crossbar device may also include a plurality of data and control lines coupled to the plurality of superconducting loops. Each line of the plurality of data and control lines is configured to provide at least one of a plurality of signals to at least a portion of the plurality of superconducting loops. The plurality of signals includes a data signal, a mirrored enable control signal, and a strobe control signal. The Josephson junction based crossbar device may also be configured to multiplex signals transmitted between the nodes of the crossbar fabric system. BRIEF DESCRIPTION OF THE FIGURES

[0011] The above, as well as additional features, will be better understood through the following illustrative and non-limiting detailed description of example embodiments, with reference to the appended drawings.

[0012] Figure 1A illustrates a schematic diagram of a crossbar circuit, in accordance with example embodiments.

[0013] Figure 1B illustrates a crossbar interconnect fabric, in accordance with example embodiments.

[0014] Figure 2 illustrates a schematic diagram of a Josephson junction based crossbar device 200, in accordance with example embodiments.

[0015] Figure 3A illustrates a circuit diagram of a Josephson junction based crossbar device, in accordance with example embodiments.

[0016] Figure 3B illustrates a circuit diagram of a Josephson junction based crossbar device, in accordance with example embodiments.

[0017] Figure 4A illustrates an initial flux biasing method, in accordance with example embodiments.

[0018] Figure 4B illustrates an initial flux biasing method, in accordance with example embodiments.

[0019] Figure 5A illustrates a signal sequence, in accordance with example embodiments.

[0020] Figure 5B illustrates a single flux quantum shifting sequence, in accordance with example embodiments.

[0021] Figure 6A illustrates a signal sequence, in accordance with example embodiments.

[0022] Figure 6B illustrates a single flux quantum shifting sequence, in accordance with example embodiments.

[0023] Figure 7A illustrates a signal sequence, in accordance with example embodiments.

[0024] Figure 7B illustrates a single flux quantum shifting sequence, in accordance with example embodiments.

[0025] Figure 8A illustrates a signal sequence, in accordance with example embodiments.

[0026] Figure 8B illustrates a single flux quantum shifting sequence, in accordance with example embodiments.

[0027] Figure 9A illustrates a signal sequence, in accordance with example embodiments.

[0028] Figure 9B illustrates a single flux quantum shifting sequence, in accordance with example embodiments.

[0029] Figure 10A illustrates a signal sequence, in accordance with example embodiments.

[0030] Figure 10B illustrates a single flux quantum shifting sequence, in accordance with example embodiments.

[0031] Figure 11A illustrates a signal sequence, in accordance with example embodiments.

[0032] Figure 11B illustrates a single flux quantum shifting sequence, in accordance with example embodiments.

[0033] Figure 12A illustrates a signal sequence, in accordance with example embodiments.

[0034] Figure 12B illustrates a single flux quantum shifting sequence, in accordance with example embodiments.

[0035] Figure 13 illustrates an array of crossbar devices, in accordance with example embodiments.

[0036] Figure 14 illustrates a mirrored enable signal, in accordance with example embodiments.

[0037] Figure 15 illustrates results of a waveform simulation, in accordance with example embodiments.

[0038] Figure 16 illustrates a method for multiplexing digital signals in a Josephson junction based crossbar device, in accordance with example embodiments.

[0039] All the figures are schematic, not necessarily to scale, and generally only show parts that are necessary to elucidate example embodiments, wherein other parts may be omitted or merely suggested. DETAILED DESCRIPTION

[0040] Various examples of systems, devices, and / or methods are described herein with reference to the accompanying drawings. Any embodiment, implementation, and / or feature described herein as being an example is not necessarily to be construed as preferred or advantageous over any other embodiment, implementation, and / or feature unless stated as such. Thus, other embodiments, implementations, and / or features may be utilized, and other changes may be made without departing from the scope of the subject matter presented herein.

[0041] Accordingly, the examples described herein are not meant to be limiting. It will be readily understood that the aspects of the present disclosure, as generally described herein, and illustrated in the figures, can be arranged, substituted, combined, separated, and designed in a wide variety of different configurations.

[0042] Further, unless the context suggests otherwise, the features illustrated in each of the figures may be used in combination with one another. Thus, the figures should be generally viewed as component aspects of one or more overall embodiments, with the understanding that not all illustrated features are necessary for each embodiment.

[0043] Additionally, any enumeration of elements, blocks, or steps in this specification or the claims is for purposes of clarity. Thus, such enumeration should not be interpreted to requireor imply that these elements, blocks, or steps adhere to a particular arrangement or are carried out in a particular order.

[0044] Moreover, terms such as “substantially” or “about” that may be used herein are meant that the recited characteristic, parameter, or value need not be achieved exactly, but that deviations or variations, including, for example, tolerances, measurement error, measurement accuracy limitations and other factors known to those skilled in the art, may occur in amounts that do not preclude the effect the characteristic was intended to provide.

[0045] Further, terms such as “A coupled to B,” “A electrically coupled to B,” “A connected to B,” “A electrically connected to B” etc., do not necessarily mean that items A and B are directly coupled to one another. For example, a first component electrically coupled to a second component is interpreted to mean that the components are either directly coupled (e.g., via a conductor) or coupled to one another via one or more resistors, capacitors, inductors, and / or other active or passive components.

[0046] The potential of superconducting digital technology as a beyond-CMOS technology derives from high energy efficiency, high computational density, and high interconnect bandwidth. The technology is based on the single-flux-quantum (SFQ) pulse, which is fast, low power, and low-dispersion / low-loss on superconductor transmission lines. Example embodiments involve various combinations of fabrication materials, density, power / clock distribution, logic and memory design, packaging, interfaces, and architecture. Crossbar Devices and Multiplexer Logic

[0047] Crossbar devices connect multiple inputs and outputs in a grid pattern. Each intersection of an input and output line has a multiplexer that can be selected to allow the signal to pass through or not as shown. This is shown in Figure 1A, which depicts a 4x4 crossbar circuit with sixteen multiplexers, each represented by a trapezoid.

[0048] In a NoC design where a crossbar interconnect is implemented, each router node may have a crossbar that connects neighboring routers, as shown in Figure 1B.

[0049] Multiplexers may be implemented in a PCL environment using traditional logic gates such as AND, OR, and NOT, but this would require many Josephson junctions which would increase the size, power consumed, and latency of the circuit. To solve this technical problem, the embodiments herein implement an area-efficient multiplexer. To illustrate, an example 2x1 multiplexer may operate according to the equation for inputs pand q where E is an enable signal and D is a data signal for each input. The enable signals satisfy the equations 0 and 1, meaning that only one input is selected at a time, which ensures that the logic operates as a multiplexer. The equation may berewritten as ! ! ! . Then, making use of De Morgan’s law, it may be furtherrewritten into the equivalent ! ! ! and further into ! !

[0050] This last equation is efficient to implement in PCL by using a single cell multiplexer as described below. This approach has several advantages over implementations using traditional logic gates, including the aforementioned improvements in size, power consumed, and latency, as well as energy efficient and device-efficient fanout of data input and output moving through the array. Example Josephson Junction Based Crossbar Devices

[0051] Figure 2 illustrates a schematic diagram of a Josephson junction based crossbar device 200, in accordance with example embodiments, which may be configured to operate as a single-cell multiplexer as described above. The Josephson junction based crossbar device 200 includes a plurality of superconducting loops 202. Each superconducting loop (e.g., superconducting loop 202a, 202b, 202c, or 202d) includes at least one Josephson junction (e.g., Josephson junction 204a, 204b, and / or 204c). In such scenarios, each loop of the plurality of superconducting loops 202 is electrically coupled to another loop in the plurality of superconducting loops 202.

[0052] As illustrated in Figure 2, the plurality of superconducting loops 202 could be electrically coupled in a sequential (i.e. series) arrangement. In some examples, the sequential arrangement can include four superconducting loops (e.g., superconducting loops 202a, 202b, 202c, and 202d). In such scenarios, each superconducting loop of the plurality of superconducting loops 202 has one or two adjacent loops. As an example, superconducting loop 202a has one adjacent loop (superconducting loop 202b), superconducting loop 202b has two adjacent loops (superconducting loop 202a and superconducting loop 202c), superconducting loop 202c has two adjacent loops (superconducting loop 202b and superconducting loop 202d), and superconducting loop 202d has one adjacent loop (superconducting loop 202c). It will be understood that other arrangements of the superconducting loops 202 are possible and contemplated in relation to the present disclosure.

[0053] The Josephson junction based crossbar device 200 also includes a plurality of data and control lines 210 coupled to the plurality of superconducting loops 202. In some embodiments, the Josephson junction based crossbar device 200 may be coupled to an AC current-bias source. In some embodiments, the AC current-bias source may be a capacitor, which in some embodiments may be coupled to a resonant clock-power distribution network. In some embodiments, each line of the plurality of data and control lines of the plurality of data and control lines 210 could include a Josephson transmission line, at least one inductor, and a resistor connected between the Josephson transmission line and a corresponding superconducting loop of the plurality of superconducting loops.

[0054] The plurality of superconducting loops 202 are configured to shift or annihilate magnetic flux quanta (e.g., SFQ 220a or SFQ 220b) in one or more of the superconducting loops in response to a combination of signals and single flux quantum (SFQ) pulses. In some embodiments, the signals include a data signal, a mirrored enable control signal, and a strobe control signal. In some embodiments, the strobe control signal includes a periodic clock signal. In some embodiments, the periodic clock signal may operate at the same frequency as the AC current-bias source described above. In some embodiments, this frequency may be 30 GHz. In some embodiments, the mirrored enable control signal includes a polarity-inverted enable signal.

[0055] In some embodiments, the signals could be provided to the superconducting loops 202 by way of the data and control lines 210. In the embodiment illustrated in Figure 2, the signals are provided by a data line 212, a mirrored enable control line 214, and / or a strobe control line 216.

[0056] In some embodiments, the data signal is configured to be transmitted to a first loop and a second loop of the plurality of superconducting loops, the mirrored enable control signal is configured to be transmitted to a second loop and a third loop of the plurality of superconducting loops, and the strobe control signal is configured to be transmitted to a third loop and a fourth loop of the plurality of superconducting loops.

[0057] In some embodiments, the plurality of superconducting loops 202 are configured to shift a magnetic flux quanta (e.g., SFQ 220a) from an initial superconducting loop (e.g., superconducting loop 202c) to an adjacent loop (e.g., superconducting loop 202b) in response to a SFQ pulse and / or control signal applied to the initial superconducting loop. In other words, the plurality of superconducting loops are configured to shift a magnetic flux quanta from an initialsuperconducting loop to an adjacent loop in response to a SFQ pulse applied to the initial superconducting loop and based on the presence of magnetic flux quanta in the plurality of superconducting loops.

[0058] In some embodiments, a magnetic flux quanta is shifted from an initial superconducting loop to an adjacent loop in a first direction along the sequential arrangement in response to a positive SFQ pulse polarity. In some embodiments, a magnetic flux quanta is shifted from an initial superconducting loop to an adjacent loop in a second direction along the sequential arrangement in response to a negative SFQ pulse polarity

[0059] In some embodiments, a readout line 230 may be coupled to the plurality of superconducting loops. In response to the shifting of SFQ between superconducting loops 202 and the signals, an output signal may be transmitted via the readout line 230.

[0060] The operation of the crossbar device may involve shifting a stored single-flux- quantum (SFQ) between superconducting loops separated by Josephson junctions in response to signals provided to the superconducting loops via the data and control lines as discussed above. The shifting mechanism is discussed below.

[0061] The principle of operation is based on magnetic flux quantization and energy conservation of the circuit. Flux is quantized in superconducting loops according to ,where is number of flux quanta ( sustained (or “trapped”) in the loop. A Josephson junctionconnected to a superconducting loop will trigger if that does not result in an increment in the circuit energy which is given by the equationwhere is the inductance of the superconducting wires. For instance, if the Josephson junction is connected to two superconducting loops with no initial flux biasing, triggering this junction will store two flux quanta in the two loops, significantly increasing the circuit energy. However, if only one of the loops has a stored flux due to initial biasing, triggering the Josephson junction will move the flux quantum from the current loop to the next one. Thus, the overall energy remains constant. In other words, if the current of a stored SFQ interferes constructively with the current associated with an input signal (e.g. a control signal as described herein) in any Josephson junction, then the critical current of that Josephson junction will be exceeded. This has the effect of moving the stored SFQ to the adjacent loop. Otherwise, the signal will be dissipated (or annihilated) across the coupling resistor with no change in the state. This is visually depicted in Table 1 below.

[0062] As shown in Table 1, by applying a control signal and depending on the presence of SFQs in the superconducting loops, SFQs may be shifted between loops and / or annihilated, which may thus cause an output signal to be transmitted via the readout line.

[0063] An alternate principle of operation is based on current through the Josephson junctions. If the signal current interferes constructively with the stored flux current the Josephson junction will trigger, moving the flux through the Josephson junction. The resistors connected to the input may absorb the voltage signal in cases where the Josephson junctions do not trigger.

[0064] The signal timing particularly important to the cell functionality, since the signal should arrive before , and should arrive before the strobe control signal (S). This may be accomplished by assigning incrementing AC clock phase assignment of the signals.

[0065] Using the above methods, logical operations may be performed by manipulating the signals, including multiplexer operations as described above.

[0066] Figure 3A illustrates a circuit diagram 300 of an embodiment of the Josephson junction based crossbar device 200 of Figure 2. The circuit diagram 300 consists of Josephson transmission line (JTL) stages along the data and control lines 310A. The current sources (with arrows) represent AC bias, which allows both positive and negative SFQ pulses to propagate at different times in the clock cycle. Resistors couple the inputs to the internals of the cell. Each junction-resistor pair is a decision-making element; if the signal current adds with the same polarity to the current of the SFQ in a superconducting loop as seen by the junction, the signal will trigger the junction to produce an SFQ pulse and move the stored pulse to the adjacent superconducting loop. Otherwise, the signal voltage may be lost across the resistor. In some embodiments, similar behavior can be achieved by replacing any or all of these coupling resistors with additional Josephson junctions. The pulsed voltage sources (with dots) represent SFQ sources to produce the initial state. The initial state shown corresponds to the zero state, but other initial states could be used. Additionally, a readout line 330A is coupled to the superconducting loops 302A that may transmit an output signal Q.

[0067] As illustrated in Figure 3A, in some embodiments, data signal is configured to be transmitted to a first and a second loop of the plurality of superconducting loops. The data signal is configured to shift a magnetic flux quantum from the first loop to the second loop and from the second loop to the first loop based on the presence of magnetic flux quanta in the plurality of superconducting loops. In some embodiments, the data signal may be provided by data line 312A.

[0068] In some embodiments, the mirrored enable control signal is configured to be transmitted to a second loop and a third loop of the plurality of superconducting loops. The mirrored enable control signal is configured to shift a magnetic flux quantum from the second loop to the third loop and from the third loop to the second loop based on the presence of magnetic flux quanta in the plurality of superconducting loops. In some embodiments, the mirrored enable control signal may be provided by mirrored enable control line 314A.

[0069] In some embodiments, the strobe control signal is configured to be transmitted to the third and a fourth loop of the plurality of superconducting loops. The strobe control signal is configured to shift a magnetic flux quantum from the third loop to the fourth loop and from thefourth loop to the third loop based on the presence of magnetic flux quanta in the plurality of superconducting loops. In some embodiments, the strobe control signal may be provided by strobe control line 316A.

[0070] Figure 3B illustrates a circuit diagram 350 of another configuration of the Josephson junction based crossbar device 200 of Figure 2. While such a configuration operates according to the same principles as the devices illustrates in Figure 2 and 3A, it may be configured in a slightly different manner; while it retains four superconducting loops as in previous examples, one of the loops is initialized with and configured to make use of half a magnetic flux quantum, as depicted in Figure 3B. Additionally, Figure 3B depicts a superconducting loop coupled to other superconducting loop(s) in a parallel configuration (as opposed to a series / sequential configuration. Thus, in some embodiments, at least two of the loops of the plurality of superconducting loops are electrically coupled in a parallel arrangement. The signal paths and interactions will be described later, but the behavior of the circuit configuration of Figure 3B with regards to input and output signals is the same as the prior embodiments. For example, the data signal, mirrored enable control signal, and strobe control signal may each be provided by data line 312B, mirrored enable control line 314B, and strobe control line 316B, respectively, as illustrated in Figure 3B.

[0071] In use, setting the initial state may not necessarily use pulsed voltage sources as depicted in Figures 3A and 3B. In some embodiments, magnetic coupling provided by way of a feed line may be used to set the initial state.

[0072] In some embodiments, an initial flux biasing may be used to set up the internalstate, where denotes a single flux quantum (SFQ), corresponding to a 2 phase rotation of aJosephson junction. In some embodiments, the initial flux bias is set using the circuit shown in Figure 4A. The current in the feed line 410 is ramped up until the current I in the feed line 410satisfies the equation / , where M is mutual coupling (i.e. the mutual inductancebetween the top and bottom inductors illustrated in Figure 4A), to store an SFQ in the loop.

[0073] Figure 4B depicts an alternative flux biasing method that may be used in someembodiments. In this alternative, the feed line 460 maintains a current / before theloop transitions into a superconducting state (i.e., where the temperature T > the critical temperature ) and the temperature T is then gradually reduced to achieve the superconducting state. The circuit initializes to the ground state with no net flux. However, this state can beunderstood as a superposition of the applied flux and a virtual flux in the loop in the opposite direction, as also illustrated in Figure 4B. Then, the current in the feed line is switched off, which traps a single flux quantum in the loop. This application and removal of the flux in the feed line can be described as a “bait and switch.”

[0074] Put another way, the crossbar device 200 may include at least one magnetically coupled feed line. In such scenarios, the plurality of superconducting loops 202 are configured to provide an initial flux state in response to a two-step flux initialization process. The two-step flux initialization process may include: 1) while cooling down the Josephson junction based crossbar, providing an initialization signal via the at least one magnetically coupled feed line; and 2) upon reaching a superconducting critical temperature of the Josephson junction based crossbar device, turning off the initialization signal such that an exact integral number of SFQ are stored in one or more of the superconducting loops.

[0075] Figure 5A depicts a signal sequence 500, which represents changes in the control and output signals associated with the crossbar device 200. In this and the following examples, D represents the data signal, Emrepresents the mirrored enable control signal, S represents the strobe control signal, and O represents the output signal (also represented with Q elsewhere in this disclosure).

[0076] Figure 5B depicts an SFQ shifting sequence 550 within the superconducting loops 202 of the crossbar device 200, in accordance with example embodiments, which results in the output signal O from zero to one and then back to zero as shown in Figure 5A. Figures 5A-8B make use of circuit 300 depicted in Figure 3A. The numbers within the circles represent the time t, which corresponds to the time within the circles shown in Figure 5A.

[0077] Prior to the actions described in Figures 5A, 5B, or any of the following drawings, the crossbar device 200 may have its “zero-state” set according to an initial flux biasing process as described above in relation to Figures 4A and 4B.

[0078] As shown in Figures 5A and 5B, at time t = 1, D goes high which triggers the left- most Josephson junction. This moves the flux quantum stored in the right loop to the left loop as shown in marker t = 2. When Em goes low it receives an inverted SFQ pulse. This voltage difference will appear across the connected resistor instead of triggering the connected Josephson junction since triggering the junction requires significantly more energy in its current configuration. Then, when S is asserted at t = 3, it triggers the connected Josephson junctionwhich moves the flux bias in the right-side loop to left and sends out an SFQ pulse through O. From t = 4 to t = 7, the signals arrive in the same order, but as inverted SFQ pulses which reverse the effect on the cell from t = 1 to t = 3 and bring the cell back to the initial flux biased configuration, and returning O to zero.

[0079] As described previously, the operating principle involves addition of currents in the Josephson junctions (e.g., Josephson junctions 204a, 204b, and 204c): the SFQ will move one superconducting loop to the left if a positive signal current adds constructively to the stored SFQ, which is a persistent current in the loop. The SFQ will move one superconducting loop to the right if a negative signal current adds to negative current in the stored SFQ. The currents of SFQ stored in adjacent loops cancel in the shared Josephson junctions, so that two SFQs do not occupy a shared loop at the same time. The Q output signal may be generated only if the S junction switches and moves the stored pulse between loops.

[0080] In some embodiments, a first and second magnetic flux quantum are stored in each of a second and a fourth superconducting loop. In response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops may involve receiving, via an address line coupled to a first and second superconducting loop, a transition edge of the data signal. In response to receiving the transition edge of the data signal, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops may also involve shifting the first magnetic flux quantum from the second superconducting loop to the first superconducting loop. Additionally, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops may also involve receiving, via an address line coupled to the second and a third superconducting loop, a transition edge of the mirrored enable control signal. Shifting or annihilating magnetic flux quanta in one or more of the superconducting loops may also involve receiving, via an address line coupled to the third and fourth superconducting loop, a transition edge of the strobe control signal. Further, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops may also involve in response to receiving the transition edge of the strobe control signal, shifting the second magnetic flux quantum from the fourth superconducting loop to the third superconducting loop. Even further, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops may also involve outputting a transition edge of an output signal to the readout line.

[0081] In some embodiments, a third and fourth magnetic flux quantum are stored in each of a first and a third superconducting loop. In response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops may involve receiving, via an address line coupled to the first and a second superconducting loop, a transition edge of the data signal. Shifting or annihilating magnetic flux quanta in one or more of the superconducting loops may also involve receiving in response to receiving the transition edge of the data signal, shifting the third magnetic flux quantum from the first superconducting loop to the second superconducting loop. Additionally, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops may also involve receiving, via an address line coupled to the second and a third superconducting loop, a transition edge of the mirrored enable control signal. Shifting or annihilating magnetic flux quanta in one or more of the superconducting loops may also involve receiving, via an address line coupled to the third and fourth superconducting loop, a transition edge of an SFQ pulse of the strobe control signal. Shifting or annihilating magnetic flux quanta in one or more of the superconducting loops may also involve in response to receiving the transition edge of the strobe control signal, shifting the fourth magnetic flux quantum from the third superconducting loop to the fourth superconducting loop. Shifting or annihilating magnetic flux quanta in one or more of the superconducting loops may also involve outputting a transition edge of an output signal to the readout line.

[0082] Figure 6A depicts a signal sequence 600, which represents changes in the control and output signals associated with the crossbar device 200. Figure 6B depicts an SFQ shifting sequence 650 within the superconducting loops 202 of the crossbar device 200, in accordance with example embodiments, which results in the output signal O remaining at zero despite changes in Emand S as shown in Figure 6A.

[0083] Figure 7A depicts a signal sequence 700, which represents changes in the control and output signals associated with the crossbar device 200. Figure 7B depicts an SFQ shifting sequence 750 within the superconducting loops 202 of the crossbar device 200, in accordance with example embodiments. In this example, Em remains at one, and thus the output signal O goes to one with the clock signal from S.

[0084] Figure 8A depicts a signal sequence 800, which represents changes in the control and output signals associated with the crossbar device 200. Figure 8B depicts an SFQ shiftingsequence 850 within the superconducting loops 202 of the crossbar device 200. In this example, Em still remains at one, and thus the output signal O goes to one with the clock signal from S as in Figure 7A.

[0085] Figures 9A-12B relate to the alternative circuit 350 depicted in Figure 3B, but otherwise are set up similarly to Figures 5A-8B, depicting signal and shifting sequences. As noted above, circuit 350 is initialized with and configured to make use of half a magnetic flux quantum in one of its superconducting loops, as depicted in the following figures. In response to signals, the current produced by the half a magnetic flux quantum may change (or be reversed), depicted as a clockwise versus anticlockwise arrow on the half a magnetic flux quantum in the following figures. For example, a control signal may cause the current of the half a magnetic flux quantum to be reversed from a clockwise direction to an anticlockwise direction, or vice versa. Despite the difference in operation, the resulting output signals and behaviors remain the same as circuit 300 described above and in relation to Figures 5A-8B.

[0086] Figure 9A depicts a signal sequence 900, which represents changes in the control and output signals associated with the crossbar device 200. Figure 9B depicts an SFQ shifting sequence 950 within the superconducting loops 202 of the crossbar device 200, in accordance with example embodiments.

[0087] Figure 10A depicts a signal sequence 1000, which represents changes in the control and output signals associated with the crossbar device 200. Figure 10B depicts an SFQ shifting sequence 1050 within the superconducting loops 202 of the crossbar device 200, in accordance with example embodiments.

[0088] Figure 11A depicts a signal sequence 1100, which represents changes in the control and output signals associated with the crossbar device 200. Figure 11B depicts an SFQ shifting sequence 1150 within the superconducting loops 202 of the crossbar device 200, in accordance with example embodiments.

[0089] Figure 12A depicts a signal sequence 1200, which represents changes in the control and output signals associated with the crossbar device 200. Figure 12B depicts an SFQ shifting sequence 1250 within the superconducting loops 202 of the crossbar device 200, in accordance with example embodiments.

[0090] Figure 13 illustrates an array of crossbar devices arranged in a 2x2 crossbar fabric 1300, in accordance with example embodiments. This arrangement (e.g., Josephsonjunction based crossbar device 100) could be considered a unit cell. An array of coupled unit cells may subsequently form a crossbar fabric, which may allow for multiple operations can be carried out simultaneously, and / or to multiplex several signals from multiple nodes (as illustrated in Figure 1B). In this particular example, B corresponds to the data signal D.

[0091] In some embodiments, a crossbar fabric system may comprise a plurality of nodes arranged in a grid pattern. Each node may comprise a plurality of input and output connections and a plurality of connections between neighboring nodes within the grid pattern. The connections are an intersection of an output-to-input connection and an input-to-output connection between two nodes. The crossbar fabric system may also comprise a Josephson junction based crossbar device coupled to each connection.

[0092] Such a Josephson junction based crossbar device as above may involve a crossbar device as described in the embodiments herein. For example, in some embodiments, the crossbar device may involve a plurality of superconducting loops. Each superconducting loop comprises at least one Josephson junction. Each loop of the plurality of superconducting loops is electrically coupled, and is configured to shift or annihilate magnetic flux quanta in one or more of the superconducting loops in response to a combination of signals and single flux quantum (SFQ) pulses. The Josephson junction based crossbar device may also involve a readout line coupled to the plurality of superconducting loops.

[0093] The Josephson junction based crossbar device may also involve a plurality of data and control lines coupled to the plurality of superconducting loops. Each line of the plurality of data and control lines is configured to provide at least one of a plurality of signals to at least a portion (i.e. a respective subset comprising one or more) of the plurality of superconducting loops. The plurality of signals includes a data signal, a mirrored enable control signal, and a strobe control signal. The crossbar device may be configured to multiplex signals transmitted between the nodes of the crossbar fabric system.

[0094] As described above, one of the signals involved in the embodiments herein is a mirrored enable control signal. By “mirrored,” the embodiments herein describe a signal that is polarity-inverted – i.e., values of 0 in the original signal become 1 in the mirrored signal, and vice versa. An example is illustrated in Figure 14, showing an enable signal E and its counterpart mirrored enable signal Em. In some embodiments, the mirrored signal may be generated by amirror cell. In some embodiments, the mirrored enable control signal includes a polarity-inverted enable signal.

[0095] Figure 15 illustrates results 1500 of a simulation of the circuit of Figure 3B using WRSpice software. The input waveforms correspond to those of Figures 9A-12B, but with each input pulse repeated three times. The results otherwise correspond to Figures 9A-12B and its accompanying description. Example Methods

[0096] Figure 16 illustrates a method 1600, in accordance with example embodiments. The method 1600 includes a process for multiplexing digital signals in a Josephson junction based crossbar device (e.g., crossbar device 200 as illustrated and described in relation to Figure 2).

[0097] The method 1600 includes, at block 1602, providing, to a plurality of superconducting loops (e.g., superconducting loops 202), a combination of a plurality of signals and single flux quantum (SFQ) pulses. Each superconducting loop comprises at least one Josephson junction (e.g., Josephson junctions 204a, 204b, and 204c). Each loop of the plurality of superconducting loops is electrically coupled. The plurality of signals includes a data signal, a mirrored enable control signal, and a strobe control signal. A plurality of data and control lines are coupled to the plurality of superconducting loops. Each line of the plurality of data and control lines is configured to provide at least one of the plurality of signals to at least a portion of the plurality of superconducting loops.

[0098] The method 1600 includes, at block 1604, in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta (e.g., SFQ 220a and / or 220b) in one or more of the superconducting loops.

[0099] In some embodiments, the method 1600 may include transmitting, via a readout line coupled to the plurality of superconducting loops, an output signal.

[0100] In some embodiments, the plurality of superconducting loops is electrically coupled in a sequential arrangement, and each superconducting loop of the plurality of superconducting loops has one or two adjacent loops.

[0101] In some embodiments, the plurality of superconducting loops are configured to shift a magnetic flux quanta from an initial superconducting loop to an adjacent loop in responseto a SFQ pulse applied to the initial superconducting loop based on the presence of magnetic flux quanta in the plurality of superconducting loops.

[0102] In some embodiments, a first and second magnetic flux quantum are stored in each of a second and a fourth superconducting loop.

[0103] In some embodiments, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops includes receiving, via an address line coupled to a first and second superconducting loop, a transition edge of the data signal. In some embodiments, a transition edge may be a rising edge or a trailing edge. In some embodiments, a positive SFQ pulse may result in a rising edge, and in some embodiments a negative SFQ pulse may result in a trailing edge.

[0104] In some embodiments, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops includes in response to receiving the transition edge of the data signal, shifting the first magnetic flux quantum from the second superconducting loop to the first superconducting loop.

[0105] In some embodiments, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops includes receiving, via an address line coupled to the second and a third superconducting loop, a transition edge of the mirrored enable control signal.

[0106] In some embodiments, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops includes receiving, via an address line coupled to the third and fourth superconducting loop, a transition edge of the strobe control signal.

[0107] In some embodiments, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops includes in response to receiving the transition edge of the strobe control signal, shifting the second magnetic flux quantum from the fourth superconducting loop to the third superconducting loop.

[0108] In some embodiments, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops includes outputting a transition edge of an output signal to the readout line.

[0109] In some embodiments, a third and fourth magnetic flux quantum are stored in each of a first and a third superconducting loop.

[0110] In some embodiments, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops includes receiving, via an address line coupled to the first and a second superconducting loop, a transition edge of the data signal.

[0111] In some embodiments, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops includes, in response to receiving the transition edge of the data signal, shifting the third magnetic flux quantum from the first superconducting loop to the second superconducting loop;

[0112] In some embodiments, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops includes receiving, via an address line coupled to the second and a third superconducting loop, a transition edge of the mirrored enable control signal;

[0113] In some embodiments, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops includes receiving, via an address line coupled to the third and fourth superconducting loop, a transition edge of the strobe control signal;

[0114] In some embodiments, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops includes, in response to receiving the transition edge of the strobe control signal, shifting the fourth magnetic flux quantum from the third superconducting loop to the fourth superconducting loop.

[0115] In some embodiments, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops includes (and thus may result in) outputting a transition edge of an output signal to the readout line. Enumerated Example Embodiments

[0116] Embodiments of the present disclosure may thus relate to one of the enumerated example embodiments (EEEs) listed below.

[0117] EEE 1 includes a Josephson junction based crossbar device comprising: a plurality of superconducting loops, wherein each superconducting loop comprises at least one Josephson junction, wherein each loop of the plurality of superconducting loops is electrically coupled, and wherein each loop of the plurality of superconducting loops is configured to shift or annihilate magnetic flux quanta in one or more of the superconducting loops in response to a combination of signals and single flux quantum (SFQ) pulses; a readout line coupled to the plurality of superconducting loops; anda plurality of data and control lines coupled to the plurality of superconducting loops, wherein each line of the plurality of data and control lines is configured to provide at least one of a plurality of signals to at least a portion of the plurality of superconducting loops, wherein the plurality of signals comprises: a data signal; a mirrored enable control signal; and a strobe control signal.

[0118] EEE 2 includes the Josephson junction based crossbar device of EEE 1, wherein the crossbar device is coupled to an AC current-bias source, and wherein each line of the plurality of data and control lines of the plurality of data and control lines comprises: a Josephson transmission line; at least one inductor; and a resistor connected between the Josephson transmission line and a corresponding superconducting loop of the plurality of superconducting loops.

[0119] EEE 3 includes the Josephson junction based crossbar device of either EEE 1 or EEE 2, wherein: the data signal is configured to be transmitted to a first loop and a second loop of the plurality of superconducting loops; the mirrored enable control signal is configured to be transmitted to the second loop and a third loop of the plurality of superconducting loops; and the strobe control signal is configured to be transmitted to the third loop and a fourth loop of the plurality of superconducting loops.

[0120] EEE 4 includes the Josephson junction based crossbar device of any of EEEs 1-3, wherein the strobe control signal comprises a periodic clock signal.

[0121] EEE 5 includes the Josephson junction based crossbar device of any of EEEs 1-4, wherein the mirrored enable control signal comprises a polarity-inverted enable signal.

[0122] EEE 6 includes the Josephson junction based crossbar device of any of EEEs 1-5, wherein the plurality of superconducting loops is electrically coupled in a sequential arrangement, wherein each superconducting loop of the plurality of superconducting loops has one or two adjacent loops.

[0123] EEE 7 includes the Josephson junction based crossbar device of EEE 6, wherein the plurality of superconducting loops are configured to shift a magnetic flux quanta from an initial superconducting loop to an adjacent loop in response to a SFQ pulse applied to the initial superconducting loop and based on the presence of magnetic flux quanta in the plurality of superconducting loops.

[0124] EEE 8 includes the Josephson junction based crossbar device of EEE 7, wherein the magnetic flux quanta is shifted from an initial superconducting loop to an adjacent loop in a first direction along the sequential arrangement in response to a positive SFQ pulse polarity and based on the presence and orientation of magnetic flux quanta in the plurality of superconducting loops, and wherein the magnetic flux quanta is shifted from an initial superconducting loop to an adjacent loop in a second direction along the sequential arrangement in response to a negative SFQ pulse polarity and based on the presence and orientation of magnetic flux quanta in the plurality of superconducting loops.

[0125] EEE 9 includes the Josephson junction based crossbar device of either EEE 7 or EEE 8, wherein: the data signal is configured to be transmitted to a first and second loop of the plurality of superconducting loops, and wherein the data signal is configured to shift a magnetic flux quantum from the first loop to the second loop and from the second loop to the first loop based on the presence of magnetic flux quanta in the plurality of superconducting loops; the mirrored enable control signal is configured to be transmitted to the second loop and a third loop of the plurality of superconducting loops, and wherein the mirrored enable control signal is configured to shift a magnetic flux quantum from the second loop to the third loop and from the third loop to the second loop based on the presence of magnetic flux quanta in the plurality of superconducting loops; and the strobe control signal is configured to be transmitted to the third and a fourth loop of the plurality of superconducting loops, and wherein the strobe control signal is configured to shift a magnetic flux quantum from the third loop to the fourth loop and from the fourth loop to the third loop based on the presence of magnetic flux quanta in the plurality of superconducting loops.

[0126] EEE 10 includes the Josephson junction based crossbar device of any of EEEs 1- 9, further comprising at least one magnetically coupled feed line, wherein the plurality ofsuperconducting loops are further configured to provide an initial flux state in response to a two- step flux initialization process, wherein the two-step flux initialization process comprises: while cooling down the Josephson junction based crossbar device, providing an initialization signal via the at least one magnetically coupled feed line; and upon reaching a superconducting critical temperature of the Josephson junction based crossbar device, turning off the initialization signal such that an exact integral number of SFQ are stored in the plurality of superconducting loops.

[0127] EEE 11 includes a method for multiplexing digital signals in a Josephson junction based crossbar device comprising: providing, to a plurality of superconducting loops, a combination of a plurality of signals and single flux quantum (SFQ) pulses, wherein each superconducting loop comprises at least one Josephson junction, wherein each loop of the plurality of superconducting loops is electrically coupled, wherein the plurality of signals comprises a data signal, a mirrored enable control signal, and a strobe control signal, wherein a plurality of data and control lines are coupled to the plurality of superconducting loops, wherein each line of the plurality of data and control lines is configured to provide at least one of a plurality of signals to at least a portion of the plurality of superconducting loops; and in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops.

[0128] EEE 12 includes the method of EEE 11, wherein the plurality of superconducting loops is electrically coupled in a sequential arrangement, wherein each superconducting loop of the plurality of superconducting loops has one or two adjacent loops, and wherein the plurality of superconducting loops are configured to shift a magnetic flux quanta from an initial superconducting loop to an adjacent loop in response to a SFQ pulse applied to the initial superconducting loop based on the presence of magnetic flux quanta in the plurality of superconducting loops.

[0129] EEE 13 includes the method of EEE 12, wherein a first and second magnetic flux quantum are stored in each of a second and a fourth superconducting loop, and wherein in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops comprises:receiving, via an address line coupled to a first and second superconducting loop, a transition edge of the data signal; in response to receiving the transition edge of the data signal, shifting the first magnetic flux quantum from the second superconducting loop to the first superconducting loop; receiving, via an address line coupled to the second and a third superconducting loop, a transition edge of the mirrored enable control signal; receiving, via an address line coupled to the third and fourth superconducting loop, a transition edge of the strobe control signal; in response to receiving the transition edge of the strobe control signal, shifting the second magnetic flux quantum from the fourth superconducting loop to the third superconducting loop; and outputting a transition edge of an output signal to a readout line.

[0130] EEE 14 includes the method of EEE 12, wherein a third and fourth magnetic flux quantum are stored in each of a first and a third superconducting loop and wherein in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops comprises: receiving, via an address line coupled to the first and a second superconducting loop, a transition edge of the data signal; in response to receiving the transition edge of the data signal, shifting the third magnetic flux quantum from the first superconducting loop to the second superconducting loop; receiving, via an address line coupled to the second and a third superconducting loop, a transition edge of the mirrored enable control signal; receiving, via an address line coupled to the third and fourth superconducting loop, a transition edge of the strobe control signal; in response to receiving the transition edge of the strobe control signal, shifting the fourth magnetic flux quantum from the third superconducting loop to the fourth superconducting loop; and outputting a transition edge of an output signal to a readout line.

[0131] In the following EEEs, the numbered magnetic flux quanta may be, but do not have to be, identical to the first and second (and / or third and fourth) magnetic flux quantum as resulting from some of the above-described method EEEs. For example, the seventh and eighthmagnetic flux quantum may be identical to the first and second magnetic flux quantum, but they may also be newly-initialized or otherwise different magnetic flux quantum.

[0132] EEE 15 includes the method of any of EEEs 12-14, wherein a fifth and sixth magnetic flux quantum are stored in each of a second superconducting loop and a fourth superconducting loop, and wherein in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops comprises: receiving, via an address line coupled to the second and a third superconducting loop, a transition edge of the mirrored enable control signal; in response to receiving the transition edge of the mirrored enable control signal, shifting the third magnetic flux quantum from the second superconducting loop to the third superconducting loop; receiving, via an address line coupled to the third and fourth superconducting loop, a transition edge of the strobe control signal; receiving, via an address line coupled to the second and a third superconducting loop, a further transition edge of the mirrored enable control signal; in response to receiving the further transition edge of the mirrored enable control signal, shifting the third magnetic flux quantum from the third superconducting loop to the second superconducting loop; and receiving, via an address line coupled to the third and fourth superconducting loop, a further transition edge of the strobe control signal.

[0133] EEE 16 includes the method of any of EEEs 12-15, wherein a seventh and eighth magnetic flux quantum are stored in each of a second superconducting loop and a fourth superconducting loop, and wherein in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops comprises: receiving, via an address line coupled to a first superconducting loop and a second superconducting loop, a transition edge of the data signal; in response to receiving the transition edge of the data signal, shifting the seventh magnetic flux quantum from the second superconducting loop to a first superconducting loop;receiving, via an address line coupled to the third and fourth superconducting loop, a transition edge of the strobe control signal; in response to receiving the transition edge of the strobe control signal, shifting the eighth magnetic flux quantum from the fourth superconducting loop to the third superconducting loop; outputting a transition edge of an output signal to a readout line; receiving, via an address line coupled to a first superconducting loop and a second superconducting loop, a further transition edge of the data signal; in response to receiving the further transition edge of the data signal, shifting the seventh magnetic flux quantum from the first superconducting loop to the second superconducting loop; receiving, via an address line coupled to the third and fourth superconducting loop, a further transition edge of the strobe control signal; in response to receiving the further transition edge of the strobe control signal, shifting the eighth magnetic flux quantum from the third superconducting loop to the fourth superconducting loop; and outputting a further transition edge of the output signal to the readout line.

[0134] EEE 17 includes the method of any of EEEs 12-16, wherein a ninth and tenth magnetic flux quantum are stored in each of a second superconducting loop and a fourth superconducting loop, and wherein in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops comprises: receiving, via an address line coupled to a third and the fourth superconducting loop, a transition edge of the strobe control signal; in response to receiving the transition edge of the strobe control signal, shifting the tenth magnetic flux quantum from the fourth superconducting loop to the third superconducting loop; outputting a transition edge of an output signal to a readout line; receiving, via an address line coupled to the third and fourth superconducting loop, a further transition edge of the strobe control signal;in response to receiving the further transition edge of the strobe control signal, shifting the tenth magnetic flux quantum from the third superconducting loop to the fourth superconducting loop; and outputting a further transition edge of the output signal to the readout line.

[0135] The following EEEs may be implemented in connection with a circuit that makes use of half a magnetic flux quantum, for example the circuit 350 described in relation to Figure 3B above.

[0136] EEE 17 includes the method of EEE 12, wherein an eleventh and twelfth magnetic flux quantum are stored in each of a second superconducting loop and a fourth superconducting loop, wherein the twelfth magnetic flux quantum is half a magnetic flux quantum producing a clockwise current, and wherein in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops comprises: receiving, via an address line coupled to a first superconducting loop and a second superconducting loop, a transition edge of the data signal; in response to receiving the transition edge of the data signal, shifting the eleventh magnetic flux quantum from the second superconducting loop to the first superconducting loop; receiving, via an address line coupled to the second, third, and fourth superconducting loops, a transition edge of the mirrored enable control signal; receiving, via an address line coupled to the fourth superconducting loop, a transition edge of the strobe control signal; in response to receiving the transition edge of the strobe control signal, reversing the twelfth magnetic flux quantum such that it produces an anticlockwise current; outputting a transition edge of an output signal to a readout line; receiving, via an address line coupled to a first superconducting loop and a second superconducting loop, a further transition edge of the data signal; in response to receiving the further transition edge of the data signal, shifting the eleventh magnetic flux quantum from the first superconducting loop to the second superconducting loop;receiving, via an address line coupled to the second, third, and fourth superconducting loop, a further transition edge of the mirrored enable control signal; receiving, via an address line coupled to the fourth superconducting loop, a further transition edge of the strobe control signal; in response to receiving the transition edge of the strobe control signal, reversing the twelfth magnetic flux quantum such that it produces a clockwise current; and outputting a further transition edge of the output signal to the readout line.

[0137] In the following EEEs, the numbered magnetic flux quanta may be, but do not have to be, identical to the eleventh and twelfth magnetic flux quantum as resulting from some of the above-described method EEEs. For example, the thirteenth and fourteenth magnetic flux quantum may be identical to the eleventh and twelfth magnetic flux quantum, but they may also be newly-initialized or otherwise different magnetic flux quantum.

[0138] EEE 18 includes the method of either EEE 12 or EEE 17, wherein a thirteenth and fourteenth magnetic flux quantum are stored in each of a second superconducting loop and a fourth superconducting loop, wherein the fourteenth magnetic flux quantum is half a magnetic flux quantum producing a clockwise current, and wherein in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops comprises: receiving, via an address line coupled to the second, third, and fourth superconducting loops, a transition edge of the mirrored enable control signal; in response to receiving the transition edge of the mirrored enable control signal, shifting the thirteenth magnetic flux quantum from the second superconducting loop to the third superconducting loop; in response to receiving the transition edge of the mirrored enable control signal, reversing the fourteenth magnetic flux quantum such that it such that it produces an anticlockwise current; receiving, via an address line coupled to the fourth superconducting loop, a transition edge of the strobe control signal; receiving, via an address line coupled to the second, third, and fourth superconducting loops, a further transition edge of the mirrored enable control signal;in response to receiving the further transition edge of the mirrored enable control signal, shifting the thirteenth magnetic flux quantum from the third superconducting loop to the second superconducting loop; in response to receiving the further transition edge of the mirrored enable control signal, reversing the fourteenth magnetic flux quantum such that it produces a clockwise current; and receiving, via an address line coupled to the fourth superconducting loop, a further transition edge of the strobe control signal.

[0139] EEE 19 includes the method of either EEE 17 or EEE 18, wherein a fifteenth and sixteenth magnetic flux quantum are stored in each of a second superconducting loop and a fourth superconducting loop, wherein the sixteenth magnetic flux quantum is half a magnetic flux quantum producing a clockwise current, and wherein in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops comprises: receiving, via an address line coupled to a first superconducting loop and a second superconducting loop, a transition edge of the data signal; in response to receiving the transition edge of the data signal, shifting the fifteenth magnetic flux quantum from the second superconducting loop to the first superconducting loop; receiving, via an address line coupled to the fourth superconducting loop, a transition edge of the strobe control signal; in response to receiving the transition edge of the strobe control signal, reversing the sixteenth magnetic flux quantum such that it produces an anticlockwise current; outputting a transition edge of an output signal to a readout line; receiving, via an address line coupled to the first superconducting loop and the second superconducting loop, a further transition edge of the data signal; in response to receiving the further transition edge of the data signal, shifting the fifteenth magnetic flux quantum from the first superconducting loop to the second superconducting loop; receiving, via an address line coupled to the fourth superconducting loop, a further transition edge of the strobe control signal;in response to receiving the transition edge of the strobe control signal, reversing the sixteenth magnetic flux quantum such that it produces a clockwise current; and outputting a further transition edge of the output signal to the readout line.

[0140] EEE 20 includes the method of any of EEEs 17-19, wherein a seventeenth and eighteenth magnetic flux quantum are stored in each of a second superconducting loop and a fourth superconducting loop, wherein the eighteenth magnetic flux quantum is half a magnetic flux quantum producing a clockwise current, and wherein in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops comprises: receiving, via an address line coupled to the fourth superconducting loop, a transition edge of the strobe control signal; in response to receiving the transition edge of the strobe control signal, reversing the eighteenth magnetic flux quantum such that it produces an anticlockwise current; outputting a transition edge of an output signal to a readout line; receiving, via an address line coupled to the fourth superconducting loop, a further transition edge of the strobe control signal; in response to receiving the transition edge of the strobe control signal, reversing the eighteenth magnetic flux quantum such that it produces a clockwise current; and outputting a further transition edge of the output signal to the readout line.

[0141] EEE 21 includes the method of EEE 11, further comprising transmitting, via a readout line coupled to the plurality of superconducting loops, an output signal.

[0142] EEE 22 includes a crossbar fabric system comprising: a plurality of nodes arranged in a grid pattern, wherein each node comprises a plurality of input and output connections; a plurality of connections between neighbouring nodes within the grid pattern, wherein a connection is an intersection of an output-to-input connection and an input-to-output connection between two nodes; and coupled to each connection, a Josephson junction based crossbar device configured to multiplex signals transmitted between the nodes of the crossbar fabric system comprising: a plurality of superconducting loops, wherein each superconducting loop comprises at least one Josephson junction, wherein each loop of the plurality ofsuperconducting loops is electrically coupled, and wherein each loop of the plurality of superconducting loops is configured to shift or annihilate magnetic flux quanta in one or more of the superconducting loops in response to a combination of signals and single flux quantum (SFQ) pulses; a readout line coupled to the plurality of superconducting loops; and a plurality of data and control lines coupled to the plurality of superconducting loops, wherein each line of the plurality of data and control lines is configured to provide at least one of a plurality of signals to at least a portion of the plurality of superconducting loops, wherein the plurality of signals comprises: a data signal; a mirrored enable control signal; and a strobe control signal. Conclusion

[0143] The present disclosure is not to be limited in terms of the particular embodiments described in this application, which are intended as illustrations of various aspects. Many modifications and variations can be made without departing from its scope, as will be apparent to those skilled in the art. Functionally equivalent methods and apparatuses within the scope of the disclosure, in addition to those described herein, will be apparent to those skilled in the art from the foregoing descriptions. Such modifications and variations are intended to fall within the scope of the appended claims.

[0144] The above detailed description describes various features and operations of the disclosed systems, devices, and methods with reference to the accompanying figures. The example embodiments described herein and in the figures are not meant to be limiting. Other embodiments can be utilized, and other changes can be made, without departing from the scope of the subject matter presented herein. It will be readily understood that the aspects of the present disclosure, as generally described herein, and illustrated in the figures, can be arranged, substituted, combined, separated, and designed in a wide variety of different configurations.

[0145] With respect to any or all of the message flow diagrams, scenarios, and flow charts in the figures and as discussed herein, each step, block, operation, and / or communication can represent a processing of information and / or a transmission of information in accordance with example embodiments. Alternative embodiments are included within the scope of theseexample embodiments. In these alternative embodiments, for example, operations described as method steps, blocks, transmissions, communications, requests, responses, and / or messages can be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved. Further, more or fewer blocks and / or operations can be used with any of the message flow diagrams, scenarios, and flow charts discussed herein, and these message flow diagrams, scenarios, and flow charts can be combined with one another, in part or in whole.

[0146] A step, block, or operation that represents a processing of information can correspond to circuitry that can be configured to perform the specific logical functions of a herein-described method or technique. Alternatively or additionally, a step or block that represents a processing of information can correspond to a module, a segment, or a portion of program code (including related data). The program code can include one or more instructions executable by a processor for implementing specific logical operations or actions in the method or technique. The program code and / or related data can be stored on any type of computer- readable medium such as a storage device including RAM, a disk drive, a solid state drive, or another storage medium.

[0147] The computer-readable medium can also include non-transitory computer- readable media such as computer-readable media that store data for short periods of time like register memory and processor cache. The computer-readable media can further include non- transitory computer-readable media that store program code and / or data for longer periods of time. Thus, the computer-readable media may include secondary or persistent long term storage, like ROM, optical or magnetic disks, solid state drives, compact-disc read-only memory (CD- ROM), for example. The computer-readable media can also be any other volatile or non-volatile storage systems. A computer-readable medium can be considered a computer-readable storage medium, for example, or a tangible storage device.

[0148] Moreover, a step, block, or operation that represents one or more information transmissions can correspond to information transmissions between software and / or hardware modules in the same physical device. However, other information transmissions can be between software modules and / or hardware modules in different physical devices.

[0149] The particular arrangements shown in the figures should not be viewed as limiting. It should be understood that other embodiments can include more or less of eachelement shown in a given figure. Further, some of the illustrated elements can be combined or omitted. Yet further, an example embodiment can include elements that are not illustrated in the figures.

[0150] While various aspects and embodiments have been disclosed herein, other aspects and embodiments will be apparent to those skilled in the art. The various aspects and embodiments disclosed herein are for purpose of illustration and are not intended to be limiting, with the true scope being indicated by the following claims.

Claims

CLAIMS What is claimed is:

1. A Josephson junction based crossbar device comprising: a plurality of superconducting loops, wherein each superconducting loop comprises at least one Josephson junction, wherein each loop of the plurality of superconducting loops is electrically coupled, and wherein each loop of the plurality of superconducting loops is configured to shift or annihilate magnetic flux quanta in one or more of the superconducting loops in response to a combination of signals and single flux quantum (SFQ) pulses; a readout line coupled to the plurality of superconducting loops; and a plurality of data and control lines coupled to the plurality of superconducting loops, wherein each line of the plurality of data and control lines is configured to provide at least one of a plurality of signals to at least a portion of the plurality of superconducting loops, wherein the plurality of signals comprises: a data signal; a mirrored enable control signal; and a strobe control signal.

2. The Josephson junction based crossbar device of claim 1, wherein the crossbar device is coupled to an AC current-bias source, and wherein each line of the plurality of data and control lines of the plurality of data and control lines comprises: a Josephson transmission line; at least one inductor; and a resistor connected between the Josephson transmission line and a corresponding superconducting loop of the plurality of superconducting loops.

3. The Josephson junction based crossbar device of claim 1, wherein: the data signal is configured to be transmitted to a first loop and a second loop of the plurality of superconducting loops; the mirrored enable control signal is configured to be transmitted to the second loop and a third loop of the plurality of superconducting loops; andthe strobe control signal is configured to be transmitted to the third loop and a fourth loop of the plurality of superconducting loops.

4. The Josephson junction based crossbar device of claim 1, wherein the strobe control signal comprises a periodic clock signal.

5. The Josephson junction based crossbar device of claim 1, wherein the plurality of superconducting loops is electrically coupled in a sequential arrangement, wherein each superconducting loop of the plurality of superconducting loops has one or two adjacent loops.

6. The Josephson junction based crossbar device of claim 5, wherein the plurality of superconducting loops are configured to shift a magnetic flux quanta from an initial superconducting loop to an adjacent loop in response to a SFQ pulse applied to the initial superconducting loop and based on the presence of magnetic flux quanta in the plurality of superconducting loops.

7. The Josephson junction based crossbar device of claim 6, wherein the magnetic flux quanta is shifted from an initial superconducting loop to an adjacent loop in a first direction along the sequential arrangement in response to a positive SFQ pulse polarity and based on the presence and orientation of magnetic flux quanta in the plurality of superconducting loops, and wherein the magnetic flux quanta is shifted from an initial superconducting loop to an adjacent loop in a second direction along the sequential arrangement in response to a negative SFQ pulse polarity and based on the presence and orientation of magnetic flux quanta in the plurality of superconducting loops.

8. The Josephson junction based crossbar device of claim 6, wherein: the data signal is configured to be transmitted to a first and second loop of the plurality of superconducting loops, and wherein the data signal is configured to shift a magnetic flux quantum from the first loop to the second loop and from the second loop to the first loop based on the presence of magnetic flux quanta in the plurality of superconducting loops; the mirrored enable control signal is configured to be transmitted to the second loop and a third loop of the plurality of superconducting loops, and wherein the mirrored enable controlsignal is configured to shift a magnetic flux quantum from the second loop to the third loop and from the third loop to the second loop based on the presence of magnetic flux quanta in the plurality of superconducting loops; and the strobe control signal is configured to be transmitted to the third and a fourth loop of the plurality of superconducting loops, and wherein the strobe control signal is configured to shift a magnetic flux quantum from the third loop to the fourth loop and from the fourth loop to the third loop based on the presence of magnetic flux quanta in the plurality of superconducting loops.

9. The Josephson junction based crossbar device of claim 1, further comprising at least one magnetically coupled feed line, wherein the plurality of superconducting loops are further configured to provide an initial flux state in response to a two-step flux initialization process, wherein the two-step flux initialization process comprises: while cooling down the Josephson junction based crossbar device, providing an initialization signal via the at least one magnetically coupled feed line; and upon reaching a superconducting critical temperature of the Josephson junction based crossbar device, turning off the initialization signal such that an exact integral number of SFQ are stored in the plurality of superconducting loops.

10. A method for multiplexing digital signals in a Josephson junction based crossbar device comprising: providing, to a plurality of superconducting loops, a combination of a plurality of signals and single flux quantum (SFQ) pulses, wherein each superconducting loop comprises at least one Josephson junction, wherein each loop of the plurality of superconducting loops is electrically coupled, wherein the plurality of signals comprises a data signal, a mirrored enable control signal, and a strobe control signal, wherein a plurality of data and control lines are coupled to the plurality of superconducting loops, wherein each line of the plurality of data and control lines is configured to provide at least one of a plurality of signals to at least a portion of the plurality of superconducting loops; and in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops.

11. The method of claim 10, wherein the plurality of superconducting loops is electrically coupled in a sequential arrangement, wherein each superconducting loop of the plurality of superconducting loops has one or two adjacent loops, and wherein the plurality of superconducting loops are configured to shift a magnetic flux quanta from an initial superconducting loop to an adjacent loop in response to a SFQ pulse applied to the initial superconducting loop based on the presence of magnetic flux quanta in the plurality of superconducting loops.

12. The method of claim 11, wherein a first and second magnetic flux quantum are stored in each of a second and a fourth superconducting loop, and wherein in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops comprises: receiving, via an address line coupled to a first and second superconducting loop, a transition edge of the data signal; in response to receiving the transition edge of the data signal, shifting the first magnetic flux quantum from the second superconducting loop to the first superconducting loop; receiving, via an address line coupled to the second and a third superconducting loop, a transition edge of the mirrored enable control signal; receiving, via an address line coupled to the third and fourth superconducting loop, a transition edge of the strobe control signal; in response to receiving the transition edge of the strobe control signal, shifting the second magnetic flux quantum from the fourth superconducting loop to the third superconducting loop; and outputting a transition edge of an output signal to a readout line.

13. The method of claim 11, wherein a third and fourth magnetic flux quantum are stored in each of a first and a third superconducting loop and wherein in response to the combination of signals and SFQ pulses, shifting or annihilating magnetic flux quanta in one or more of the superconducting loops comprises: receiving, via an address line coupled to the first and a second superconducting loop, a transition edge of the data signal;in response to receiving the transition edge of the data signal, shifting the third magnetic flux quantum from the first superconducting loop to the second superconducting loop; receiving, via an address line coupled to the second and a third superconducting loop, a transition edge of the mirrored enable control signal; receiving, via an address line coupled to the third and fourth superconducting loop, a transition edge of the strobe control signal; in response to receiving the transition edge of the strobe control signal, shifting the fourth magnetic flux quantum from the third superconducting loop to the fourth superconducting loop; and outputting a transition edge of an output signal to a readout line.

14. The method of claim 10, further comprising: transmitting, via a readout line coupled to the plurality of superconducting loops, an output signal.

15. A crossbar fabric system comprising: a plurality of nodes arranged in a grid pattern, wherein each node comprises a plurality of input and output connections; a plurality of connections between neighbouring nodes within the grid pattern, wherein a connection is an intersection of an output-to-input connection and an input-to-output connection between two nodes; and coupled to each connection, a Josephson junction based crossbar device configured to multiplex signals transmitted between the nodes of the crossbar fabric system comprising: a plurality of superconducting loops, wherein each superconducting loop comprises at least one Josephson junction, wherein each loop of the plurality of superconducting loops is electrically coupled, and wherein each loop of the plurality of superconducting loops is configured to shift or annihilate magnetic flux quanta in one or more of the superconducting loops in response to a combination of signals and single flux quantum (SFQ) pulses; a readout line coupled to the plurality of superconducting loops; anda plurality of data and control lines coupled to the plurality of superconducting loops, wherein each line of the plurality of data and control lines is configured to provide at least one of a plurality of signals to at least a portion of the plurality of superconducting loops, wherein the plurality of signals comprises: a data signal; a mirrored enable control signal; and a strobe control signal.

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