RELATED APPLICATIONS

[0001] This application claims priority from U.S. Patent Application Serial

No. 15/886626, filed 1 February 2019, which is incorporated herein in its entirety.

TECHNICAL FIELD

[0002] The present invention relates generally to quantum and classical digital superconducting circuits, and specifically to reciprocal quantum logic (RQL) gates that provide majority, AND, and OR functions.

BACKGROUND

[0003] In the field of digital logic, extensive use is made of well known and highly developed complimentary metal-oxide semiconductor (CMOS) technology. As CMOS has begun to approach maturity as a technology, there is an interest in alternatives that may lead to higher performance in terms of speed, power dissipation computational density, interconnect bandwidth, and the like. An alternative to CMOS technology comprises superconductor based single flux quantum circuitry, utilizing superconducting Josephson junctions (JJs), with typical signal power of around 4 nanowatts (nW), at a typical data rate of 20 gigabits per second (Gb/s) or greater, and operating temperatures of around 4 kelvins.

[0004] A majority gate is a logical gate that returns true if and only if more than 50% of its inputs are true. Phase-mode logic allows digital values to be encoded as superconducting phases of one or more JJs. For example, a logical“1” may be encoded as a high phase and a logical“0” may be encoded as a low phase. For example, the phases may be encoded as being zero (meaning, e.g., logical“0”) or 2p (meaning e g., logical“1”). These values persist across RQL clock cycles because there is no requirement for a reciprocal pulse to reset the JJ phase.

SUMMARY

[00051 One example includes a reciprocal quantum logic (RQL) gate circuit having input and output stages. The input stage has at least two logical inputs each asserted based on receiving a positive single flux quantum (SFQ) pulse. The input stage has two or more storage loops, each logical input being associated with at least one of the storage loops. Each of the storage loops associated with a logical input includes an input Josephson junction (JJ), a storage inductor, and a logical decision JJ. The logical decision JJ is common to all the storage loops associated with the logical inputs and is configured to trigger based on biasing provided by one or more currents stored in the storage loops and a bias signal provided to the circuit. The output stage includes Josephson transmission line (JTL) circuitry configured to assert an output based on a triggering of the logical decision JJ.

[0006] Another example includes a method of determining a logic value. One or more positive SFQ pulses are provided to assert one or more logical inputs of an RQL gate having at least two logical inputs. One or more positive currents are thereby placed in one or more input storage loops in the RQL gate. The RQL gate can have at least three such storage loops, for example. A logical decision JJ in the RQL gate is thereby triggered. An assertion signal is thereby propagated from an output of the RQL gate.

[0007] Yet another example includes a circuit having at least two logical input JTLs each connected to a dovetail node, each logical input JTL comprising a storage loop input inductor connected at a respective first node, to an input JJ and a storage inductor, the storage loop input inductor, input JJ, and storage inductor of each logical input JTL being sized to provide unidirectional data flow. The circuit further includes a logical decision JJ connected between the dovetail node and a low-voltage node, such that respective storage loops are formed by the input JJ and storage inductor of each input JTL and the logical decision JJ. The circuit further includes output JTL circuitry connecting the dovetail node and a logical output node to amplify a logical decision signal made by the logical decision JJ. The circuit further includes a bias input providing a bias signal having an AC component. The circuit is configured to provide an asserted or de-asserted logical output signal at the output node based on asserted or de-asserted logical input signals provided to the logical input JTLs, respectively. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] FIG. 1 is a block diagram of an example reciprocal quantum logic (RQL) gate.

[0009] FIG. 2A is a circuit diagram of an example 2-of-3 majority gate,

[0010] FIGS. 2B-2E illustrate the functioning of the circuit of FIG. 2 A as input signals propagate through the circuit to produce an output signal.

[0011 ] FIG. 3 is a circuit diagram of an example two-input AND gate,

[0012] FIG. 4 is a circuit diagram of an example two-input OR gate,

[0013] FIG. 5 is a circuit diagram of an example three-input AND gate.

[0014] FIGS. 6A and 6B are flow diagrams of example methods of determining a logical output from an RQL gate having at least two logical inputs based on single flux quantum (SFQ) pulse inputs.

DETAILED DESCRIPTION

[0015] This disclosure relates generally to logical gate circuits for use in reciprocal quantum logic (RQL) systems and related methods. This disclosure more specifically relates to majority gates, AND gates, and OR gates.

[0016] Reciprocal quantum logic (RQL) logic gates can integrate a Josephson transmission line (JTL) into their output to provide the required amplification to drive a load. FIG. 1 shows RQL gate 100 having at least two logical inputs II through NI and output O.

Gate 100 includes amplifying output stage 102, configured to provide output Q, and input stage 104, configured to receive the two or more inputs II through NI, which can consist, for example, of positive or negative single flux quantum (SFQ) pulses corresponding to asserted or de-asserted logic states, respectively. Each input has associated with it at least one storage loop among storage loops 106-1 through 106-n. Although input stage 104 is illustrated as having one storage loop per input, each input can have more than one storage loop associated with it.

Logical decision Josephson junction (JJ) 108 is common to (i.e., shared by) all logical input storage loops, and triggers based on one or more inputs II through NI. The assertion or de-assertion of output Q is based on the triggering of logical decision JJ 108. For example, output O can propagate a positive SFQ pulse corresponding to an asserted output logic state and a negative SFQ pulse corresponding to a de-asserted output logic state. Output stage 102 includes a Josephson transmission line (JTL) to amplify the output of logical decision JJ 108.

[0017] The triggering of logical decision JJ 108 can be based not only on inputs II through NI, but also on a bias signal 112 provided to input stage 104. Bias signal 112 can provide both AC and DC bias. Thus, for example, bias signal 1 12 can act as a clock to RQL gate 100, causing the evaluation of the inputs II through NI to produce the output O at certain points in time according to the AC component of bias signal 112.

[0018] FIG. 2A illustrates an RQL gate that can have a number of configurations to provide a number of different logical functions. Specifically the illustrated configuration provides an RQL majority gate circuit 200, producing an asserted output only when a majority of the logical inputs are asserted. More specifically, gate 200 is a 2-of-3 majority gate, producing an assertion signal at output MO only when two or three of inputs A, B, and C are asserted. Gate circuit 200 has a JTL output stage 202 to provide signal amplification and an input stage 204 having a number of JTL input branches that join at dovetail node 206. Together with logical decision Josephson junction (JJ) J2, the input branches form storage loops to receive and store inputs until a logical decision can be made, i.e., until a logic condition is met.

[0019] In input stage 204, a separate input storage loop is associated with each input.

Thus, for example, the input storage loop for input A includes JJs Jla and J2, as well as inductor L2a. Leading inductor Lla allows input A to be connected to a driving JTL or to the output of another gate. Logical decision JJ J2, which is common to all input storage loops, performs the logic operation of majority gate 200. The output of logical decision JJ J2 serves as the input of JTL stage 202.

[0020] The selections of component sizes in each storage loop in input stage 204 provide a unidirectional data flow. Circuit 200 operates on SFQ pulses, which each place one Fo (about 2.07 mA-pH) of current into a storage loop. The magnitude of current through such a storage loop is determined by the size of the storage inductor in the storage loop. Thus, for each input, the inductance value of the storage loop input inductor (e.g., Lla) can be small (e.g , between about 8 pH and 9 pH, e.g., 8.5 pH) in comparison to the inductance value of the storage inductor (e.g., L2a). On the other hand, the storage inductor can size to be relatively large (e.g., between about 30 pH and 40 pH, e.g., 35 pH) (e.g., about four times larger than the

corresponding storage loop input inductor) to reduce the magnitude of the stored current induced by an input SFQ pulse. In some examples the magnitude of a current introduced at an input (e.g.. A) is about four times larger than the current stored in a storage loop. The input JJ for input A, I la is also sized such that the driving JTL is capable of flipping this JJ to put current into the storage loop, but the current in the storage loop is never sufficient to unflip input JJ Jla and allow the stored pulse to back out of the input.

[0021] The storage loops associated with inputs B and C can have the same structure as the storage loop for input A, all overlapping at logical decision JJ J2. Output MO may also be connected to a JTL or to the input of another gate, for example, to propagate positive or negative output pulses representing the assertion or de- assertion of gate 200 to logical“high” or“low,” respectively.

[0022] Logical decision JJ J2 performs the logic function of the input stage 204 of gate 200. The combination of any two inputs, plus the bias BIAS, is sufficient to switch logical decision JJ .12 in either direction. As mentioned with respect to bias signal 112 in gate 100 of FIG. 1, an AC component (e.g., a sine wave component) of bias signal BIAS in gate 200 of FIG. 2A can act as a clock signal to input stage 204 which can evaluate the logical inputs twice per cycle of the clock signal. The AC phase of bias signal BIAS can have alternating positive and negative portions. During the positive portion of the AC phase, input stage 204 evaluates inputs A through C to decide whether the output of input stage 204 should be asserted; during the negative portion of the AC phase, input stage 204 evaluates inputs A through C to decide whether the output of input stage 204 should be de- asserted.

[0023] The functioning of a single input branch of input stage 204 will now be described.

As shown in FIG. 2B, an input pulse, e.g., a single flux quantum (SFQ) pulse, arriving at input A induces a positive superconducting current 206 through leading inductor LI a and input JJ Jla, which in turn triggers input JJ Jla, raising its superconducting phase to 2p. The triggering of input JJ Jla induces an equal and opposite current 208 (e.g., one Fo worth of current) in leading inductor Lla, annihilating the initial input current 206, and also induces a positive

superconducting current 210 in the loop formed by input JJ J la, input loop storage inductor L2a, and logical decision JJ J2, as shown in FIG. 2C. This storage loop current 210 alone is insufficient to trigger logical decision JJ J2, and will remain trapped indefinitely in its storage loop if no further inputs are applied. A negative input pulse arriving at input A would reverse the above-described effects, annihilating the positive storage loop current 210 and returning the circuit to its initial state. Inputs B and C operate in exactly the same manner, as they are perfectly symmetrical with input A.

[0024] Storage loop current from one input alone is insufficient to trigger logical decision

JJ J2, even with the AC and DC bias BIAS, because of the majority structure of input stage 204. The additional load presented to logical decision JJ J2 by the components associated with unasserted inputs B and C inhibits logical decision JJ J2 from triggering. Thus, assertion of a majority of inputs is required to cause J2 to trigger in circuit 200.

[0025] The functioning of input stage 204 wi ll now be described for the condition when a majority of the inputs are asserted, i.e., when positive currents associated with at least two input branches circulate in storage loops associated with at least two inputs, each input having been asserted in the manner described above. Loop currents in the storage loops induced by positive input pulses at respective inputs will persist until subsequent negative pulses on the respective inputs remove them, or until the clocking function of the AC component of bias signal B IAS triggers logical decision JJ J2 to transform the inputs into a logic decision. Because of this storage functionality, inputs needed to amount to a majority number of input assertions need not arrive within the same clock cycle.

[0026] FIG. 2D shows the state of circuit 200 after two inputs (in the illustrated case, inputs A and C) have been asserted. Current 210 circulates in the storage loop formed by JJs J la and J2 and storage inductor L2a, while current 210 circulates in the storage loop formed by JJs Jlc and J2 and storage inductor L2c. The majority of asserted inputs bias logical decision JJ J2 towards a positive transition, but due to the size of input loop storage inductors L2a, L2b, and L2c, the storage loop currents are insufficient to cause this transition without additional bias current provided by the AC and DC bias BIAS. When the AC bias component has reached sufficient positive magnitude, i.e., when input stage 204 of gate 200 is positively“clocked,” logical decision JJ J2 triggers. FIG. 2E shows the result of this transition. Stored positive currents in input loop storage inductors are annihilated 214, 216 by the resulting pulse coming out of logical decision JJ J2. The triggering also induces currents in any storage loops associated with inputs that were not asserted (e.g., current 218 in the storage loop associated with input B), but such currents are negative currents, i.e., in the opposite direction of storage loop currents induced by input assertion signals. Additionally, a current 220 is driven through inductors L4 and L5 and output JJ .13, or in other words, into output stage 202 to be amplified. This current, in combination with the AC bias, will trigger junction J3 propagating as an output signal out of the output MO of gate 200. Since all inputs are symmetric, this same series of events can happen with any combination of two or more asserted inputs to drive the output MO of gate 200 logical “high,” giving the correct logical function for asserting the output of a 2-of-3 majority gate.

[0027] Any negative currents induced in unasserted inputs bias logical decision JJ J2 towards a negative transition, but not sufficiently to cause the transition alone, even with the AC and DC bias BIAS. This puts input stage 204 in the correct state to perform the correct logical function for de-asserting the output of input stage 204. Negative pulses arriving at any of the initially asserted inputs will provide negatively biasing currents in at least two of the three storage loops, such that in combination with the AC and DC bias BIAS they will unflip logical decision JJ J2 by causing it to transition out of its 2p phase, thereby de-asserting the output of input stage 204 back to logical“low.” This will occur when the AC bias has reached sufficient negative magnitude, i.e., on the negative portion of the AC bias component of bias signal BIAS. If, instead, a positive input was to arrive at an input not previously asserted, it would annihilate the respective stored negative current and negative input pulses would be required at any two of the previously asserted inputs before de-asserting the output of input stage 204 and thus de-asserting the output MO of gate 200, again providing the correct function for a 2-of 3 majority gate. [0028] Amplifying output stage 202 includes a JTL that propagates a pulse from logical decision JJ J2 through inductors L4 and L5 to trigger output JJ J3 and thus send a pulse out output MO, which assertion signal or de-assertion signal is indicative of a majority of inputs A, B, C being asserted, or de-asserted, respectively. Larger fan-in gates, such as a 3-of-5 majority gate, a 4-of-7 majority gate, etc., can be constructed by providing additional input branches dovetailing at node 206 and sizing components such that logical decision JJ 12 is biased to trigger only upon a majority of asserted inputs regardless of the number of input branches.

[0029] Gate 200 can serve as the basis for two-input logic gates such as AND and OR gates. Grounding one of the inputs (i.e , connecting one of the inputs to a circuit ground, effectively tying it to logical“low”) creates a two-input AND gate with the remaining two inputs. Alternatively, using a DC bias to induce one Fo (i.e., one SFQ pulse) of current on one of the inputs (effectively tying it to logical“high”) creates a two-input OR gate from the remaining two inputs.

[0030] FIG. 3 shows an example AND gate 300, specifically, an AND2 gate (i.e., a two- input AND gate) that is similar in configuration to the majority gate of FIG. 2, but with the third input C from FIG. 2 effectively tied to logical“low” by connecting it to a circuit ground.

Consequently leading inductor Lie and input JJ Jlc from FIG. 2 are eliminated in input stage 304 of gate 300, as compared to input stage 204 of gate 200. In AND gate 300, L2c can be made slightly larger than L2a and L2h so as to include some additional inductance to compensate for the removed input junction J lc.

[0031 ] In AND gate 300 of FIG. 3, once logical decision JJ J2 triggers in response to asserted inputs A and B, positive currents in storage inductors L2a and L2b are destroyed, a negative current is induced into substitute storage inductor L2c, and a positive current is propagated into the output stage 302 for amplification as output AO. Thereaf ter, if any negative pulses are applied to de-assert any previously asserted inputs among logical inputs A and B, one or more negative currents stored in any of the storage loops associated with the logical inputs combines with the negative current stored in substitute storage inductor L2c to bias logical decision JJ J2 to untrigger upon the next negative portion of the AC component of the bias signal BIAS, which in turn propagates a negati ve pulse out of the output of input stage 304 into output stage 302 and thus de-asserts output AO.

[0032] FIG. 4 shows an example OR gate 400 specifically, an OR2 gate (i.e., a two-input

OR gate), which is modified from the example majority gate 200 in a similar fashion to the two- input AND gate 300 of FIG. 3, hut has transformer-coupled input inductor L2c in place of a storage inductor. In OR gate 400, output OO is asserted if either or both of logical inputs A or B is asserted. Transformer-coupled input inductor L2c is transformer-coupled to DC flux bias line 406. In a similar configuration, not illustrated, bias quantizing JJ Jlc (not shown) can he connected between, on one side, transformer-coupled input inductor DC_c_0 (not shown) and substitute storage inductor L2c, and, on the other side, a circuit ground such that quantizing JJ Jlc (not shown) quantizes the DC bias current supplied through DC bias DC_c_0 (not shown) and improves operating margins. In such configuration, DC_c_0 would be tied to the circuit ground on the other side from the node where it is connected to quantizing JJ Jlc.

[0033] In the illustrated circuit 400 DC current provided through DC flux bias line 406 stays constant throughout syste operation. At system start-up, the DC current through DC flux bias line 406 couples current into input inductor L2c (or DC_c_0, in the alternate, non-illustrated configuration) to which it is transformer-coupled via the AC transient that occurs at system power-up. In the illustrated configuration 400, this puts a positive current (e.g., one Fo of current) into inductor L2c once at the beginning of operation which contributes to the biasing of logical decision JJ J2 just as much as biasing from either of the logical inputs A, B. In the alternate non-illustrated configuration, this triggers bias quantizing JJ Jlc once at the beginning of operation, putting a positive current into substitute storage inductor L2c, which contributes to the biasing of logical decision JJ J2 just as much as biasing from either of the logical inputs A, B.

[0034] Upon assertion of either of the logical inputs A, B, logical decision JJ J2 in input stage 404 of OR gate 400 of FIG. 4 then effectively sees“two” out of“three” inputs asserted, one of the“two” inputs being the asserted logical input and the other of the“two” asserted inputs being the non-logical, phantom“input” initiated by the DC bias. Logical decision JJ J2 therefore triggers in response to at least one asserted input among logical inputs A, B. Upon such triggering, the positive current in substitute storage inductor L2c is destroyed, Jlc does not unirigger, positive currents in storage inductors L2a and/or L2b are destroyed should the inputs associated with those storage inductors have been asserted, negative currents are induced in the storage inductors associated with any unasserted inputs, and a positive current is propagated into output stage 402. The amplifying action of output stage 402 consequently provides an amplified signal at output OO in FIG. 4. (The non-illustrated OR2 gate configuration with a quantizing junction functions similarly.)

[0035] Thereafter, if negative pulses are applied to de-assert all of previously asserted inputs among logical inputs A and B, the negative currents stored in the storage loops associated with the logical inputs combine to bias logical decision JJ J2 to un trigger upon the next negative portion of the AC component of the bias signal BIAS, which in turn propagates a negative pulse into output stage 402 and a negative pulse out of output OO. This un triggering of logical decision JJ J2 restores the positive current to substitute storage inductor L2c, bringing the circuit back to its initial state, i.e., the state following start-up injection of initial positive current into substitute storage inductor L2c via DC flux bias line 406.

[0036] FIG. 5 illustrates a three·· input AND gate 500 that retains all three inputs A, B, C of circuit 200, and includes input stage 504 and output stage 502, but is configured to initialize one of the internal storage loops to one Fo of current in the counter-clockwise direction by providing such current to DC flux bias line 506. In AND gate 500, the initial current works against the central, logical decision JJ J2 triggering in the positive direction. A positive input pulse must first arrive on this input (i.e., logical input C, as illustrated) so as to annihilate the stored current (i.e., stored in L2c, as illustrated). The remaining two inputs then function as described above. In alternative implementations, 1/3 of a Fo of counter-clockwise current could be initialized into each of the three storage loops, by providing DC flux bias lines transformer- coupled to all three loops (not shown) in similar fashion to how one is shown in FIG. 5

(506/L2c), or 1/2 Fo of counter-clockwise current could be initialized into two of them, by- providing DC flux bias lines transformer- coupled to those two storage loops (not shown), to yield the same effect as puting one Fo of current in the counter-clockwise direction in only one of the storage loops.

[0037] Larger fan-in gates, such as 3-input AND and OR gates can be constructed by providing additional input dovetailing branches and sizing components such that logical decision JJ .12 is biased to trigger only upon appropriate input assertion conditions, regardless of the number of input branches. Similarly, an OA21 gate can constructed by modifying a 3-of-5 majority gate input stage structure to provide one input to two parallel branches, or to a single branch having doubled JJ sizes and halved inductor sizes, and by effectively tying one of the five inputs to logical“low” by connecting it to a circuit ground.

[0038] FIG. 6A shows method 600 of determining a logical output from an RQL gate having at least one logical input based on SFQ pulse inputs. One or more positive SFQ pulses are provided 602 to assert one or more logical inputs of an RQL gate having at least two logical inputs to place 604 one or more currents in one or more input storage loops associated with the asserted inputs e.g., one loop per input. The RQL gate can be, for example, like any of gates 100, 200, 300, 400, or 500 shown in FIGS. 1-5, or can be extensions of such examples providing a greater number of inputs and/or combining or splitting input storage loop branches, as discussed previously. A JJ that is configured to trigger based on the assertion of a certain number of the logical inputs, or certain ones of the logical inputs, then triggers 606. The JJ can be so configured, for example by making it common to all of the input storage loops, by effectively tying to logical“high” or logical“low” additional inputs not counted among the logical inputs, by providing appropriate biasing, and/or by appropriate component sizing. An assertion signal, generated as a result of the triggering, then propagates 608 from an output of the RQL gate. The assertion signal can result from an amplification of a signal resulting from the triggering of the logical decision JJ. For example, the amplification can be provided by a JTL. The assertion signal can be, for example, a single positive SFQ pulse.

[0039] FIG. 6B shows method 650 of determining a logical output from an RQL gate based on SFQ pulse inputs, which can continue from method 600 shown in FIG. 6A. Negative SFQ pulses are provided 610 to de-assert one or more logical inputs of an RQL gate to place 612 one or more currents in one or more input storage loops associated with the asserted inputs, e.g., one loop per input, where the gate has more than two such storage loops. The placed currents can be negative currents, i.e., currents equal and opposite to the currents placed 604 in method 600. Again, the RQL gate can be, for example, like any of gates 100, 200, 300, 400, or 500 shown in FIGS. 1-5, or can be extensions of such examples providing a greater number of inputs and/or combining or splitting input storage loop branches, as discussed previously. A JJ that is configured to untrigger based on the de-assertion of a certain number of the logical inputs, or certain ones of the logical inputs, then untriggers 614. The JJ can be so configured, for example, by making it common to all of the input storage loops, by effectively tying to logical “high” or logical“low” additional inputs not counted among the logical inputs, by providing appropriate biasing, and/or by appropriate component sizing. A de-assertion signal, generated as a result of the triggering, then propagates 616 from an output of the RQL gate. The de-assertion signal can be, for example, a single negative SFQ pulse, opposite to the pulse propagated 608 in method 700.

[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.