Systems and methods for applying flux to a quantum-coherent superconducting circuit

1. A system for applying flux to a quantum-coherent superconducting circuit, the system comprising:

a long-Josephson junction (LJJ);

an inductive loop coupled to a midpoint of the LJJ, in parallel with the LJJ, and inductively coupled to the quantum-coherent superconducting circuit; and

a single flux quantum (SFQ) controller configured to apply a combination of a positive single flux quantum (SFQ) pulse and a negative SFQ pulse with respect to at least one of a first end of the LJJ and a second end of the LJJ to set a flux quantum of the inductive loop to a first value of control flux and a second value of control flux, respectively, that is applied to the quantum-coherent superconducting circuit.

2. The system of claim 1 , wherein the applying the combination of the positive SFQ pulse and the negative SFQ pulse comprises:

applying the positive SFQ pulse to the first end of the LJJ that propagates the positive SFQ pulse to a matched load at the second end of the LJJ, while also applying the flux quantum to the inductive loop to set the first value of control flux; and

applying the negative SFQ pulse to the first end of the LJJ that propagates the negative SFQ pulse to the matched load at the second end of the LJJ, after the applying of the positive SFQ pulse to the first end, while also removing the flux quantum from the inductive loop resulting in the second value of control flux being applied to the quantum-coherent superconducting circuit.

3. The system of claim 1 , wherein the applying the combination of the positive SFQ pulse and the negative SFQ pulse comprises:

applying the negative SFQ pulse to the second end of the LJJ that propagates the negative SFQ pulse to the first end of the LJJ, while also applying the flux quantum to the inductive loop to set the first value of control flux; and

applying the positive SFQ pulse to the second end of the LJJ that propagates the positive SFQ pulse to the first end of the LJJ, after the applying of the negative SFQ pulse to the second end, while also removing the flux quantum from the inductive loop resulting in the second value of control flux being applied to the quantum-coherent superconducting circuit.

4. The system of claim 1 , wherein the inductive loop is DC flux biased to establish a half of flux quantum that establishes a bi-stable persistent current in the inductive loop that is initially in a first direction.

5. The system of claim 4 , wherein applying the flux quantum to the inductive loop with the positive SFQ pulse results in the first value of control flux applied to the quantum-coherent superconducting circuit and is due to a change of the bi-stable persistent current in the inductive loop changing to a second direction in the inductive loop opposite the first direction.

6. The system of claim 1 , wherein the quantum coherent superconducting circuit is a qubit.

7. An N-bit digital-to-analog converter comprising N systems of claim 1 , coupled between a shift register and a qubit, wherein each of the different N systems have different coupling efficiencies to the qubit each associated with a significance of an associated bit of the N-bit digital-to-analog converter.

8. The system of claim 1 , wherein the LJJ is implemented as one of a Josephson junction array in a long-Josephson-junction limit arrangement and a single wide Josephson junction arrangement.

9. A system for actuating a flux-tunable coupler comprising the system of claim 1 , coupled to a flux tunable coupler that is coupled to a first qubit and a second qubit.

10. A system for applying flux to a quantum-coherent superconducting circuit, the system comprising:

a long-Josephson junction (LJJ) implemented as a Josephson junction array in a long-Josephson-junction limit arrangement;

an inductive loop coupled to the LJJ at a midpoint of the LJJ, in parallel with the LJJ, and inductively coupled to the quantum-coherent superconducting circuit;

a DC source inductively coupled to the inductive loop to provide a DC flux bias to establish a half of flux quantum that establishes a bi-stable persistent current in the inductive loop that is initially in a first direction; and

a single flux quantum (SFQ) controller configured to apply:

a first negative single flux quantum (SFQ) pulse to a first end of the LJJ that propagates the first negative SFQ pulse to a second end of the LJJ, while also applying a flux quantum to the inductive loop resulting in a first value of control flux being applied to the quantum-coherent superconducting circuit; and

a second negative SFQ pulse to the second end of the LJJ that propagates the second negative SFQ pulse to the first end of the LJJ, while also removing the flux quantum from the inductive loop resulting in a second value of control flux being applied to the quantum-coherent superconducting circuit.

11. The system of claim 10 , wherein the applying the flux quantum to the inductive loop with the first negative SFQ pulse resulting in the first value of control flux applied to the quantum-coherent superconducting circuit is due to a change of the bi-stable persistent current in the inductive loop changing to a second direction in the inductive loop.

12. The system of claim 11 , wherein the removing the flux quantum from the inductive loop resulting in the second value of control flux applied to the quantum-coherent superconducting circuit is due to a change of the bi-stable persistence current in the inductive loop changing back to the first direction.

13. A method for applying flux to a quantum-coherent superconducting circuit, the method comprising:

applying a DC flux bias to an inductive loop coupled to a long-Josephson junction (LJJ), in parallel with the LJJ, and inductively coupled to the quantum-coherent superconducting circuit to establish a half of flux quantum that establishes a bi-stable persistent current in the inductive loop that is initially in a first direction;

applying a combination of a positive single flux quantum (SFQ) pulse and a negative SFQ pulse with respect to at least one of a first end of the LJJ and a second end of the LJJ to set a flux quantum of the inductive loop to a first value of control flux and a second value of control flux, respectively, that is applied to the quantum-coherent superconducting circuit.

14. The method of claim 13 , wherein the applying the combination of the positive SFQ pulse and the negative SFQ pulse comprises:

applying the positive SFQ pulse to the first end of the LJJ that propagates the positive SFQ pulse to a matched load at the second end of the LJJ, after the applying of a positive SFQ pulse to the first end, while also applying the flux quantum to the inductive loop to set the first value of control flux; and

applying the negative SFQ pulse to the first end of the LJJ that propagates the negative SFQ pulse to the matched load at the second end of the LJJ, after the applying of the positive SFQ pulse to the first end, while also removing the flux quantum from the inductive loop resulting in the second value of control flux being applied to the quantum-coherent superconducting circuit.

15. The method of claim 14 , wherein applying the flux quantum to the inductive loop with the positive SFQ pulse to in the first value of control flux is due to a change of the bi-stable persistent current in the inductive loop changing to a second direction opposite the first direction.

16. The method of claim 13 , wherein the LJJ is implemented as one of a Josephson junction array in a long-Josephson-junction limit arrangement and a single wide Josephson junction arrangement.

17. The method of claim 13 , wherein the applying the combination of the positive SFQ pulse and the negative SFQ pulse comprises:

applying the negative SFQ pulse to the second end of the LJJ that propagates the negative SFQ pulse to the first end of the LJJ, while also applying the flux quantum to the inductive loop to set the first value of control flux; and

applying the positive SFQ pulse to the second end of the LJJ that propagates the positive SFQ pulse to the first end of the LJJ, after the applying of the negative SFQ pulse to the second end, while also removing the flux quantum from the inductive loop resulting in the second value of control flux being applied to the quantum-coherent superconducting circuit.

18. The system of claim 1 ,

wherein the LJJ comprises a parallel array of un-shunted Josephson junctions connected in parallel with capacitors; and

wherein the un-shunted Josephson junctions are interconnected by a series of inductors.