Parametrically activated quantum logic gates

1. A method comprising:

obtaining operating parameters for one or more of a plurality of qubit devices in a quantum processor circuit, the plurality of qubit devices comprising a fixed-frequency qubit device and a tunable qubit device, the operating parameters based on measurements of the quantum processor circuit under an operating condition, the operating condition comprising a flux modulation applied to the tunable qubit device; and

based on the operating parameters, selecting gate parameters of a two-qubit quantum logic gate for application to a pair of qubits defined by the fixed-frequency qubit device and the tunable qubit device;

generating a control signal configured to modulate, at a modulation frequency, a transition frequency of the tunable qubit device, the modulation frequency being determined based on a transition frequency of the fixed-frequency qubit device; and

applying the two-qubit quantum logic gate to the pair of qubits by communicating the control signal to a control line coupled to the tunable qubit device;

wherein the control signal is a first control signal, the modulation frequency is a first modulation frequency, the fixed-frequency qubit device is a first fixed-frequency qubit device that defines a first qubit, the two-qubit quantum logic gate is a first two-qubit quantum logic gate, the pair of qubits is a first pair of qubits, and the method further comprises:

generating a second control signal configured to modulate the transition frequency of the tunable qubit device at a second modulation frequency, the second modulation frequency being determined based on a transition frequency of a second fixed-frequency qubit device in the quantum processor circuit; and

applying a second two-qubit quantum logic gate to a second pair of qubits in the quantum processor circuit by communicating the second control signal to the control line coupled to the tunable qubit device, the second pair of qubits comprising a second qubit defined by the tunable qubit device and a third qubit defined by the second fixed-frequency qubit device.

2. The method of claim 1 , wherein the operating parameters include an effective coupling strength between the qubit devices during the flux modulation.

3. The method of claim 1 , wherein the operating parameters are obtained for a range of modulation amplitude of the flux modulation.

4. The method of claim 1 , wherein selecting gate parameters comprises selecting initial gate parameters, and the method further comprises generating refined gate parameters from the initial gate parameters.

5. The method of claim 4 , wherein the refined gate parameters are generated based on spectroscopic measurements of the two-qubit quantum logic gate applied to the quantum processor circuit.

6. The method of claim 1 , wherein the gate parameters include a flux modulation amplitude and a flux modulation frequency.

7. The method of claim 6 , further comprising selecting a filter for a flux modulation control line based on the flux modulation frequency.

8. The method of claim 1 , wherein selecting gate parameters of a two-qubit quantum logic gate comprises selecting parameters of the control signal for delivery to the control line coupled to the tunable qubit device, and the gate parameters correspond to:

a modulation amplitude of the flux modulation produced by the control signal;

the modulation frequency of the flux modulation produced by the control signal; and

a duration of the control signal.

9. The method of claim 8 , further comprising identifying single-qubit phase corrections for the two-qubit quantum logic gate.

10. The method of claim 1 , wherein selecting gate parameters of a two-qubit quantum logic gate comprises selecting gate parameters of a Bell-Rabi gate, a controlled-Z gate, an iSWAP gate or a square-root-of-iSWAP gate.

11. The method of claim 1 , further comprising benchmarking the two-qubit quantum logic gate based on the selected gate parameters.

12. The method of claim 1 , wherein:

the tunable qubit device comprises a superconducting circuit loop that receives a first magnetic flux that tunes the transition frequency of the tunable qubit device, and the control line comprises a flux-bias device that is inductively coupled to the superconducting circuit loop to control the first magnetic flux; and

generating the control signal to modulate the transition frequency of the tunable qubit device at the modulation frequency comprises generating the control signal to modulate the first magnetic flux at half the modulation frequency.

13. The method of claim 1 , wherein:

the tunable qubit device comprises a superconducting circuit loop that receives a first magnetic flux that tunes the transition frequency of the tunable qubit device, and the control line comprises a flux-bias device that is inductively coupled to the superconducting circuit loop to control the first magnetic flux; and

generating the control signal to modulate the transition frequency of the tunable qubit device at the modulation frequency comprises generating the control signal to modulate the first magnetic flux at the modulation frequency.

14. The method of claim 1 , wherein the operating condition comprises the flux modulation applied to the tunable qubit device at a flux modulation frequency between 0.02 GigaHertz and 0.40 GigaHertz.

15. The method of claim 1 , wherein the operating condition comprises the flux modulation applied to the tunable qubit device at a flux modulation frequency between 40 MegaHertz and 160 MegaHertz.

16. A method comprising:

obtaining measurements of a coherence time of a qubit defined by a tunable qubit device in a quantum processor circuit comprising a plurality of qubit devices, the plurality of qubit devices comprising a fixed-frequency qubit device coupled to the tunable qubit device, the measurements representing values of the coherence time during a flux modulation applied to the tunable qubit device, the measurements corresponding to a range of modulation amplitudes of the flux modulation;

based on the measurements, identifying a modulation amplitude control value associated with a maximum coherence time of the qubit; and

based on the identified modulation amplitude control value, selecting a gate parameter of a two-qubit quantum logic gate for the fixed-frequency qubit device and the tunable qubit device;

wherein identifying the modulation amplitude control value comprises identifying a first modulation amplitude control value corresponding to the maximum measurement of the coherence time.

17. The method of claim 16 , wherein the tunable qubit device comprises a superconducting circuit loop that defines a flux quantum Φ 0 and receives a first magnetic flux that tunes a transition frequency of the tunable qubit device, and the flux modulation comprises a modulation of the first magnetic flux at a modulation frequency.

18. The method of claim 17 , wherein the modulation amplitude control value represents a voltage amplitude of a control signal that produces the modulation of the first magnetic flux.

19. The method of claim 17 , wherein the modulation amplitude control value corresponds to a flux modulation amplitude between 0.45Φ 0 and 0.65Φ 0 .

20. The method of claim 16 , wherein the fixed-frequency qubit device is a first fixed-frequency qubit device, and the plurality of qubit devices comprises:

the tunable qubit device; and

a plurality of fixed-frequency qubit devices each capacitively coupled to the tunable qubit device, wherein the plurality of fixed-frequency qubit devices includes the first fixed-frequency qubit device.

21. The method of claim 16 , wherein the gate parameters include the first modulation amplitude control value.

22. The method of claim 16 , wherein:

the tunable qubit device comprises a superconducting circuit loop that defines a flux quantum;

the first modulation amplitude control value corresponds to a first flux modulation amplitude; and

the gate parameters include a second modulation amplitude control value that corresponds to a second flux modulation amplitude, wherein the magnitude of difference between the first flux modulation amplitude and the second flux modulation amplitude is less than 0.1 of the flux quantum.

23. The method of claim 22 , comprising:

after identifying the first modulation amplitude, obtaining spectroscopic measurements of the two-qubit quantum logic gate applied to a pair of qubits defined by the fixed-frequency qubit device and the tunable qubit device; and

identifying the second modulation amplitude control value based on the spectroscopic measurements.

24. The method of claim 16 , wherein the coherence time is a transverse coherence time T 2 .

25. The method of claim 16 , further comprising obtaining measurements of a transition frequency shift of the tunable qubit device during a flux modulation applied to the tunable qubit device, the measurements of the transition frequency shift corresponding to a range of modulation amplitudes of the flux modulation, wherein the gate parameters are selected based in part on the measurements of the transition frequency shift.

26. A method comprising:

obtaining measurements of a quantum processor circuit comprising a plurality of qubit devices, the plurality of qubit devices comprising a fixed-frequency qubit device and a tunable qubit device;

based on the measurements and by operation of one or more processors, computing multiple distinct gate conditions for applying a two-qubit quantum logic gate to a pair of qubits defined by the fixed-frequency qubit device and the tunable qubit device;

identifying one or more of the distinct gate conditions that satisfy an operating criterion associated with the two-qubit quantum logic gate;

based on the one or more gate conditions that satisfy the operating criterion, selecting gate parameters for the two-qubit quantum logic gate;

wherein:

obtaining measurements of the quantum processor circuit includes obtaining measurements of a mean transition frequency of the tunable qubit device during a flux modulation applied to the tunable qubit device, the measurements of the mean transition frequency corresponding to a range of modulation amplitudes of the flux modulation, and

the gate parameters are selected based in part on the measurements of the mean transition frequency;

generating a first control signal configured to modulate a transition frequency of the tunable qubit device at a first modulation frequency; and

applying the two-qubit quantum logic gate to the pair of qubits by communicating the control signal to a control line coupled to the tunable qubit device;

wherein the fixed-frequency qubit device is a first fixed-frequency qubit device that defines a first qubit, the two-qubit quantum logic gate is a first two-qubit quantum logic gate, the pair of qubits is a first pair of qubits, and the method further comprises:

generating a second control signal configured to modulate the transition frequency of the tunable qubit device at a second modulation frequency; and

applying a second two-qubit quantum logic gate to a second pair of qubits in the quantum processor circuit by communicating the second control signal to the control line coupled to the tunable qubit device, the second pair of qubits comprising a second qubit defined by the tunable qubit device and a third qubit defined by a second fixed-frequency qubit device.

27. The method of claim 26 , further comprising identifying resonant conditions for a plurality of transitions to be suppressed in the quantum processor circuit during application of the two-qubit quantum logic gate, wherein the one or more gate conditions that satisfy the operating criterion are identified based on avoiding the resonant conditions.

28. The method of claim 26 , wherein identifying one or more of the distinct gate conditions that satisfy the operating criterion comprises identifying a gate condition that is at least a minimum distance, in a modulation frequency and modulation amplitude domain, from resonant conditions of transitions to be suppressed in the quantum processor circuit during application of the two-qubit quantum logic gate.

29. The method of claim 26 , wherein the tunable qubit device comprises a superconducting circuit loop that defines a flux quantum Φ 0 and receives a first magnetic flux that tunes a transition frequency of the tunable qubit device, and applying the two-qubit quantum logic gate comprises modulating the first magnetic flux at a modulation frequency.

30. The method of claim 26 , wherein the multiple distinct gate conditions are computed for a range of modulation amplitudes, and each distinct gate condition includes:

a modulation amplitude of a flux modulation;

a modulation frequency of the flux modulation; and

a duration of the flux modulation.

31. The method of claim 30 , wherein identifying one or more of the distinct gate conditions that satisfy an operating criterion associated with the two-qubit quantum logic gate comprises identifying the gate condition that includes the minimum duration.

32. The method of claim 26 , comprising identifying one or more of the distinct gate conditions that satisfy multiple operating criteria associated with the two-qubit quantum logic gate.

33. The method of claim 26 , wherein each of distinct gate conditions includes a modulation frequency that is based on:

a transition frequency of the tunable qubit device; and

a transition frequency of the fixed-frequency qubit device.

34. The method of claim 33 , wherein each of the distinct gate conditions further includes a modulation amplitude, and the modulation frequency in each gate condition is based on a transition frequency shift of the tunable qubit device under the modulation amplitude included in the gate condition.

35. The method of claim 26 , wherein selecting gate parameters for the two-qubit quantum logic gate comprises selecting parameters of a control signal for delivery to the control line coupled to the tunable qubit device, and the gate parameters correspond to:

a modulation amplitude of a flux modulation produced by the control signal;

a modulation frequency of the flux modulation produced by the control signal; and

a duration of the control signal.

36. The method of claim 35 , further comprising identifying single-qubit phase corrections for the two-qubit quantum logic gate.

37. The method of claim 26 , wherein selecting gate parameters for the two-qubit quantum logic gate comprises selecting gate parameters of a Bell-Rabi gate, a controlled-Z gate, an iSWAP gate or a square-root-of-iSWAP gate.

38. The method of claim 26 , further comprising benchmarking the two-qubit quantum logic gate based on the selected gate parameters.

39. A method comprising:

obtaining measurements of a quantum processor circuit comprising a plurality of qubit devices, the plurality of qubit devices comprising a fixed-frequency qubit device and a tunable qubit device;

based on the measurements and by operation of one or more processors, computing multiple distinct gate conditions for applying a two-qubit quantum logic gate to a pair of qubits defined by the fixed-frequency qubit device and the tunable qubit device;

identifying one or more of the distinct gate conditions that satisfy an operating criterion associated with the two-qubit quantum logic gate;

based on the one or more gate conditions that satisfy the operating criterion, selecting gate parameters for the two-qubit quantum logic gate;

wherein the multiple distinct gate conditions are computed for a range of modulation amplitudes, and each distinct gate condition includes:

a modulation amplitude of a flux modulation;

a modulation frequency of the flux modulation; and

a duration of the flux modulation,

generating a first control signal configured to modulate a transition frequency of the tunable qubit device at a first modulation frequency; and

applying the two-qubit quantum logic gate to the pair of qubits by communicating the control signal to a control line coupled to the tunable qubit device;

wherein the fixed-frequency qubit device is a first fixed-frequency qubit device that defines a first qubit, the two-qubit quantum logic gate is a first two-qubit quantum logic gate, the pair of qubits is a first pair of qubits, and the method further comprises:

generating a second control signal configured to modulate the transition frequency of the tunable qubit device at a second modulation frequency; and

applying a second two-qubit quantum logic gate to a second pair of qubits in the quantum processor circuit by communicating the second control signal to the control line coupled to the tunable qubit device, the second pair of qubits comprising a second qubit defined by the tunable qubit device and a third qubit defined by a second fixed-frequency qubit device.

40. The method of claim 39 , further comprising identifying resonant conditions for a plurality of transitions to be suppressed in the quantum processor circuit during application of the two-qubit quantum logic gate, wherein the one or more gate conditions that satisfy the operating criterion are identified based on avoiding the resonant conditions.

41. The method of claim 39 , wherein identifying one or more of the distinct gate conditions that satisfy the operating criterion comprises identifying a gate condition that is at least a minimum distance, in a modulation frequency and modulation amplitude domain, from resonant conditions of transitions to be suppressed in the quantum processor circuit during application of the two-qubit quantum logic gate.

42. The method of claim 39 , wherein the tunable qubit device comprises a superconducting circuit loop that defines a flux quantum Φ 0 and receives a first magnetic flux that tunes a transition frequency of the tunable qubit device, and applying the two-qubit quantum logic gate comprises modulating the first magnetic flux at a modulation frequency.

43. The method of claim 39 , wherein:

obtaining measurements of the quantum processor circuit includes obtaining measurements of a mean transition frequency of the tunable qubit device during a flux modulation applied to the tunable qubit device, the measurements of the mean transition frequency corresponding to a range of modulation amplitudes of the flux modulation, and

the gate parameters are selected based in part on the measurements of the mean transition frequency.

44. The method of claim 39 , wherein identifying one or more of the distinct gate conditions that satisfy an operating criterion associated with the two-qubit quantum logic gate comprises identifying the gate condition that includes the minimum duration.

45. The method of claim 39 , comprising identifying one or more of the distinct gate conditions that satisfy multiple operating criteria associated with the two-qubit quantum logic gate.

46. The method of claim 39 , wherein each of distinct gate conditions includes a modulation frequency that is based on:

a transition frequency of the tunable qubit device; and

a transition frequency of the fixed-frequency qubit device.

47. The method of claim 46 , wherein each of the distinct gate conditions further includes a modulation amplitude, and the modulation frequency in each gate condition is based on a transition frequency shift of the tunable qubit device under the modulation amplitude included in the gate condition.

48. The method of claim 39 , wherein selecting gate parameters for the two-qubit quantum logic gate comprises selecting parameters of a control signal for delivery to the control line coupled to the tunable qubit device, and the gate parameters correspond to:

a modulation amplitude of a flux modulation produced by the control signal;

a modulation frequency of the flux modulation produced by the control signal; and

a duration of the control signal.

49. The method of claim 48 , further comprising identifying single-qubit phase corrections for the two-qubit quantum logic gate.

50. The method of claim 39 , wherein selecting gate parameters for the two-qubit quantum logic gate comprises selecting gate parameters of a Bell-Rabi gate, a controlled-Z gate, an iSWAP gate or a square-root-of-iSWAP gate.

51. The method of claim 39 , further comprising benchmarking the two-qubit quantum logic gate based on the selected gate parameters.

52. A method comprising:

obtaining measurements of a quantum processor circuit comprising a plurality of qubit devices, the plurality of qubit devices comprising a fixed-frequency qubit device and a tunable qubit device;

based on the measurements and by operation of one or more processors, computing multiple distinct gate conditions for applying a two-qubit quantum logic gate to a pair of qubits defined by the fixed-frequency qubit device and the tunable qubit device;

identifying one or more of the distinct gate conditions that satisfy an operating criterion associated with the two-qubit quantum logic gate;

based on the one or more gate conditions that satisfy the operating criterion, selecting gate parameters for the two-qubit quantum logic gate;

wherein selecting gate parameters for the two-qubit quantum logic gate comprises selecting parameters of a control signal for delivery to a control line coupled to the tunable qubit device, and the gate parameters correspond to:

a modulation amplitude of a flux modulation produced by the control signal;

a modulation frequency of the flux modulation produced by the control signal; and

a duration of the control signal,

generating a first control signal configured to modulate a transition frequency of the tunable qubit device at a first modulation frequency; and

applying the two-qubit quantum logic gate to the pair of qubits by communicating the first control signal to the control line coupled to the tunable qubit device;

wherein the fixed-frequency qubit device is a first fixed-frequency qubit device that defines a first qubit, the two-qubit quantum logic gate is a first two-qubit quantum logic gate, the pair of qubits is a first pair of qubits, and the method further comprises:

generating a second control signal configured to modulate the transition frequency of the tunable qubit device at a second modulation frequency; and

applying a second two-qubit quantum logic gate to a second pair of qubits in the quantum processor circuit by communicating the second control signal to the control line coupled to the tunable qubit device, the second pair of qubits comprising a second qubit defined by the tunable qubit device and a third qubit defined by a second fixed-frequency qubit device.

53. The method of claim 52 , further comprising identifying resonant conditions for a plurality of transitions to be suppressed in the quantum processor circuit during application of the two-qubit quantum logic gate, wherein the one or more gate conditions that satisfy the operating criterion are identified based on avoiding the resonant conditions.

54. The method of claim 52 , wherein identifying one or more of the distinct gate conditions that satisfy the operating criterion comprises identifying a gate condition that is at least a minimum distance, in a modulation frequency and modulation amplitude domain, from resonant conditions of transitions to be suppressed in the quantum processor circuit during application of the two-qubit quantum logic gate.

55. The method of claim 52 , wherein the tunable qubit device comprises a superconducting circuit loop that defines a flux quantum Φ 0 and receives a first magnetic flux that tunes a transition frequency of the tunable qubit device, and applying the two-qubit quantum logic gate comprises modulating the first magnetic flux at a modulation frequency.

56. The method of claim 52 , wherein:

obtaining measurements of the quantum processor circuit includes obtaining measurements of a mean transition frequency of the tunable qubit device during a flux modulation applied to the tunable qubit device, the measurements of the mean transition frequency corresponding to a range of modulation amplitudes of the flux modulation, and

the gate parameters are selected based in part on the measurements of the mean transition frequency.

57. The method of claim 52 , wherein the multiple distinct gate conditions are computed for a range of modulation amplitudes, and each distinct gate condition includes:

a modulation amplitude of a flux modulation;

a modulation frequency of the flux modulation; and

a duration of the flux modulation.

58. The method of claim 57 , wherein identifying one or more of the distinct gate conditions that satisfy an operating criterion associated with the two-qubit quantum logic gate comprises identifying the gate condition that includes the minimum duration.

59. The method of claim 52 , comprising identifying one or more of the distinct gate conditions that satisfy multiple operating criteria associated with the two-qubit quantum logic gate.

60. The method of claim 52 , wherein each of distinct gate conditions includes a modulation frequency that is based on:

a transition frequency of the tunable qubit device; and

a transition frequency of the fixed-frequency qubit device.

61. The method of claim 60 , wherein each of the distinct gate conditions further includes a modulation amplitude, and the modulation frequency in each gate condition is based on a transition frequency shift of the tunable qubit device under the modulation amplitude included in the gate condition.

62. The method of claim 52 , further comprising identifying single-qubit phase corrections for the two-qubit quantum logic gate.

63. The method of claim 52 , wherein selecting gate parameters for the two-qubit quantum logic gate comprises selecting gate parameters of a Bell-Rabi gate, a controlled-Z gate, an iSWAP gate or a square-root-of-iSWAP gate.

64. The method of claim 52 , further comprising benchmarking the two-qubit quantum logic gate based on the selected gate parameters.