Quantum Control by Modulating Tunable Devices in a Superconducting Circuit

1 . A quantum computing method comprising:

identifying values of parameters for a control signal to apply a control operation to a qubit defined by a tunable qubit device in a superconducting quantum processing unit;

generating the control signal according to the values of the parameters, the control signal comprising a plurality of modulation tones; and

applying the control operation to the qubit by delivering the control signal to a flux bias device associated with the tunable qubit device, wherein the control signal controls a magnetic flux applied to the tunable qubit device by the flux bias device and renders the qubit insensitive to flux noise.

2 . The method of claim 1 , comprising determining the values of the parameters based on values of qubit device parameters of the tunable qubit device.

3 . The method of claim 1 , comprising determining the values of the parameters based on values of qubit device parameters of the superconducting quantum processing unit, wherein the superconducting quantum processing unit comprises a fixed-frequency qubit device, and the qubit device parameters comprise at least one of a range of qubit operating frequency and anharmonicity of the tunable qubit device, an operating frequency and anharmonicity of the fixed-frequency qubit device, and a coupling between the tunable qubit device and the fixed-frequency qubit device.

4 . The method of claim 1 , wherein the control operation comprises a quantum logic gate.

5 . The method of claim 1 , wherein the superconducting quantum processing unit comprises a fixed-frequency qubit device, and the control operation comprises a two-qubit quantum logic gate applied to a pair of qubits defined by the fixed-frequency qubit device and the tunable qubit device.

6 . The method of claim 1 , wherein the plurality of modulation tones comprises a fundamental tone with a fundamental frequency and one or more harmonics of the fundamental tone with one or more harmonic frequencies.

7 . The method of claim 1 , wherein the control signal is a bichromatic modulation signal comprising a first modulation tone with a first modulation frequency and a second modulation tone with a second modulation frequency, and the second modulation frequency is equal to two or more integer multiples of the first modulation frequency.

8 . The method of claim 1 , wherein identifying the values of the parameters comprises identifying values of parameters of a digital waveform.

9 . The method of claim 1 , wherein the parameters are identified by an optimal control theory system or a machine learning system.

10 . The method of claim 1 , wherein identifying the values of the parameters comprises:

determining an array of dynamical sweet spots corresponding to a set of multiple values of modulation parameters in a parameter space; and

selecting the values of the modulation parameters from the set according to one or more predetermined criteria.

11 . The method of claim 10 , wherein determining the array of dynamical sweet spots comprises:

determining a dephasing rate that is a function of a first slope of a time-averaged frequency with respect to a parking flux and a second slope of a time-averaged frequency with respect to a modulation amplitude.

12 . The method of claim 10 , wherein the one or more predetermined criteria comprise maximizing a fidelity of the control operation.

13 . The method of claim 10 , wherein the one or more predetermined criteria comprise maximizing a central sideband weight.

14 . The method of claim 10 , wherein the one or more predetermined criteria comprise minimizing a dephasing rate.

15 . The method of claim 10 , wherein the parameter space comprises at least one of a number of the modulation tones, modulation frequencies of the modulation tones, amplitudes of the modulation tones, relative phases, or relative durations.

16 . The method of claim 15 , wherein the control signal comprises a fundamental tone and one or more harmonics of the fundamental tone, the modulation parameters comprise a modulation frequency of the fundamental tone, and the value of the modulation frequency is determined by a time-averaged frequency of the tunable qubit device.

17 . A quantum computing system comprising:

a superconducting quantum processing unit comprising a tunable qubit device and a flux bias device associated with the tunable qubit device; and

a control system communicably coupled to the quantum processing unit, the control system configured to perform operations comprising:

identifying values of parameters for a control signal to apply a control operation to a qubit defined by the tunable qubit device;

generating the control signal according to the values of the parameters, the control signal comprising a plurality of modulation tones; and

applying the control operation to the qubit by delivering the control signal to the flux bias device, wherein the control signal controls a magnetic flux applied to the tunable qubit device by the flux bias device and renders the qubit insensitive to flux noise.

18 - 32 . (canceled)

33 . A quantum computing system comprising:

a superconducting quantum processing unit comprising a tunable qubit device and a flux bias device associated with the tunable qubit device; and

means for obtaining a control signal to apply a control operation to a qubit defined by the tunable qubit device, the control signal comprising a plurality of modulation tones, the control signal configured to control a magnetic flux applied to the tunable qubit device and render the qubit insensitive to flux noise; and

a signal delivery system configured to deliver the control signal to the flux bias device.

34 - 49 . (canceled)