Systems and methods for operation of a frequency multiplexed resonator input and/or output for a superconducting device
A superconducting readout system employing a microwave transmission line, and a microwave superconducting resonator communicatively coupled to the microwave transmission line, and including a superconducting quantum interference device (SQUID), may be advantageously calibrated at least in part by measuring a resonant frequency of the microwave superconducting resonator in response to a flux bias applied to the SQUID, measuring a sensitivity of the resonant frequency in response to the flux bias, and selecting an operating frequency and a sensitivity of the microwave superconducting resonator based at least in part on a variation of the resonant frequency as a function of the flux bias. The flux bias may be applied to the SQUID by an interface inductively coupled to the SQUID. Calibration of the superconducting readout system may also include determining at least one of a propagation delay, a microwave transmission line delay, and a microwave transmission line phase offset.
1. A method of operation of an apparatus, the apparatus comprising a superconducting readout system, the superconducting readout system comprising: a microwave transmission line; a microwave superconducting resonator communicatively coupled to the microwave transmission line, the microwave superconducting resonator comprising a first superconducting quantum interference device (SQUID); and a first interface inductively communicatively coupled to the first SQUID, the first interface selectively operable to apply a first flux bias to the first SQUID, the method comprising:
measuring a resonant frequency of the microwave superconducting resonator in response to the first flux bias;
measuring a sensitivity of the resonant frequency of the microwave superconducting resonator in response to the first flux bias; and
selecting an operating frequency and a sensitivity of the microwave superconducting resonator based at least in part on a variation of the resonant frequency as a function of the first flux bias, wherein selecting an operating frequency and a sensitivity of the microwave superconducting resonator includes adjusting the first flux bias applied to the first SQUID by the first interface.
2. The method of claim 1 , wherein the superconducting readout system further comprises a second SQUID and a second interface inductively communicatively coupled to the second SQUID, the second interface selectively operable to apply a second flux bias to the second SQUID, the method further comprising:
measuring a resonant frequency of the microwave superconducting resonator in response to the first and the second flux bias;
measuring a sensitivity of the resonant frequency of the microwave superconducting resonator in response to the first and the second flux bias; and
selecting an operating frequency and a sensitivity of the microwave superconducting resonator based at least in part on the resonant frequency and the sensitivity of the microwave superconducting resonator, wherein selecting an operating frequency and a sensitivity of the microwave superconducting resonator includes adjusting the first and the second flux bias applied to each of the first and the second SQUID by the first and the second interface respectively.
3. The method of claim 1 , further comprising at least approximating an operating frequency for the microwave superconducting resonator by sweeping an operating frequency band selected to include a nominal operating bandwidth of the microwave superconducting resonator.
4. The method of claim 3 , wherein at least approximating an operating frequency for the microwave superconducting resonator by sweeping an operating frequency band includes:
attempting to optimize a signal power for the microwave transmission line;
performing a measurement of at least one of a gain and a phase of a complex transmission response of the superconducting readout system; and
determining a respective resonant frequency of the microwave superconducting resonator, wherein determining the respective resonant frequency of the microwave superconducting resonator includes at least one of finding a dip in the gain that exceeds a first threshold, and a rate of change in the phase that exceeds a second threshold.
5. The method of claim 4 , wherein performing a measurement of at least one of a gain and a phase to determine a respective resonant frequency of the microwave superconducting resonator includes performing a measurement of at least one of a gain and a phase using a vector network analyzer.
6. The method of claim 3 , wherein sweeping an operating frequency band selected to include a nominal operating bandwidth of the microwave superconducting resonator includes configuring the first and the second SQUID of the microwave superconducting resonator in an unbiased state.
7. The method of claim 1 , the superconducting readout system further comprising a readout electronics digital-to-analog converter (DAC), the method further comprising selecting an output power for the readout electronics DAC, and determining averaging protocol to achieve a defined signal-to-noise at the selected output power of the readout electronics DAC.
8. The method of claim 1 , further comprising determining at least one of a propagation delay through the superconducting readout system, a microwave transmission line delay, and a microwave transmission line phase offset.
9. The method of claim 8 , wherein determining a microwave transmission line delay and a microwave transmission line phase offset includes:
performing a frequency sweep;
fitting a straight line to a measured phase as a function of frequency;
estimating a microwave transmission line delay from a slope of the straight line; and
estimating the phase offset from a y-intercept of the straight line.
10. The method of claim 1 , the superconducting readout system further comprising a cryogenic amplifier, the method further comprising calibrating the cryogenic amplifier.
11. The method of claim 1 , the superconducting readout system further comprising an amplifier and an attenuator, the method further comprising adjusting at least one of a gain of the amplifier and an attenuation of the attenuator to provide at least approximately linear operation of the superconducting readout system.
12. The method of claim 1 , further comprising measuring a complex transmission response of the microwave transmission line.
13. The method of claim 1 , wherein selecting an operating frequency and a sensitivity of the microwave superconducting resonator includes selecting an operating frequency and a sensitivity of the microwave superconducting resonator by defining an objective function and attempting to optimize the objective function by adjusting the first flux bias.
14. The method of claim 13 , wherein attempting to optimize the objective function includes using at least one of a gradient-descent method, a Nelder-Mead method, and a Newton-Raphson method.
15. The method of claim 1 , wherein measuring a resonant frequency of the microwave superconducting resonator in response to the first flux bias includes measuring a resonant frequency by a vector-network analyzer.
16. The method of claim 1 , wherein measuring a sensitivity of the resonant frequency of the microwave superconducting resonator in response to the first flux bias includes measuring a sensitivity of the resonant frequency of the microwave superconducting resonator by a current source and a vector-network analyzer (VNA).
17. The method of claim 1 , further comprising assessing performance of the superconducting readout system.
18. The method of claim 1 , wherein the method of operation calibrates the superconducting readout system.
19. The method of claim 1 , wherein the method of operation selects an operating point for the superconducting readout system.
20. A computing system comprising:
at least one nontransitory processor-readable storage medium that stores at least one of processor-executable instructions or data; and
at least one processor communicatively coupled to the at least one nontransitory processor-readable storage medium; and
a superconducting readout system communicatively coupled to the at least one processor, the superconducting readout system comprising: a microwave transmission line; a microwave superconducting resonator communicatively coupled to the microwave transmission line, the microwave superconducting resonator comprising a first superconducting quantum interference device (SQUID); and a first interface inductively communicatively coupled to the first SQUID, the first interface selectively operable to apply a first flux bias to the first SQUID, the at least one processor operable to:
measure a resonant frequency of the microwave superconducting resonator in response to the first flux bias;
measure a sensitivity of the resonant frequency of the microwave superconducting resonator in response to the first flux bias; and
select an operating frequency and a sensitivity of the microwave superconducting resonator based at least in part on a variation of the resonant frequency as a function of the first flux bias, wherein selecting an operating frequency and a sensitivity of the microwave superconducting resonator includes adjusting the first flux bias applied to the first SQUID by the first interface.