Leakage in restless quantum gate calibration

Abstract

Quantum computers require high-fidelity quantum gates. These gates are obtained by routine calibration tasks that eat into the availability of cloud-based devices. Restless circuit execution speeds up characterization and calibration by foregoing qubit reset between circuits. Postprocessing the measured data recovers the desired signal. However, since the qubits are not reset, leakage - typically present at the beginning of the calibration - may cause issues. Here we develop a simulator of restless circuit execution based on a Markov chain to study the effect of leakage. In the context of error-amplifying single-qubit gates sequences, we show that restless calibration tolerates up to 0.5% of leakage, which is large compared to the 10-4 gate fidelity of modern single-qubit gates. Furthermore, we show that restless circuit execution with leaky gates reduces by 33% the sensitivity of the ORBIT cost function developed by J. Kelly et al. which is typically used in closed-loop optimal control [Phys. Rev. Lett. 112, 240504 (2014)0031-900710.1103/PhysRevLett.112.240504]. Our results are obtained with standard qubit state discrimination showing that restless circuit execution is resilient against misclassified noncomputational states. In summary, the restless method is sufficiently robust against leakage in both standard and closed-loop optimal control gate calibration to provided accurate results.