Experimental Bayesian estimation of quantum state preparation, measurement, and gate errors in multi-qubit devices

Abstract

We introduce a Bayesian method for the estimation of single qubit errors in quantum devices, and use it to characterize these errors on three 27-qubit superconducting qubit devices. We self-consistently estimate up to seven parameters of each qubit's state preparation, readout, and gate errors, analyze the stability of these errors as a function of time, and demonstrate easily implemented approaches for mitigating different errors before a quantum computation experiment. On the investigated devices we find non-negligible qubit reset errors that cannot be parametrized as a diagonal mixed state, but manifest as a coherent phase of a superposition with a small contribution from the qubit's excited state. We are able to mitigate such errors by applying pre-rotations on the initialized qubits, which we demonstrate with multi-qubit entangled states. Our results demonstrate that Bayesian estimation can resolve small parameters - including those pertaining to quantum gate errors - with a high relative accuracy, at a lower measurement cost as compared with standard characterization approaches.

v3 contains small corrections and clarifications

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• Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
• Decoherence benchmarking of superconducting qubits
• Self-guided quantum tomography
• Robust and Efficient High-dimensional Quantum State Tomography
• Accelerated Randomized Benchmarking
• Measurement Error Mitigation for Variational Quantum Algorithms
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• Atomic clock locking with Bayesian quantum parameter estimation: scheme and experiment
• Self-consistent quantum measurement tomography based on semidefinite programming
• Learning interactions between Rydberg atoms