Multi-qubit Randomized Benchmarking Using Few Samples

Abstract

Randomized benchmarking (RB) is an efficient and robust method to characterize gate errors in quantum circuits. Averaging over random sequences of gates leads to estimates of gate errors in terms of the average fidelity. These estimates are isolated from the state preparation and measurement errors that plague other methods like channel tomography and direct fidelity estimation. A decisive factor in the feasibility of randomized benchmarking is the number of sampled sequences required to obtain rigorous confidence intervals. Previous bounds were either prohibitively loose or required the number of sampled sequences to scale exponentially with the number of qubits in order to obtain a fixed confidence interval at a fixed error rate. Here we show that, with a small adaptation to the randomized benchmarking procedure, the number of sampled sequences required for a fixed confidence interval is dramatically smaller than could previously be justified. In particular, we show that the number of sampled sequences required is essentially independent of the number of qubits and scales favorably with the average error rate of the system under investigation. We also show that the number of samples required for long sequence lengths can be made substantially smaller than previous rigorous results (even for single qubits) as long as the noise process under investigation is not unitary. Our results bring rigorous randomized benchmarking on systems with many qubits into the realm of experimental feasibility.

v3: Added discussion of the impact of variance heteroskedasticity on the RB fitting procedure. Close to published version

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• Nonstabilizerness determining the hardness of direct fidelity estimation
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• Real Randomized Benchmarking
• Statistical analysis of randomized benchmarking
• Robust and Efficient Hamiltonian Learning
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• Modeling Noisy Quantum Circuits Using Experimental Characterization
• Suppression of mid-circuit measurement crosstalk errors with micromotion
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• Estimating gate-set properties from random sequences
• Robust certification of arbitrary outcome quantum measurements from temporal correlations
• Operational, gauge-free quantum tomography
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• Coherent randomized benchmarking
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• Duality theory for Clifford tensor powers
• Hardware-efficient random circuits to classify noise in a multi-qubit system