Multiqubit Randomized Benchmarking Using Few Samples*

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 that 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 samples 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. Here, we introduce a bound on the number of sampled sequences that dramatically outperforms previous bounds. In particular, we show that the number of sampled sequences required for a fixed confidence interval is essentially independent of the number of qubits. We also show that the number of samples required with a single qubit is substantially smaller than previous rigorous results, especially in the limit of large sequence lengths. Our results bring rigorous randomised benchmarking on systems with many qubits closer to experimental feasibility.