# Multi-qubit Randomized Benchmarking Using Few Samples

## TL;DR

This paper improves the efficiency of multi-qubit randomized benchmarking by reducing the number of samples needed, making it more practical for large quantum systems and providing more reliable error estimates.

## Contribution

It introduces a small adaptation to RB that significantly decreases the sample complexity, especially for systems with many qubits and non-unitary noise.

## Key findings

- Sample complexity is essentially independent of the number of qubits.
- Sample size scales favorably with the average error rate.
- Long sequence lengths require fewer samples for non-unitary noise processes.

## 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.