Randomized Benchmarking Using Unitary t-Design for Average Fidelity Estimation of Practical Quantum Circuit

TL;DR

This paper introduces a randomized benchmarking method using unitary t-designs to accurately estimate average fidelity and unitary errors in practical quantum circuits, improving efficiency and applicability.

Contribution

It proposes a new randomized benchmarking approach with unitary t-designs, providing practical bounds and analysis tools for large-scale quantum circuits.

Findings

Bound on the number of sequences for n-qubit systems

Decomposition of unitary t-designs using local random unitaries

Quantitative analysis of average fidelity and errors

Abstract

Randomized benchmarking is a useful scheme for evaluation the average fidelity of a noisy quantum circuit. However, it is insensitive to the unitary error. Here, we propose a method of randomized benchmarking in which a unitary t-design is applied and by which the unitary error estimation can be converted to analysis of pseudo-randomness on a set of unitary operators. We give a bound on the number of randomized benchmarking sequences, when performing a unitary t-design on n-qubit d-dimensional system. By applying local random unitary operators, a decomposition of a unitary t-design, the bound is more practical than the previous bound for multi-qubit circuit. We also give a rigorous bound of a diamond norm between arbitrary and uniform distributions of a set of unitary operators to form an \epsilon-approximate unitary t-design. It can be used to quantitatively analyze the corresponding average fidelity and errors in a large-scale quantum circuit.