Sampling Groups of Pauli Operators to Enhance Direct Fidelity Estimation

TL;DR

This paper introduces an improved direct fidelity estimation protocol that groups Pauli operators to reduce measurement costs and variance, significantly enhancing efficiency for quantum state fidelity assessment.

Contribution

The paper proposes a novel grouping strategy for Pauli operators in fidelity estimation, reducing the number of measurements and variance compared to standard methods.

Findings

Achieves one-third reduction in measurement copies for 8-qubit states

Reduces estimator variance by an order of magnitude

Uses only local measurements for improved efficiency

Abstract

Direct fidelity estimation is a protocol that estimates the fidelity between an experimental quantum state and a target pure state. By measuring the expectation values of Pauli operators selected through importance sampling, the method is exponentially faster than full quantum state tomography. We propose an enhanced direct fidelity estimation protocol that uses fewer copies of the experimental state by grouping Pauli operators before the sampling process. We derive analytical bounds on the measurement cost and estimator variance, showing improvements over the standard method. Numerical simulations validate our approach, demonstrating that for 8-qubit Haar-random states, our method achieves a one-third reduction in the required number of copies and reduces variance by an order of magnitude using only local measurements. These results underscore the potential of our protocol to enhance the efficiency of fidelity estimation in current quantum devices.