Direct Fidelity Estimation from Few Pauli Measurements

TL;DR

This paper introduces a simple, efficient method for estimating the fidelity of a prepared quantum state using only a few Pauli measurements, significantly reducing the measurement complexity compared to full tomography.

Contribution

It presents a novel fidelity estimation technique that requires constant measurements and can be extended to quantum channels, improving efficiency over existing methods.

Findings

Requires only a constant number of Pauli measurements

Provides fidelity estimates with a small additive error

Faster than full quantum state tomography by a factor of the state space dimension

Abstract

We describe a simple method for certifying that an experimental device prepares a desired quantum state rho. Our method is applicable to any pure state rho, and it provides an estimate of the fidelity between rho and the actual (arbitrary) state in the lab, up to a constant additive error. The method requires measuring only a constant number of Pauli expectation values, selected at random according to an importance-weighting rule. Our method is faster than full tomography by a factor of d, the dimension of the state space, and extends easily and naturally to quantum channels.