Direct Fidelity Estimation for Generic Quantum States

TL;DR

This paper introduces a new quantum fidelity estimation protocol that efficiently assesses the accuracy of generic quantum states with reduced measurement and communication costs, scaling favorably with the Hilbert space dimension.

Contribution

The authors develop a novel fidelity estimation method for generic quantum states with computational cost scaling as the square root of the Hilbert space dimension, improving efficiency over existing protocols.

Findings

Computational cost scales as the square root of the Hilbert space dimension.

Reduces the number of measurements and communication costs.

Leverages quantum amplitude estimation and classical shadow tomography.

Abstract

Verifying the proper preparation of quantum states is essential in modern quantum information science. Various protocols have been developed to estimate the fidelity of quantum states produced by different parties. Direct fidelity estimation is a leading approach, as it typically requires a number of measurements that scale linearly with the Hilbert space dimension, making it far more efficient than full state tomography. In this article, we introduce a novel fidelity estimation protocol for generic quantum states, with an overall computational cost that scales only as the square root of the Hilbert space dimension. Furthermore, our protocol significantly reduces the number of required measurements and the communication cost between parties to finite. This protocol leverages the quantum amplitude estimation algorithm in conjunction with classical shadow tomography to achieve these improvements.