Efficient sampling for Pauli-measurement-based shadow tomography in direct fidelity estimation

TL;DR

This paper introduces efficient local Pauli measurement strategies for direct fidelity estimation in quantum states, improving measurement bounds and eliminating preprocessing, thus enhancing the practicality of shadow tomography.

Contribution

It develops new sampling methods using local Pauli measurements for DFE, providing tighter bounds and simplifying the measurement process compared to previous Clifford-based approaches.

Findings

Tighter measurement bounds for GHZ and W states by factors of 14.22 and 16.

Protocols require only local Pauli measurements with no preprocessing.

Enhanced feasibility of quantum state property estimation with classical shadows.

Abstract

A constant number of random Clifford measurements allows the classical shadow protocol to perform direct fidelity estimation (DFE) with high precision. However, estimating properties of an unknown quantum state is expected to be more feasible with random Pauli measurements than with random Clifford measurements in the near future. Inspired by the importance sampling technique applied to sampling Pauli measurements for DFE, we show that similar strategies can be derived from classical shadows. Specifically, we describe efficient methods using only local Pauli measurements to perform DFE with GHZ, W, and Dicke states, establishing tighter bounds (by factor of $14.22$ and $16$ for GHZ and W, respectively) on the number of measurements required for desired precision. These protocols are derived by adjusting the distribution of observables. Notably, they require no preprocessing steps other than the sampling algorithms.