Efficient protocol to estimate the Quantum Fisher Information Matrix for Commuting-Block Circuits

TL;DR

This paper presents a resource-efficient protocol for estimating the Quantum Fisher Information Matrix in commuting-block quantum circuits, reducing the number of state preparations and measurements needed, thus enabling more practical quantum parameter sensitivity analysis.

Contribution

The authors introduce a novel method to compute off-diagonal QFIM elements in commuting-block circuits with significantly fewer resources than previous approaches.

Findings

Reduces quantum state preparations from O(m^2) to O(L^2).

Decreases classical measurements and post-processing requirements.

Enhances the practicality of QFIM estimation in variational quantum algorithms.

Abstract

The Quantum Fisher Information Matrix (QFIM) is a fundamental quantity in various subfields of quantum physics. It plays a crucial role in the study of parameterized quantum states, as it quantifies their sensitivity to variations in its parameters. Recently, the QFIM has been successfully employed to enhance the optimization of variational quantum algorithms. However, its practical applicability is often hindered by the high resource requirements for its estimation. In this work, we introduce a novel protocol for computing the off-block-diagonal elements of the QFIM between different layers in a particular class of variational quantum circuits, known as commuting-block circuits. Our approach significantly reduces the quantum resources required, specifically lowering the number of distinct quantum state preparations from $O(m^2)$ to $O(L^2)$, where $m$ is the total number of parameters and $L$ is the number of layers in the circuit. Consequently, our protocol also minimizes the number of classical measurements and post-processing operations needed to estimate the QFIM, leading to a substantial improvement in computational efficiency.