Shadow measurements for feedback-based quantum optimization

TL;DR

This paper demonstrates that using classical shadows in feedback-based quantum optimization significantly reduces measurement resources needed for estimating observables, especially in MaxCut problems, enabling more efficient quantum algorithms.

Contribution

The study implements the FALQON algorithm with classical shadows, showing a substantial reduction in measurement complexity compared to direct estimation methods.

Findings

Classical shadows can reduce measurement count by up to 16 times.

Measurement requirements grow logarithmically with the number of observables.

Classical shadows are effective for low-locality Pauli observable estimation.

Abstract

Improving the performance of quantum algorithms is a fundamental task to achieve quantum advantage. In many cases, extracting information from quantum systems poses an important challenge for practical implementations in real-world quantum computers, given the high resource cost of performing state tomography. In this scenario, randomized measurements emerged as a promising tool. In particular, the classical shadows protocol allows one to retrieve expected values of low-weight Pauli observables by performing only local measurements. In this paper, we present an implementation of the recently introduced Feedback-based algorithm for quantum optimization (FALQON) with the Ket quantum programming platform, for solving the MaxCut optimization problem. We employ classical shadows for the feedback routine of parameter estimation and compare this approach with the direct estimation of observables. Our results show that depending on the graph geometry for the MaxCut problem, the number of measurements required to estimate expected values of observables with classical shadows can be up to 16 times lower than with direct observable estimation. Furthermore, by analyzing complete graphs, we numerically confirm a logarithmic growth in the required number of measurements relative to the number of observables, reinforcing that classical shadows can be a useful tool for estimating low-locality Pauli observables in quantum algorithms.