Efficient online quantum state estimation using a matrix-exponentiated gradient method

TL;DR

This paper introduces an efficient online quantum state estimation algorithm based on a matrix-exponentiated gradient method, demonstrating convergence and superior performance over traditional methods in noisy environments.

Contribution

The paper presents a novel online quantum state estimation algorithm using a matrix-exponentiated gradient approach with adaptive learning rates and averaging techniques.

Findings

Converges to the true quantum state in both noiseless and noisy conditions.

Outperforms batch maximum-likelihood and least-squares estimators in accuracy.

Offers reduced runtime complexity compared to traditional methods.

Abstract

In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that determines how much weight is given to the new measurement results obtained in each step. We show convergence of the running state estimate in probability to the true state for both noiseless and noisy measurements. We find that in the latter case the learning rate has to be chosen adaptively and decreasing to guarantee convergence beyond the noise threshold. As a practical alternative we then propose to use running averages of the measurement statistics and a constant learning rate to overcome the noise problem. The proposed algorithm is numerically compared with batch maximum-likelihood and least-squares estimators. The results show a superior performance of the new algorithm in terms of accuracy and runtime complexity.