Learning Non-Markovian Noise via Ensemble Optimal Control

TL;DR

This paper introduces a machine learning-based control scheme to optimize measurement timing in non-Markovian quantum systems, improving parameter estimation precision by leveraging environmental memory effects.

Contribution

It presents a novel ensemble training approach to determine optimal measurement times, enhancing estimation accuracy in non-Markovian quantum noise estimation.

Findings

Achieves measurement uncertainties near the quantum Cramér-Rao bound.

The protocol is robust to training errors.

Exploits non-Markovian memory effects to improve precision.

Abstract

We study the estimation of parameters pertaining to non-Markovian quantum open systems, such as the dissipation rate and environmental memory time. A key challenge is identifying the optimal measurement time, which must allow sufficient time to acquire information about the environment, yet be short enough to avoid dissipation that erases the information. Using machine learning approaches, we develop an optimized control scheme trained over a representative ensemble to fix the optimal measurement time at a prescribed runtime. The protocol is robust to errors in the training process, enhances precision by exploiting non-Markovian memory effects, and achieves measurement uncertainties approaching the quantum limits set by the Cram\'{e}r-Rao bound.