Quantum estimation of a time dependent perturbation

TL;DR

This paper develops a hybrid quantum-classical estimation framework for time-dependent perturbations in quantum systems, using Hidden Markov Models and Past Quantum States, demonstrated through magnetic field sensing with a quantum spin.

Contribution

It introduces a novel hybrid quantum-classical filtering method combining Hidden Markov Models and Past Quantum States for dynamic perturbation estimation.

Findings

Effective estimation of fluctuating magnetic fields demonstrated

Hybrid approach improves accuracy over classical methods

Applicable to quantum sensing and metrology

Abstract

We analyze the estimation of a time dependent perturbation acting on a continuously monitored quantum system. We describe the temporal fluctuations of the perturbation by a Hidden Markov Model, and we combine quantum measurement theory and classical filter theory into a time evolving hybrid quantum and classical trajectory. The forward-backward analysis that permits smoothed estimates of classical Hidden Markov Models has a counterpart in the theory of retrodiction and Past Quantum States. As a specific example, we apply our hybrid trajectory and Past Quantum State theory to the sensing of a fluctuating magnetic field by microwave interrogation of a single quantum spin.