Frequency Tracking and Parameter Estimation for Robust Quantum State-Estimation

TL;DR

This paper introduces a method combining classical frequency estimation with Bayesian techniques to robustly track quantum states and estimate unknown Hamiltonian parameters in a computationally efficient manner.

Contribution

It demonstrates that classical frequency estimation methods can significantly reduce computational complexity in Bayesian quantum state and parameter estimation.

Findings

Classical frequency estimation improves robustness against Hamiltonian uncertainties.

The combined approach achieves accurate parameter estimates with lower computational cost.

The method is effective for single-qubit systems with unknown Hamiltonian parameters.

Abstract

In this paper we consider the problem of tracking the state of a quantum system via a continuous measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation. However, even a small error in the assumed Hamiltonian can render this approach useless. The natural answer to this problem is to include the parameters of the Hamiltonian as part of the estimation problem, and the full Bayesian solution to this task provides a state-estimate that is robust against uncertainties. However, this approach requires considerable computational overhead. Here we consider a single qubit in which the Hamiltonian contains a single unknown parameter. We show that classical frequency estimation techniques greatly reduce the computational overhead associated with Bayesian estimation and provide accurate estimates for the qubit frequency