Rapid estimation of drifting parameters in continuously measured quantum systems

TL;DR

This paper presents a rapid, real-time method for estimating unknown, possibly drifting Hamiltonian parameters in continuously measured quantum systems, improving tracking and accuracy while accounting for realistic noise and inefficiencies.

Contribution

It introduces a computationally fast, statistically optimal likelihood-based estimation method that works directly on raw measurement data for real-time parameter tracking in quantum systems.

Findings

The method accurately estimates the Rabi frequency in a qubit.

Estimation quality depends on measurement strength and duration.

Trade-offs exist between estimation accuracy and sensitivity to drift.

Abstract

We investigate the determination of a Hamiltonian parameter in a quantum system undergoing continuous measurement. We demonstrate a computationally rapid yet statistically optimal method to estimate an unknown and possibly time-dependent parameter, where we maximize the likelihood of the observed stochastic readout. By dealing directly with the raw measurement record rather than the quantum state trajectories, the estimation can be performed while the data is being acquired, permitting continuous tracking of the parameter during slow drifts in real time. Furthermore, we incorporate realistic nonidealities, such as decoherence processes and measurement inefficiency. As an example, we focus on estimating the value of the Rabi frequency of a continuously measured qubit, and compare maximum likelihood estimation to a simpler fast Fourier transform. Using this example, we discuss how the quality of the estimation depends on both the strength and duration of the measurement; we also discuss the trade-off between the accuracy of the estimate and the sensitivity to drift as the estimation duration is varied.