Multi-parameter estimation along quantum trajectories with Sequential Monte Carlo methods

TL;DR

This paper introduces a hybrid quantum-classical estimation method combining stochastic master equations with Sequential Monte Carlo techniques to simultaneously estimate quantum states and classical parameters, demonstrated on a nonlinear Duffing oscillator.

Contribution

It presents a novel integration of quantum state estimation with classical SMC methods for joint parameter and state estimation in quantum systems.

Findings

Effective estimation of quantum states and parameters demonstrated on Duffing oscillator.

Sequential Monte Carlo methods improve parameter estimation accuracy.

Method offers a scalable approach for complex quantum systems.

Abstract

This paper proposes an efficient method for the simultaneous estimation of the state of a quantum system and the classical parameters that govern its evolution. This hybrid approach benefits from efficient numerical methods for the integration of stochastic master equations for the quantum system, and efficient parameter estimation methods from classical signal processing. The classical techniques use Sequential Monte Carlo (SMC) methods, which aim to optimize the selection of points within the parameter space, conditioned by the measurement data obtained. We illustrate these methods using a specific example, an SMC sampler applied to a nonlinear system, the Duffing oscillator, where the evolution of the quantum state of the oscillator and three Hamiltonian parameters are estimated simultaneously.