Parameter estimation from measurements along quantum trajectories

TL;DR

This paper develops stable particle quantum filters for parameter estimation in open quantum systems, applicable in both discrete and continuous time, and demonstrates their effectiveness on superconducting qubit data.

Contribution

It introduces a new stable formulation of particle quantum filters for parameter estimation in continuous-time quantum systems, ensuring positivity and efficiency.

Findings

Proven stability of the new particle quantum filter formulation.

Algorithm preserves positivity of quantum states and probabilities.

Successful estimation of detection efficiency in superconducting qubits.

Abstract

The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the measurement outcomes. We then describe the structure of the corresponding particle quantum filters for estimating constant parameter and we prove their stability. In the continuous-time (diffusive) case, we propose a new formulation of these particle quantum filters. The interest of this new formulation is first to prove stability, and also to provide an efficient algorithm preserving, for any discretization step-size, positivity of the quantum states and parameter classical probabilities. This algorithm is tested on experimental data to estimate the detection efficiency for a superconducting qubit whose fluorescence field is measured using a heterodyne detector.