Quantum filter reduction for measurement-feedback control via unsupervised manifold learning

TL;DR

This paper introduces a method to simplify quantum system models using unsupervised manifold learning, enabling faster simulation and effective feedback control of atom-cavity dynamics.

Contribution

It presents a novel approach to derive low-dimensional models of quantum systems via local tangent space alignment, improving simulation speed and control accuracy.

Findings

Models accurately reproduce quantum jump dynamics.

Significantly faster numerical integration than full equations.

Effective feedback control based on simplified models.

Abstract

We derive simple models for the dynamics of a single atom coupled to a cavity field mode in the absorptive bistable parameter regime by projecting the time evolution of the state of the system onto a suitably chosen nonlinear low-dimensional manifold, which is found by use of local tangent space alignment. The output field from the cavity is detected with a homodyne detector allowing observation of quantum jumps of the system between states with different average numbers of photons in the cavity. We find that the models, which are significantly faster to integrate numerically than the full stochastic master equation, largely reproduce the dynamics of the system, and we demonstrate that they are sufficiently accurate to facilitate feedback control of the state of the system based on the predictions of the models alone.