Stabilizing feedback controls for quantum systems

TL;DR

This paper develops methods for stabilizing quantum systems using feedback control based on quantum filtering, combining geometric control and probabilistic techniques to achieve stabilization around specific eigenstates.

Contribution

It introduces a novel approach for global feedback stabilization of quantum filters using geometric and probabilistic methods, addressing partial observation challenges.

Findings

Quantum filtering equations can be analyzed as classical stochastic differential equations.

Methods for global stabilization of quantum filters around eigenstates are developed.

The approach bridges quantum control with classical stochastic control techniques.

Abstract

No quantum measurement can give full information on the state of a quantum system; hence any quantum feedback control problem is neccessarily one with partial observations, and can generally be converted into a completely observed control problem for an appropriate quantum filter as in classical stochastic control theory. Here we study the properties of controlled quantum filtering equations as classical stochastic differential equations. We then develop methods, using a combination of geometric control and classical probabilistic techniques, for global feedback stabilization of a class of quantum filters around a particular eigenstate of the measurement operator.