Quadratic control of quantum processes

TL;DR

This paper develops a method for controlling quantum stochastic flows affected by quantum noise using algebraic Riccati equations, providing a feedback control law within the AFQ calculus framework.

Contribution

It introduces a novel control approach for quantum stochastic processes driven by white noise, linking control design to solutions of stochastic Riccati equations.

Findings

Control law derived from algebraic Riccati equation

Applicable to quantum Brownian motion and similar processes

Provides a feedback control strategy for quantum noise management

Abstract

Within the framework of the Accardi-Fagnola-Quaegebeur (AFQ) representation free calculus of \cite{b}, we consider the problem of controlling the size of a quantum stochastic flow generated by a unitary stochastic evolution affected by quantum noise. In the case when the evolution is driven by first order white noise (which includes quantum Brownian motion) the control is shown to be given in terms of the solution of an algebraic Riccati equation. This is done by first solving the problem of controlling (by minimizing an associated quadratic performance criterion) a stochastic process whose evolution is described by a stochastic differential equation of the type considerd in \cite{b}. The solution is given as a feedback control law in terms of the solution of a stochastic Riccati equation.