H∞ Control of Linear Quantum Stochastic Systems

Abstract

The purpose of this paper is to formulate and solve a H?controller synthesis problem for a class of non-commutative linear stochastic systems which includes many examples of interest in quantum technology. A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the Strict Bounded Real Lemma is derived. This enables a quantum version of the two Riccati solution to the H?control problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements.