Quantum Noises, Physical Realizability and Coherent Quantum Feedback Control

TL;DR

This paper investigates the conditions under which linear systems can be physically realized as quantum systems by introducing quantum noises, providing formulas and algorithms for implementation and control design.

Contribution

It derives expressions for the number of quantum noise channels needed for physical realizability and offers an algorithm for suboptimal quantum control design.

Findings

Explicit formula for noise channels required for realization

Conditions for implementing transfer functions with quantum noises

Algorithm for suboptimal coherent quantum LQG control

Abstract

Physical Realizability addresses the question of whether it is possible to implement a given linear time invariant (LTI) system as a quantum system. A given synthesized quantum controller described by a set of stochastic differential equations does not necessarily correspond to a physically meaningful quantum system. However, if additional quantum noises are permitted in the implementation, it is always possible to implement an arbitrary LTI system as a quantum system. In this paper, we give an expression for the number of introduced noise channels required to implement a given LTI system as a quantum system. We then consider the special case where only the transfer function to be implemented is of interest. We give results showing when it is possible to implement a transfer function as a quantum system by introducing the same number of quantum noises as there are system outputs. Finally, we demonstrate the utility of these results by providing an algorithm for obtaining a suboptimal solution to a coherent quantum LQG control problem.