Fault-tolerant Coherent H-infinity Control for Linear Quantum Systems

TL;DR

This paper develops a fault-tolerant coherent H-infinity control method for linear quantum systems with Markovian faults, ensuring robustness and physical realizability, demonstrated through a quantum optics example.

Contribution

It extends physical realization conditions to time-varying quantum systems and designs a fault-tolerant H-infinity controller using LMIs and additional noise techniques.

Findings

Successfully designed a quantum H-infinity controller for a quantum optics system.

Demonstrated fault tolerance against Markovian jumping faults in quantum systems.

Validated the control strategy with a practical optical component implementation.

Abstract

Robustness and reliability are two key requirements for developing practical quantum control systems. The purpose of this paper is to design a coherent feedback controller for a class of linear quantum systems suffering from Markovian jumping faults so that the closed-loop quantum system has both fault tolerance and H-infinity disturbance attenuation performance. This paper first extends the physical realization conditions from the time-invariant case to the time-varying case for linear stochastic quantum systems. By relating the fault tolerant H-infinity control problem to the dissipation properties and the solutions of Riccati differential equations, an H-infinity controller for the quantum system is then designed by solving a set of linear matrix inequalities (LMIs). In particular, an algorithm is employed to introduce additional noises and to construct the corresponding input matrices to ensure the physical realizability of the quantum controller. For real applications of the developed fault-tolerant control strategy, we present a linear quantum system example from quantum optics, where the amplitude of the pumping field randomly jumps among different values. It is demonstrated that a quantum H-infinity controller can be designed and implemented using some basic optical components to achieve the desired control goal.