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This paper is concerned with coherent quantum control design for translationinvariant networks of identical quantum stochastic systems subjected toexternal quantum noise. The network is modelled as an open quantum harmonicoscillator and is governed by a set of linear quantum stochastic differentialequations. The dynamic variables of this quantum plant satisfy the canonicalcommutation relations. Similar large-scale systems can be found, for example,in quantum metamaterials and optical lattices. The problem under considerationis to design a stabilizing decentralized coherent quantum controller in theform of another translation invariant quantum system, directly coupled to theplant, so as to minimize a weighted mean square functional of the dynamicvariables of the interconnected networks. We consider this problem in thethermodynamic limit of infinite network size and present first-order necessaryconditions for optimality of the controller.

Decentralized Coherent Quantum Control Design for Translation Invariant Linear Quantum Stochastic Networks with Direct Coupling