Any Quantum Network is Structurally Controllable by a Single Driving Signal

Abstract

Control theory concerns with the question if and how it is possible to drive the behavior of a complex dynamical system. A system is said to be controllable if we can drive it from any initial state to any desired final state in finite time. For many complex networks, the precise knowledge of system parameters lacks. But, it is possible to make a conclusion about network controllability by inspecting its structure. Classical theory of structural controllability is based on the Lin's structural controllability theorem, which gives necessary and sufficient conditions to conclude if any network is structurally controllable. Due to this fundamental theorem we may identify a minimum driver vertex set, whose control with independent driving signals is sufficient to make the whole system controllable. I show that the Lin's theorem does not impose any limitations on quantum networks structural controllability. By local operations and classical communication, one can modify any quantum network to make it structurally controllable by a single driving signal.