Efficient optimization of state preparation in quantum networks using quantum trajectories

The wavefunction Monte-Carlo method, also referred to as the use of 'quantum jump trajectories', allows efficient simulation of open systems by independently tracking the evolution of many pure-state 'trajectories'. This method is ideally suited to simulation by modern, highly parallel computers. Here we show that Krotov's method of numerical optimal control, unlike others, can be modified in a simple way so that it becomes fully parallel in the pure states without losing its effectiveness. This provides a highly efficient method for finding optimal control protocols for open quantum systems and networks. We apply this method to the problem of generating entangled states in a network consisting of systems coupled in a unidirectional chain. We show that due to the existence of a dark state subspace in the network, nearly optimal control protocols can be found for this problem by using only a single pure-state trajectory in the optimization, further increasing the efficiency.