Efficient optimization of state preparation in quantum networks using quantum trajectories

TL;DR

This paper introduces a parallelized optimal control method for open quantum systems using quantum trajectories, enabling efficient state preparation in quantum networks, especially leveraging dark-state subspaces for improved performance.

Contribution

The authors adapt Krotov's method for parallel execution on pure-state trajectories, significantly enhancing the efficiency of quantum control optimization in networks.

Findings

Parallelized Krotov's method effectively optimizes control protocols.

Dark-state subspaces enable near-optimal control with minimal trajectories.

Method demonstrates high efficiency in entangled state generation.

Abstract

The wave-function 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.