Quantum Simulation of a Discrete-Time Quantum Stochastic Walk
Abstract
Quantum walks have been shown to have a wide range of applications, from artificial intelligence, to photosynthesis, and quantum transport. Quantum stochastic walks (QSWs) generalize this concept to additional non-unitary evolution. In this paper, we propose a trajectory-based quantum simulation protocol to effectively implement a family of discrete-time QSWs in a quantum device. After deriving the protocol for a 2-vertex graph with a single edge, we show how our protocol generalizes to a graph with arbitrary topology and connectivity. The straight-forward generalization leads to simple scaling of the protocol to complex graphs. Finally, we show how to simulate a restricted class of continuous-time QSWs by a discrete-time QSW, and how this is amenable to our simulation protocol for discrete-time QSWs.
Cite
@article{arxiv.2004.06151,
title = {Quantum Simulation of a Discrete-Time Quantum Stochastic Walk},
author = {Peter K. Schuhmacher and Luke C. G. Govia and Bruno G. Taketani and Frank K. Wilhelm},
journal= {arXiv preprint arXiv:2004.06151},
year = {2021}
}