Quantum simulation of a discrete-time quantum stochastic walk

¹ Theoretical Physics, Saarland University - D-66123 Saarbrücken, Germany
² Institute for quantum computing analytics (PGI12), Forschungszentrum Jülich - D-52425 Jülich, Germany
³ Raytheon BBN Technologies - 10 Moulton Street, Cambridge, MA, 02138, USA
⁴ Departamento de Física, Universidade Federal de Santa Catarina - 88040-900, Florianópolis, Brazil

^(a) peter@lusi.uni-sb.de

Received: 4 June 2020
Accepted: 10 February 2021

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 straightforward 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.