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arXiv · 2004.06151

Quantum Simulation of a Discrete-Time Quantum Stochastic Walk

Peter K. Schuhmacher·Luke C. G. Govia·Bruno G. Taketani·Frank K. Wilhelm
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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.

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Peter K. Schuhmacher, Luke C. G. Govia, Bruno G. Taketani, Frank K. Wilhelm. 2020-04-13. Quantum Simulation of a Discrete-Time Quantum Stochastic Walk. https://doi.org/10.1209/0295-5075/133/50003

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