Self-avoiding quantum walks

TL;DR

This paper introduces a quantum walk model with memory that enables the walker to avoid revisiting sites, allowing the study of quantum analogs of classical self-avoiding walks and their diverse diffusive behaviors.

Contribution

It proposes a novel quantum walk framework with memory, enabling control over walk dynamics and bridging classical self-avoiding walks with quantum counterparts.

Findings

Quantum walk can mimic classical self-avoiding walk behavior.

Parameters control transition between quantum and classical diffusion.

Close correspondence observed between classical and quantum self-avoiding walks.

Abstract

Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random walks have found numerous applications, most notably in the modeling of protein folding. We consider the analogous problem in the quantum setting. We complement a quantum walk with a memory register that records where the walker has previously resided. The walker is then able to avoid returning back to previously visited sites. We parameterise the strength of the memory recording and the strength of the memory back-action on the walker's motion, and investigate their effect on the dynamics of the walk. We find that by manipulating these parameters the walk can be made to reproduce ideal quantum or classical random walk statistics, or a plethora of more elaborate diffusive phenomena. In some parameter regimes we observe a close correspondence between classical self-avoiding random walks and the quantum self-avoiding walk.