Reversion of Quantum Walks via interventions on coin space

TL;DR

This paper introduces a method to reverse the evolution of quantum walks by intervening on the coin space, enabling control over particle positions and potential applications in quantum computing.

Contribution

It presents a novel scheme for reversing n-dimensional quantum walks through interventions on the coin degree of freedom, with analytical proof and practical implications.

Findings

Single intervention reverses quantum walk on a line

Number of interventions scales with walk dimensionality

Scheme enables periodic bounded quantum walks

Abstract

In this study we show a way of achieving the reverse evolution of n-dimensional quantum walks by introducing interventions on the coin degree of freedom during the forward progression of the coin-walker system. Only a single intervention is required to reverse a quantum walker on a line to its initial positon and the number of interventions increases with the dimensionality of the walk. We present an analytical treatment to prove these results. This reversion scheme can be used to generate periodic bounded quantum walks and to control the locations where particle can be found with highest probability. From the point of view of quantum computations and simulations, this scheme could be useful in resetting quantum operations and implementing certain quantum gates.