Generic quantum walk using a coin-embedded shift operator

TL;DR

This paper introduces a versatile quantum walk model that incorporates a coin-embedded shift operator, unifying discrete and continuous variants while preserving the coin's control capabilities.

Contribution

A new generic quantum walk framework using a coin-embedded shift operator that unifies DTQW and CTQW, maintaining the coin's control features.

Findings

Standard DTQW and CTQW are special cases of the generic model.

The model retains the coin degree of freedom in both variants.

It provides a unified approach to quantum walk dynamics.

Abstract

The study of quantum walk processes has been widely divided into two standard variants, the discrete-time quantum walk (DTQW) and the continuous-time quantum walk (CTQW). The connection between the two variants has been established by considering the limiting value of the coin operation parameter in the DTQW, and the coin degree of freedom was shown to be unnecessary [26]. But the coin degree of freedom is an additional resource which can be exploited to control the dynamics of the QW process. In this paper we present a generic quantum walk model using a quantum coin-embedded unitary shift operation $U_{C}$. The standard version of the DTQW and the CTQW can be conveniently retrieved from this generic model, retaining the features of the coin degree of freedom in both variants.