Path integral approach to one-dimensional discrete-time quantum walk

TL;DR

This paper presents a path-integral method for analyzing one-dimensional discrete-time quantum walks, deriving a closed-form expression for the walker's state amplitudes at any step, offering new insights into their foundations and applications.

Contribution

It introduces a novel path-integral framework for quantum walks, enabling explicit amplitude calculations at arbitrary steps, which was not previously available.

Findings

Derived a closed-form expression for quantum walk amplitudes.

Provided a new foundational approach to quantum walk analysis.

Enhanced understanding of quantum walk dynamics and potential applications.

Abstract

Discrete-time quantum walk in one-dimension is studied from a path-integral perspective. This enables derivation of a closed-form expression for amplitudes corresponding to any coin-position basis of the state vector of the quantum walker at an arbitrary step of the walk. This provides a new approach to the foundations and applications of quantum walks.