Quantum walk on circles in phase space

TL;DR

This paper introduces a generalized quantum walk on multiple concentric circles in phase space by combining Hadamard coin flips with simultaneous displacements, inspired by the Jaynes-Cummings model.

Contribution

It presents a novel variation of quantum walks in phase space, connecting theoretical models with physical implementations via the Jaynes-Cummings system.

Findings

Quantum walk signature observed in phase distribution

Generalization to multiple concentric circles demonstrated

Dispersive limit of Jaynes-Cummings model supports the approach

Abstract

We propose a variation of the quantum walk on a circle in phase space by conjoining the Hadamard coin flip with simultaneous displacement of the walker's location in phase space and show that this generalization is a proper quantum walk albeit over multiple concentric circles in phase instead of just over one circle. We motivate the conjoining of Hadamard and displacement operations by showing that the Jaynes-Cummings model for coin+walker approximately yields this description in the dispersive limit. The quantum walk signature is evident in the phase distribution of the walker provided that appropriate pulse durations are applied for each coin flip.