Decoherence on a two-dimensional quantum walk using four- and two-state particle

TL;DR

This paper investigates how decoherence affects two-dimensional quantum walks with two- and four-state particles, demonstrating that two-state particles are more robust and maintain symmetries better than four-state particles like the Grover walk.

Contribution

It provides a comparative analysis of decoherence effects on two- and four-state quantum walks, highlighting the robustness and symmetry properties of two-state particles.

Findings

Two-state quantum walks are more resistant to decoherence than four-state Grover walks.

Symmetries in two-state walks break down in Grover walks under decoherence.

Two-state particles exhibit advantages over four-state particles in quantum walk robustness.

Abstract

We study the decoherence effects originating from state flipping and depolarization for two-dimensional discrete-time quantum walks using four-state and two-state particles. By quantifying the quantum correlations between the particle and position degree of freedom and between the two spatial ($x-y$) degrees of freedom using measurement induced disturbance (MID), we show that the two schemes using a two-state particle are more robust against decoherence than the Grover walk, which uses a four-state particle. We also show that the symmetries which hold for two-state quantum walks breakdown for the Grover walk, adding to the various other advantages of using two-state particles over four-state particles.