Optimizing the discrete time quantum walk using a SU(2) coin

TL;DR

This paper introduces a generalized discrete time quantum walk using SU(2) coins, optimizing variance and bias in the position distribution to enhance quantum walk performance in search and mixing tasks.

Contribution

It presents a novel SU(2)-based quantum walk framework with parameter tuning for optimized variance, bias, and measurement entropy, improving quantum walk applications.

Findings

Optimized quantum walk variance scales as N^2.

Bias in position distribution can be controlled via coin parameters.

Enhanced mixing time and search efficiency demonstrated.

Abstract

We present a generalized version of the discrete time quantum walk, using the SU(2) operation as the quantum coin. By varying the coin parameters, the quantum walk can be optimized for maximum variance subject to the functional form $\sigma^2 \approx N^2$ and the probability distribution in the position space can be biased. We also discuss the variation in measurement entropy with the variation of the parameters in the SU(2) coin. Exploiting this we show how quantum walk can be optimized for improving mixing time in an $n$-cycle and for quantum walk search.