The expressive power of quantum walks in terms of language acceptance

TL;DR

This paper explores how discrete time quantum walks can accept certain languages with certainty and can perform quantum state discrimination when given quantum inputs, highlighting their computational and informational capabilities.

Contribution

It introduces two methods for quantum walks to accept languages with certainty and connects quantum input processing to quantum state discrimination.

Findings

Quantum walks can accept some languages with certainty.

Quantum walks can perform quantum state discrimination with quantum inputs.

The study links language acceptance to quantum computational power.

Abstract

Discrete time quantum walks are known to be universal for quantum computation. This has been proven by showing that they can simulate a universal quantum gate set. In this paper, we examine computation by quantum walks in terms of language acceptance, and present two ways in which discrete time quantum walks can accept some languages with certainty. These walks can take quantum as well as classical inputs, and we show that when the input is quantum, the walks can also be interpreted as performing the task of quantum state discrimination.