Formal languages analysed by quantum walks

TL;DR

This paper explores how discrete time quantum walks can accept certain formal languages with certainty, demonstrating their potential for quantum language recognition and state discrimination.

Contribution

It introduces methods for quantum walks to accept languages with certainty and interprets quantum inputs as performing state discrimination.

Findings

Quantum walks can accept some languages with certainty.

Quantum inputs enable state discrimination.

Quantum walks demonstrate language recognition capabilities.

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 gate set. In this paper we examine computation 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 be interpreted as performing state discrimination.