Quantum walk based search algorithms

TL;DR

This survey explains how quantum walks can be used to develop search algorithms, including Grover's search and others, by quantizing classical Markov chains and applying them to various computational problems.

Contribution

It provides an intuitive overview of quantum walk-based search algorithms, detailing the MNRS algorithm and their application to multiple complex search problems.

Findings

Quantum walks can be effectively applied to search problems.

The MNRS algorithm simplifies quantum walk implementation.

Quantum algorithms outperform classical counterparts in specific tasks.

Abstract

In this survey paper we give an intuitive treatment of the discrete time quantization of classical Markov chains. Grover search and the quantum walk based search algorithms of Ambainis, Szegedy and Magniez et al. will be stated as quantum analogues of classical search procedures. We present a rather detailed description of a somewhat simplified version of the MNRS algorithm. Finally, in the query complexity model, we show how quantum walks can be applied to the following search problems: Element Distinctness, Matrix Product Verification, Restricted Range Associativity, Triangle, and Group Commutativity.