String Comparison on a Quantum Computer Using Hamming Distance

TL;DR

This paper extends a quantum algorithm for Hamming distance to handle arbitrary-long alphabets, implements it using QisKit, and demonstrates its application in bioinformatics and software engineering, discussing its resource needs.

Contribution

It introduces an extended quantum algorithm for string comparison with larger alphabets and provides practical implementation and examples.

Findings

Algorithm successfully compares strings with arbitrary-long alphabets.

Implementation is accessible via QisKit without quantum computing expertise.

Resource analysis indicates when quantum comparison becomes practical.

Abstract

The Hamming distance is ubiquitous in computing. Its computation gets expensive when one needs to compare a string against many strings. Quantum computers (QCs) may speed up the comparison. In this paper, we extend an existing algorithm for computing the Hamming distance. The extension can compare strings with symbols drawn from an arbitrary-long alphabet (which the original algorithm could not). We implement our extended algorithm using the QisKit framework to be executed by a programmer without the knowledge of a QC (the code is publicly available). We then provide four pedagogical examples: two from the field of bioinformatics and two from the field of software engineering. We finish by discussing resource requirements and the time horizon of the QCs becoming practical for string comparison.