Models of Quantum Algorithms in Sets and Relations

TL;DR

This paper introduces a novel abstract model of quantum algorithms using sets and relations, providing insights into quantum computation's structure and its relation to physical theories, despite being unphysical.

Contribution

It constructs models of key quantum algorithms within the QCRel framework, offering new tools for analyzing quantum computation semantics and extending intuition into new mathematical settings.

Findings

Models of Deutsch-Jozsa, Grover's, and GroupHomID algorithms in QCRel

Enhanced understanding of quantum speedups and physical theories

New methods for analyzing quantum computational structures

Abstract

We construct abstract models of blackbox quantum algorithms using a model of quantum computation in sets and relations, a setting that is usually considered for nondeterministic classical computation. This alternative model of quantum computation (QCRel), though unphysical, nevertheless faithfully models its computational structure. Our main results are models of the Deutsch-Jozsa, single-shot Grovers, and GroupHomID algorithms in QCRel. These results provide new tools to analyze the semantics of quantum computation and improve our understanding of the relationship between computational speedups and the structure of physical theories. They also exemplify a method of extending physical/computational intuition into new mathematical settings.