Geometric-Algebra Quantum-Like Algorithms: Simon's Algorithm

TL;DR

This paper extends geometric-algebraic methods to implement Simon's quantum algorithm, demonstrating advantages over traditional quantum mechanics-based approaches and contributing to the development of quantum-like algorithms.

Contribution

It introduces a geometric-algebraic framework for Simon's algorithm, avoiding quantum mechanics and showcasing potential benefits of this approach.

Findings

Successfully implements Simon's algorithm using geometric algebra.

Highlights advantages of quantum-mechanics-free approaches.

Contributes to the development of quantum-like algorithms.

Abstract

This is continuation of the approach to performing quantum algorithms using geometric structures which was presented by Aerts and Czachor. We solve the Simon's problem which, next to the Shor's alghorithm, is a representative of a quantum hidden subgroup class. We also highlight some advantages resulting from the fact that no quantum mechanics is involved.