Numerical Exploration of the Pythagorean Theorem Using HOBO Algorithm

TL;DR

This paper presents a new HOBO-based method for finding Pythagorean triples, leveraging higher-order binary optimization to better model complex mathematical relationships than traditional QUBO approaches.

Contribution

It introduces a novel HOBO formulation for Pythagorean triples, improving the modeling of complex equations over existing QUBO methods.

Findings

HOBO effectively models Pythagorean triples.

HOBO outperforms QUBO in expressiveness for complex equations.

The method demonstrates potential for solving other mathematical problems.

Abstract

This paper introduces a novel method for finding integer sets that satisfy the Pythagorean theorem by leveraging the Higher-Order Binary Optimization (HOBO) formulation. Unlike the Quadratic Unconstrained Binary Optimization (QUBO) formulation, which struggles to express complex mathematical equations, HOBO's ability to model higher-order interactions between binary variables makes it well-suited for addressing more complex and expressive problem settings.