Title: Geometric Proof of Algorithm Completeness using Quantum Simulation

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

This paper presents a novel approach to algorithm verification, leveraging the power of quantum simulation to establish completeness. Traditional verification methods often rely on exhaustive testing, which is computationally intractable for complex algorithms. We propose a geometric proof demonstrating the completeness of an algorithm through the simulation of its execution on a quantum computer. This technique offers a fundamentally new pathway to rigorous algorithm validation, potentially enabling the verification of algorithms that are currently beyond the reach of classical methods. The core mechanism involves constructing a geometric structure representing the algorithm's state space, and quantum simulation is used to demonstrate that this structure is fully explored, guaranteeing correctness. The resulting geometric proof provides a rigorous, automated, and computationally feasible method for verifying algorithm completeness.

DOI: 10.5281/zenodo.22330837

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