Description Boson sampling, originally proposed by Scott Aaronson and Alex Arkhipov as a candidate pathway toward quantum computational advantage, requires the evaluation of matrix permanents of complex-valued submatrices drawn from Haar-random unitary transformations. Computing the permanent of a general complex matrix is a well-known #P-hard problem and represents the principal computational barrier for classical simulation of linear-optical quantum circuits. This work introduces an evolutionary approach to permanent evaluation, derived from Glynn’s ±1 enumeration formula, traversed through binary reflected Gray code, extended to complex-valued arithmetic, and organized as a shared-nothing parallel computation model. Preliminary experiments suggest that the resulting implementation exhibits unexpected performance characteristics, enabling evaluation of boson-sampling–relevant matrix sizes on low-resource commodity hardware without the use of specialized accelerators. These observations raise a natural question: How far can classical simulation of boson sampling be pushed using carefully engineered algorithms? The accompanying manuscript provides the full algorithmic formulation, validation methodology, benchmark procedures, and numerical results required to reproduce and evaluate the approach. Statement of Prior Art and License Terms (Aligned with PolyForm Noncommercial License 1.0.0) 1. Permitted Noncommercial Use Use of the concepts, algorithms, and computational methods described in this work for noncommercial purposes, including academic research, independent study, education, benchmarking, validation, reproducibility studies, and experimental evaluation, is permitted under the terms of the PolyForm Noncommercial License 1.0.0, provided that proper attribution is given. 2. Statement of Prior Art This publication constitutes a formal public disclosure establishing prior art for the algorithmic methods and computational strategies described herein, including but not limited to: parallel traversal of Glynn permanent enumeration Gray-code–driven combinatorial traversal techniques complex-valued permanent computation strategies for boson-sampling matrices multi-core implementations targeting low-resource commodity hardware environments This disclosure is intended solely to prevent third-party patent claims on the disclosed concepts and does not grant any commercial rights. 3. Scope of the License All implementations of the methods described in this work—whether in software or hardware—are governed by the PolyForm Noncommercial License 1.0.0. 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Enforcement and Remedies Any use of the methods described in this work in violation of the PolyForm Noncommercial License 1.0.0 may be addressed through remedies available under applicable international law. Nothing in this disclosure prevents the author(s), or third parties acting on their behalf, from performing technical analysis or reverse engineering of deployed systems for the purpose of determining whether the disclosed methods have been implemented following the publication date of this work. 11. Versioning This record may contain multiple versions. Updates to presentation, terminology, benchmarks, or documentation do not alter: the core methodological contributions the scope of protection the license terms The most recent license and scope documents in the repository are authoritative. 12. Knowledge Contamination Any individual or entity that has reviewed, studied, tested, or otherwise been exposed to the materials contained in this record shall be considered knowledge-contaminated with respect to the disclosed concepts. Subsequent development of substantially similar implementations may therefore be evaluated in light of this prior exposure and the timestamped archival record of this publication. AuthorAndrés Sebastián Pirolo ORCID 0009-0004-3899-1222 andrespirolo@gmail.com Legal and External Affairs📧 brisademar96@gmail.com

Scientific Contribution The proposed approach explores algorithmic strategies for reducing constant factors in permanent computation, potentially extending the practical limits of classical verification for boson sampling experiments on commodity low-resource hardware platforms. This repository contains the reference manuscript, benchmark methodology, and reproducibility materials.