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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Knowledge Contamination and Attribution Exposure to this work constitutes prior knowledge of the disclosed techniques. Subsequent implementations making material use of the described concepts remain subject to attribution and license requirements as defined by the PolyForm Noncommercial License 1.0.0. 8. Intellectual Property Ownership Nothing in this document shall be construed as transferring ownership of intellectual property. All intellectual property rights remain with the author(s), subject only to the permissions explicitly granted under the PolyForm Noncommercial License 1.0.0. 9. No Additional Rights Granted This document does not grant any rights beyond those expressly provided by the PolyForm Noncommercial License 1.0.0. In the event of any conflict, the terms of the PolyForm Noncommercial License 1.0.0 shall prevail. 10. 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
This deposit establishes a public provenance record for PRIMBIT and a family of spherical, geometric, modal, and computational research engines developed under the direction and authorship of Edgar Marcelo Quiroz Robles. The record documents the relationship between the arithmetic/spectral PRIMBIT framework and subsequent Spherical Engine research branches developed through PRIMBIT-guided iterative investigation. It provides selected non-enabling technical fingerprints intended to identify the existence, continuity, and distinctive technical character of these research architectures without disclosing their confidential implementation. The documented research family includes spherical modal computation, axis/sphere/Grassmannian geometric structures, qudit-related spherical operator structures, multi-sphere spectral computation, and geometric memory/process research branches. A separate SHA-256 manifest included in this deposit provides cryptographic commitments to a larger private source corpus containing detailed development records, calculations, iterations, and technical specifications. Those source files remain confidential. Internal operators, transformation rules, coupling mechanisms, Hamiltonians, gate-synthesis procedures, implementation architecture, algorithms, parameters, source code, calibration procedures, complexity-reduction mechanisms, and other proprietary technical details are intentionally withheld from this public archival version. The mathematical and computational materials documented here form part of an ongoing research programme. This record does not claim that universal quantum computation, computational advantage over conventional classical simulation, or physical implementation without quantum hardware has already been experimentally established. This deposit is intended to establish public research provenance, authorship attribution, technical continuity, and an archival timestamp. It makes no allegation regarding any third party.