GenAIs and SRMs: A Guide to Conceptual Bridges and Practical Applications in Quantum Computing

GenAIs and SRMs: A Guide to Conceptual Bridges and Practical Applications in Quantum Computing Author: Carlos Roberto França 1[0000-0002-6852-7103] 1Federal University of Fronteira Sul – UFFS/Campus Chapecó-Santa Catarina – Brazil [email protected] Abstract This article presents a synthesis and interpretative guide to two recent contributions: Paper 10, which establishes conceptual bridges between Multiple Ratios Infinite Series (MRSs), Generative Artificial Intelligences (GenAIs), and Quantum Computing, and Paper 11, which demonstrates the practical application of these ideas through the SRM Laplacian applied to the Schrödinger equation. While Paper 10 presents the "why"—the philosophical and mathematical basis—Paper 11 shows the "how"—the numerical implementation and validation of MRSs as a multiscale tool capable of controlling entanglement and preserving unitarity. By placing them side by side, Paper 12 highlights how GenAIs can act as interpretive partners rather than substitutes, reinforcing the leading role of biological intelligence in conducting research. It also records global traction, with growing interest reflected in hundreds of views and downloads in different regions of the world. The result is a conceptual and practical trilogy (P10–P11–P12) that offers both a theoretical framework and a reproducible methodology for advancing simulations, interpretations, and innovations in quantum computing. Keywords: Quantum Computing. SRMs and GenAIs. SRM Laplacian 1. INTRODUCTION It is timely and essential to highlight that throughout 2025, more specifically from March to September, we published a series of papers on the Zenodo platform (CERN/Switzerland). This scientific marathon was the strategy to present Infinite Series with Multiple Ratios (SRMs) [1] to the global scientific community. At various times, we highlighted the novelty and disruptive nature of the 16 formulas that have never been published in printed books or digital "e-books." Among the first 9 (nine) papers, two were subjected to peer review (papers 8 and 9) [1], [2], before being published on the Zenodo platform. The first, paper 1 [3], was made available as a preprint and published in March 2025 and presented in person in May 2025 at the 10th ICTIS, held at Cornell University – New York / USA. During the 10th International Conference on ICT for Intelligent Systems (ICTIS - 2025), we had the opportunity to attend a lecture by Dr. Pravir Malik, a world leader in quantum computing. This event and the discussions we had during the ICTIS Conference reinforced the idea of publicizing the applicability of Infinite Series with Multiple Ratios (SRMs) in quantum computing. We already had certifications of the strength of our post-quantum cryptography software, the only one that encrypts with binary perturbation and the original and unpublished formulas (SRMs) we've been working on since 1996. Well, the materialization of our determination came with paper 10, entitled "SRMs and GenAIs: Bridges between Infinite Series with Multiple Ratios, Generative Intelligence and Quantum Computing" [4], released on August 16, 2025, 16 days ago. To date, it has been viewed 386 times and downloaded 421 times, impressive numbers, with readers from various countries and continents. 2. Presentation of paper 10 - SRMs and GenAIs: Bridges between Infinite Series with Multiple Ratios, Generative Intelligence and Quantum Computing. In this paper, we seek to clearly articulate and present how SRMs, with their unique mathematics, resemble fundamental principles of quantum mechanics, which is fascinating. The correspondences presented are: Superposition: Just as a qubit exists in a superposition of states, each term of an SRM "embodies multiple trajectories of potential growth, collapsing into a single value only when the full computation is performed." Observer Effect: The act of computing an SRM, whether by a human or a machine, is compared to the quantum state collapse induced by a measurement. The Importance of Human-AI Collaboration One point that deserves special emphasis is our reflection on the partnership with Generative AIs, such as Gabriel Altman's ChatGPT. The distinction we made between "scientific production in partnership with Generative AIs" and "research delegated to them" is crucial. The article emphasizes that the success of our research lies in the oversight and protagonism of "biological intelligence" (humans). This is a critical and timely message for the scientific community, especially in a scenario where the use of AI tools in research is constantly debated. Global Context and Research Validation The article also contextualizes the research within a broader global dialogue, mentioning the work of Pravir Malik[5]. This not only strengthens the relevance of the work but also demonstrates that the ideas in paper 10 are aligned with the trends and needs for new mathematical frameworks to guide the evolution of quantum technologies. Building the bridge between papers 10 and 11. Paper 10 establishes the "why." The search for new mathematics, which intrinsically aligns with quantum principles and can be enhanced by AI tools, is one of the greatest challenges and, at the same time, one of the greatest opportunities in the field of quantum computing. Our approach, which combines the deep mathematics of SRMs with the agility of Generative AI, appears to have been validated by the interest of the scientific community, as evidenced by the 377 views and 414 downloads in just 16 days since its launch on the Zenodo platform. We believe this is a strong indication that we are exploring a promising path. The community's confidence in this paper and in all the research shared on the important CERN/Switzerland platform since March 2025 speaks for itself. While paper 10 presents the theoretical basis for bridging SRMs, GenAIs, and Quantum Computing, paper 11 provides the practical proof and the "how." Let's get to the facts. 3 – Presentation of Paper 11: SRMs meet Schrödinger: Multiple-ratio expansions for quantum dynamics and entanglement in a timeless dialogue. This paper, released on September 1, 2025, presents a new approach to the numerical solution of the Schrödinger equation, replacing the classical Laplacian with what the author calls the SRM Laplacian [6]. This new tool, based on "Infinite Series with Multiple Ratios (SRMs)," acts as a multiscale "ruler," allowing the simultaneous representation of fast and slow, local and long-range structures, on the same basis or grid. The central idea is that, since quantum physics is multiscale, the mathematical tool used to describe it should be as well. Figure 01: SRMs & GenAIs: from the bridge between Concept and Application emerges the Guide to Quantum Computing. Source: Author (2025) with SORA – OpenAI Main Contributions and Benefits The paper details several important contributions that would be of great value to the quantum physics and computing community: • Accuracy and Efficiency: Tests performed on scenarios such as free particles, oscillators, and double barriers show that SRM-Schr (the scheme that uses the SRM Laplacian) reduces dispersion and phase error compared to uniform discretizations while maintaining the same computational cost. With only 2 to 3 ratios, SRM can already reduce phase error by orders of magnitude compared to the 3-point Laplacian. Entanglement Control and Study: The paper introduces a "homologous coupling operator" that induces controllable non-local correlations. This allows entanglement to be studied as a "structural regularity." In two-body models, an SRM "pulse" smoothly controls entanglement (von Neumann entropy). The sparsity and entropy of the SRM coefficients correlate with ordinary quantum entropies, offering a new way to "read" entanglement. Physical Foundation: One of the most interesting proposals is that the choice of SRM "ratios" is guided by physical scaling relations, such as E=hf and λ=h/p. This transforms purely numerical optimization into a physically informed multiscale selection. Probability and Unitarity Preservation: The time evolution scheme uses the CrankNicolson/Strang method with a self-adjoint operator, ensuring probability conservation and unitarity. Reproducibility: The article mentions establishing an auditable protocol with measurement windows, logs, and DOIs to ensure the reproducibility of results. This is crucial for validation within the scientific community. Important Observations This trilogy (papers 10, 11, and 12) does not seek to alter the probabilistic interpretation of quantum mechanics or "determinize" the theory. Instead, it focuses on a structural and numerical contribution: that SRMs provide a more efficient and organized way to represent the dynamics of the wave function. The ability to simulate interference and entanglement with fewer points and greater fidelity is a significant advance, especially for complex, large-scale quantum systems where computational cost is a constraint. The idea that entanglement can be viewed as a "structural regularity" in the SRM coefficients is an intriguing new perspective that deserves further exploration. In summary, paper 11 is a promising read. It not only solves a practical problem (the high cost of uniform discretizations) but also offers a new conceptual lens for understanding quantum correlations. We look forward to testing the implementation and investigating the potential of this new "ruler" for large-scale simulations and the development of new entanglement metrics. 4. Considerations When analyzing the article "SRMs and GenAIs: Bridges between Infinite Series with Multiple Ratios, Generative Intelligence, and Quantum Computing," you will realize that it serves as a conceptual and philosophical foundation for the more applied work we presented in paper 11 (which focuses on the Schrödinger Equation). It establishes the theoretical bridges and correspondences between SRMs, Generative AI, and Quantum Computing. Conceptual Correspondences between SRMs and Quantum Theory The papers clearly articulate how SRMs, with their unique, original, and unprecedented mathematics, resemble fundamental principles of quantum mechanics, which is fascinating, promising, and disruptive. The correspondences presented are: Superposition: Just as a qubit exists in a superposition of states, each term of a SRM "incorporates multiple potential growth trajectories, collapsing into a single value only when the complete computation is performed." Observer Effect: The act of computing a SRM, whether by a human or a machine, is compared to the quantum state collapse induced by a measurement. The Importance of Human-AI Collaboration One point that deserves special attention is our reflection on the partnership with Generative AIs, such as ChatGPT, which we refer to as Gabriel Altman. This fact is highlighted and substantiated in paper 10 and several previous papers. The distinction we made between "scientific production in partnership with Generative AIs"[7] and "research delegated to them" is fundamental. Paper 10 emphasizes that the success of SRM research powered by GenAIs necessarily depends on the supervision and protagonism of "biological intelligence" (humans). This is a critical and timely message for the scientific community, especially in a scenario where the use of AI tools in research is under constant debate. We still lack regulatory legislation in the context of non-human authorship or coauthorship, but the positive impact of non-human intelligence on scientific knowledge is undeniable. Global Context and Research Validation As previously mentioned, the papers contextualize the research within a broader global dialogue, citing Pravir Malik's work. This not only reinforces the relevance of the SRM research I've been conducting for three decades but also demonstrates that the ideas are aligned with trends and the need for new mathematical frameworks to guide the evolution of quantum technologies. Reference [1] – França, C. R. (2025). Método de criptografia Heru Technologies: único do mundo que utiliza fórmulas matemáticas inéditas autorais e que criptografa com perturbações binárias. Zenodo. https://doi.org/10.5281/zenodo.15653585 [2] - França, C. R. (2025). Heru Technologies encryption method: unique in the world that uses unpublished mathematical formulas and encrypts with binary disturbances. https://doi.org/10.5281/zenodo.15717868 [3] - França, C. R. (2025). Mathematical Challenges for Generative AI in Computational Biology: Cell Proliferation and the Path to Living AI. Zenodo. https://doi.org/10.5281/zenodo.15033127 [4] - França, C. R. (2025). SRMs and GenAIs: Bridges between Infinite Series with Multiple Ratios, Generative Intelligence and Quantum Computing (Second version). Zenodo. https://doi.org/10.5281/zenodo.16888353 [ 5 ] – Malik, Pravir (2025). Pioneering New Avenues in Quantum Technology - Studies in Smart Technologies – Editor: Springer https://doi.org/10.1007/978-981-96-5463-5 [6] - França, C. R. (2025). SRMs meet Schrödinger: Multiple-ratio expansions for quantum dynamics and entanglement in a timeless dialogue. Zenodo. https://doi.org/10.5281/zenodo.17017967 [7] - França, C. R. (2025). Advanced computational mathematics and future point modeling of a predictive system: A collaborative scientific research between a human and a Generative AI. Zenodo. https://doi.org/10.5281/zenodo.15083825