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Topological, Quantum, and Molecular Information Approaches to Computation and Intelligence
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Institut FEMTO-ST CNRS UMR 6174, Université Marie et Louis Pasteur, 15 B Avenue des Montboucons, F-25044 Besançon, France
Department of Computer Science, University of Massachusetts Amherst, Amherst, MA 01003, USA
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Topological, Quantum, and Molecular Information Approaches to Computation and Intelligence

Abstract submission deadline
31 October 2026
Manuscript submission deadline
31 December 2026
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537

Topic Information

Dear Colleagues,

This Topic explores the interplay between topological, quantum, and molecular information structures, and their roles in shaping intelligent computation across both artificial and biological systems. We welcome pioneering theoretical and experimental contributions that draw upon topological quantum computing, braid groups, modular tensor categories, and molecular regulatory mechanisms—including those based on DNA, RNA, and miRNA—to propose novel frameworks for learning, inference, decision-making, and biologically inspired computation.

We also encourage submissions that investigate fundamental physical or algebraic architectures of cognition and natural intelligence, especially those grounded in quantum symmetries, non-Abelian computation, and topological robustness.

The goal is to foster collaboration across quantum physics, mathematics, artificial intelligence, molecular biology, and information theory, with an emphasis on frameworks that integrate logic, structure, and evolution into new paradigms of computation.

Topics (non‑exhaustive)

  • Anyon-based topological quantum computing (e.g., SU(2)_k, Fibonacci anyons)
  • Modular tensor categories and braid group representations in computation
  • Quantum neural networks and variational quantum learning
  • Quantum-inspired AI: cognition, decision theory, and hybrid architectures
  • SL(2,C) symmetries and topological operations in learning models
  • Algebraic and topological modeling of DNA, RNA, and miRNA dynamics
  • Quantum and classical logic in gene regulation and molecular computation
  • Category-theoretic modeling of biological information networks
  • Quantum/molecular models of consciousness (e.g., with microtubules, anyon cognition)
  • Topological invariants and non-locality in cognitive architectures

Dr. Michel Planat
Prof. Dr. Edward A. Rietman
Topic Editors

 

Keywords

  • topological quantum computing
  • modular tensor categories
  • quantum artificial intelligence
  • quantum cognition
  • braid groups and anyons
  • group representations and SL(2,C) symmetry
  • category theory in computation
  • hybrid quantum–classical systems
  • molecular information systems
  • natural computation and intelligence

Participating Journals

Journal Name Impact Factor CiteScore Launched Year First Decision (median) APC
Entropy
entropy 		2.0 5.2 1999 21.8 Days CHF 2600 Submit
International Journal of Molecular Sciences
ijms 		4.9 9.0 2000 20.5 Days CHF 2900 Submit
International Journal of Topology
ijt 		- - 2024 15.0 days * CHF 1000 Submit
Machine Learning and Knowledge Extraction
make 		6.0 9.9 2019 25.5 Days CHF 1800 Submit
Mathematics
mathematics 		2.2 4.6 2013 18.4 Days CHF 2600 Submit
Quantum Reports
quantumrep 		1.3 3.0 2019 18.5 Days CHF 1400 Submit
Symmetry
symmetry 		2.2 5.3 2009 17.1 Days CHF 2400 Submit

* Median value for all MDPI journals in the first half of 2025.


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Published Papers (1 paper)

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19 pages, 398 KB  
Article
From Fibonacci Anyons to B-DNA and Microtubules via Elliptic Curves
by Michel Planat
Quantum Rep. 2025, 7(4), 49; https://doi.org/10.3390/quantum7040049 - 17 Oct 2025
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Abstract
By imposing finite order constraints on Fibonacci anyon braid relations, we construct the finite quotient G=Z5⋊2I, where 2I is the binary icosahedral group. The Gröbner basis decomposition of its [...] Read more.
By imposing finite order constraints on Fibonacci anyon braid relations, we construct the finite quotient G=Z5⋊2I, where 2I is the binary icosahedral group. The Gröbner basis decomposition of its SL(2,C) character variety yields elliptic curves whose L-function derivatives L′(E,1) remarkably match fundamental biological structural ratios. Specifically, we demonstrate that the Birch–Swinnerton-Dyer conjecture’s central quantity: the derivative L′(E,1) of the L-function at 1 encodes critical cellular geometries: the crystalline B-DNA pitch-to-diameter ratio (L′(E,1)=1.730 matching 34Å/20Å=1.70), the B-DNA pitch to major groove width (L′=1.58) and, additionally, the fundamental cytoskeletal scaling relationship where L′(E,1)=3.570≈25/7, precisely matching the microtubule-to-actin diameter ratio. This pattern extends across the hierarchy Z5⋊2P with 2P∈{2O,2T,2I} (binary octahedral, tetrahedral, icosahedral groups), where character tables of 2O explain genetic code degeneracies while 2T yields microtubule ratios. The convergence of multiple independent mathematical pathways on identical biological values suggests that evolutionary optimization operates under deep arithmetic-geometric constraints encoded in elliptic curve L-functions. Our results position the BSD conjecture not merely as abstract number theory, but as encoding fundamental organizational principles governing cellular architecture. The correspondence reveals arithmetic geometry as the mathematical blueprint underlying major biological structural systems, with Gross–Zagier theory providing the theoretical framework connecting quantum topology to the helical geometries that are essential for life. Full article
(This article belongs to the Topic Topological, Quantum, and Molecular Information Approaches to Computation and Intelligence)
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