Topological, Quantum, and Molecular Information Approaches to Computation and Intelligence

Abstract submission deadline

31 October 2026

Manuscript submission deadline

31 December 2026

Viewed by

1522

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

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.

Preprints.org is a multidisciplinary platform offering a preprint service designed to facilitate the early sharing of your research. It supports and empowers your research journey from the very beginning.

MDPI Topics is collaborating with Preprints.org and has established a direct connection between MDPI journals and the platform. Authors are encouraged to take advantage of this opportunity by posting their preprints at Preprints.org prior to publication:

1. Share your research immediately: disseminate your ideas prior to publication and establish priority for your work.
2. Safeguard your intellectual contribution: Protect your ideas with a time-stamped preprint that serves as proof of your research timeline.
3. Boost visibility and impact: Increase the reach and influence of your research by making it accessible to a global audience.
4. Gain early feedback: Receive valuable input and insights from peers before submitting to a journal.
5. Ensure broad indexing: Web of Science (Preprint Citation Index), Google Scholar, Crossref, SHARE, PrePubMed, Scilit and Europe PMC.

Published Papers (2 papers)

Order results

Content type Publication Date

Result details

Normal Extended Compact

Journals

All Entropy IJMS International Journal of Topology MAKE Mathematics Quantum Reports Symmetry

Show export options expand_more Show export options expand_less

Select all

Export citation of selected articles as:

Plain Text BibTeX BibTeX (without abstracts) Endnote Endnote (without abstracts) Tab-delimited RIS

Error

Oops... you haven't selected anything for export.

Ok

clear

40 pages, 1231 KB  

Open AccessReview

Quaternionic and Octonionic Frameworks for Quantum Computation: Mathematical Structures, Models, and Fundamental Limitations

by Johan Heriberto Rúa Muñoz, Jorge Eduardo Mahecha Gómez and Santiago Pineda Montoya

Quantum Rep. 2025, 7(4), 55; https://doi.org/10.3390/quantum7040055 - 26 Nov 2025

Viewed by 219

Abstract

We develop detailed quaternionic and octonionic frameworks for quantum computation grounded on normed division algebras. Our central result is to prove the polynomial computational equivalence of quaternionic and complex quantum models: Computation over $\mathbb{H}$ is polynomially equivalent to the standard complex quantum circuit [...] Read more.

We develop detailed quaternionic and octonionic frameworks for quantum computation grounded on normed division algebras. Our central result is to prove the polynomial computational equivalence of quaternionic and complex quantum models: Computation over $\mathbb{H}$ is polynomially equivalent to the standard complex quantum circuit model and hence captures the same complexity class BQP up to polynomial reductions. Over $\mathbb{H}$, we construct a complete model—quaternionic qubits on right $\mathbb{H}$-modules with quaternion-valued inner products, unitary dynamics, associative tensor products, and universal gate sets—and establish polynomial equivalence with the standard complex model; routes for implementation at fidelities exceeding $99\%$ via pulse-level synthesis on current hardware are discussed. Over $\mathbb{O}$, non-associativity yields path-dependent evolution, ambiguous adjoints/inner products, non-associative tensor products, and possible failure of energy conservation outside associative sectors. We formalize these obstructions and systematize four mitigation strategies: Confinement to associative subalgebras, $G_2$-invariant codes, dynamical decoupling of associator terms, and a seven-factor algebraic decomposition for gate synthesis. The results delineate the feasible quaternionic regime from the constrained octonionic landscape and point to applications in symmetry-protected architectures, algebra-aware simulation, and hypercomplex learning. Full article

(This article belongs to the Topic Topological, Quantum, and Molecular Information Approaches to Computation and Intelligence)

►▼ Show Figures

Figure 1

19 pages, 398 KB  

Open AccessArticle

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

Viewed by 827

Abstract

By imposing finite order constraints on Fibonacci anyon braid relations, we construct the finite quotient $G={\mathbb{Z}}_5⋊2I$, 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 $G={\mathbb{Z}}_5⋊2I$, where $2I$ is the binary icosahedral group. The Gröbner basis decomposition of its $SL(2,\mathbb{C})$ character variety yields elliptic curves whose L-function derivatives $L^{\prime }(E,1)$ remarkably match fundamental biological structural ratios. Specifically, we demonstrate that the Birch–Swinnerton-Dyer conjecture’s central quantity: the derivative $L^{\prime }(E,1)$ of the L-function at 1 encodes critical cellular geometries: the crystalline B-DNA pitch-to-diameter ratio ($L^{\prime }(E,1)=1.730$ matching $34\AA /20\AA =1.70$), the B-DNA pitch to major groove width ($L^{\prime }=1.58$) and, additionally, the fundamental cytoskeletal scaling relationship where $L^{\prime }(E,1)=3.570\approx 25/7$, precisely matching the microtubule-to-actin diameter ratio. This pattern extends across the hierarchy ${\mathbb{Z}}_5⋊2P$ with $2P\in \{2O,2T,2I\}$ (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)

Show export options expand_more Show export options expand_less

Select all

Export citation of selected articles as:

Plain Text BibTeX BibTeX (without abstracts) Endnote Endnote (without abstracts) Tab-delimited RIS

 

Error

Oops... you haven't selected anything for export.

Ok

clear

Displaying articles 1-2