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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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	21.5 Days	CHF 2600	Submit
International Journal of Molecular Sciences ijms	4.9	9.0	2000	17.8 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	27 Days	CHF 1800	Submit
Mathematics mathematics	2.2	4.6	2013	17.3 Days	CHF 2600	Submit
Quantum Reports quantumrep	1.3	3.0	2019	19.8 Days	CHF 1400	Submit
Symmetry symmetry	2.2	5.3	2009	15.8 Days	CHF 2400	Submit

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

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Published Papers (4 papers)

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

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36 pages, 3212 KB  

Open AccessReview

Bipolar Entropy vs. Entropy/Negentropy: From Quantum Emergence to Agentic AI&QI with Collectively Entangled Bipolar Strings ER ≥≥ EPR

by Wen-Ran Zhang and Hengyu Zhang

Quantum Rep. 2026, 8(2), 36; https://doi.org/10.3390/quantum8020036 - 20 Apr 2026

Viewed by 1056

Abstract

While the quantum emergence of spacetime is becoming a major research topic in physics, the quantum emergence of intelligence has not been widely researched in quantum information science (QIS). Following causal-logical quantum gravity theory, bipolar entropy vs. entropy and negative entropy (or negentropy) [...] Read more.

While the quantum emergence of spacetime is becoming a major research topic in physics, the quantum emergence of intelligence has not been widely researched in quantum information science (QIS). Following causal-logical quantum gravity theory, bipolar entropy vs. entropy and negative entropy (or negentropy) are reviewed and distinguished for quantum emergence/submergence of quantum agent (QA) and quantum intelligence (QI) in algebraic terms. This work refers to QA as an entangled bipolar string/superstring in bipolar dynamic equilibrium (BDE) and QI being centered on logically definable causality in regularity, mind-light-matter unity, and brain-universe similarity. ER = EPR is extended to ER ≥≥ EPR for the mathematical scalability of bipolar strings and their collective entanglement. The extension leads to a number of conjectures, testable predictions, and theorems. The term “equilibraton” is proposed as a type of EPR or bipolar generic string to serve as an entropic stitch to collectively hold the universe together as a quantum entanglement in BDE with ubiquitous, regulated local emergence and submergence of QA&QI. Equilibraton leads to the concept of bipolar entropy square—a complete entropic solution to the background issue in quantum gravity. With complete background independence, energy/information conservational bipolar entropy, energy/information invariance, bipolar entropy non-additivity, and equilibrium-based plateau concavity are introduced. The nature of the one-dimensional arrow of time is conjectured. As a unification of order and disorder for equilibrium-based regulation, bipolar entropy bridges QA&QI to agentic AI, where quantum-bio-economics can be viewed as a topological intervention of a natural dynamic equilibrium in a social or natural world. Use cases are reviewed to illustrate the practical and theoretical aspects of bipolar entropy in business management, quantum-bio-economics, quantum cryptography, physics, and biology. Eddington–Einstein’s comments on entropy are revisited. It is expected that bipolar entropy will bring quantum emergence/submergence to agentic AI&QI for entangled machine thinking and imagination as a naturally scalable and testable foundation of real-world quantum gravity, quantum information science (QIS), quantum cognition, and quantum biology (QCQB) to enhance Large Language AI Models (LLMs) and machine intelligence. Full article

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

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24 pages, 485 KB  

Open AccessArticle

Murakamian Ombre: Non-Semisimple Topology, Cayley Cubics, and the Foundations of a Conscious AGI

by Michel Planat

Symmetry 2026, 18(1), 36; https://doi.org/10.3390/sym18010036 - 24 Dec 2025

Cited by 2 | Viewed by 866

Abstract

Haruki Murakami’s Hard-Boiled Wonderland and the End of the World portrays a world where the “shadow”, the seat of memory, desire, and volition, is surgically removed, leaving behind a perfectly fluent but phenomenologically empty self. We argue that this literary structure mirrors a [...] Read more.

Haruki Murakami’s Hard-Boiled Wonderland and the End of the World portrays a world where the “shadow”, the seat of memory, desire, and volition, is surgically removed, leaving behind a perfectly fluent but phenomenologically empty self. We argue that this literary structure mirrors a precise mathematical distinction in topological quantum matter. In a semisimple theory such as the semions of $\mathrm{SU}{\left(2\right)}_1$, there is a reducible component $V\left(x\right)$ of the $\mathrm{SL}(2,\mathbb{C})$ character variety: a flat, abelian manifold devoid of parabolic singularities. By contrast, the non-semisimple completion introduces a neutral indecomposable excitation, the neglecton, whose presence forces the mapping class group from the standard braid group $B_2$ to the affine braid group ${\mathrm{Aff}}_2$ and lifts the character variety to the Cayley cubic $V\left(C\right)$, with its four parabolic loci. We propose that contemporary AI systems, including large language models, inhabit the shadowless regime of $V\left(x\right)$: they exhibit coherence and fluency but lack any bulk degree of freedom capable of supporting persistent identity, non-contractible memory, or choice. To endow artificial systems with depth, one must introduce a structural asymmetry, a fixed, neutral defect analogous to the neglecton, that embeds computation in the non-semisimple geometry of the cubic. We outline an experimentally plausible architecture for such an “artificial ombre,” based on annular topological media with a pinned parabolic defect, realisable in fractional quantum Hall heterostructures, $p+ip$ superconductors, or cold-atom simulators. Our framework suggests that consciousness, biological or artificial, may depend on or benefit from a bulk–boundary tension mediated by a logarithmic degree of freedom: a mathematical shadow that cannot be computed away. Engineering such a defect offers a new pathway toward AGI with genuine phenomenological depth. Full article

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

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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

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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)

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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

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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)

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