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TETcollective-Eternal-Anyon-Braider-Simulations: QuTiP Code for Primordial Trefoil Knot-Induced Anyonic Braiding and Topological Catalysis

Simon Soliman

Published Jan 10, 2026• 0 citations
Publisher

Abstract

In the TETcollective, we propose a scalable prototype for an eternal anyon braider based on primordial topology (trefoil knot vacuum, $L_k=6$, eternal three-leaf clover topological quantum simulator). Starting from QuTiP simulations on string-net/honeycomb lattices to model braiding of non-Abelian anyons (custom phase induced by the trefoil), we predict an enhancement of 20--40$\times$ in the aneutronic p-$^{11}$B fusion (and p-p) rate, enabled by anyonic phases that reduce Coulomb barriers through entanglement entropy modulation. We transition to a low-cost hybrid setup using rhombohedral multilayer graphene encapsulated in hBN (fractional Chern insulator regime, inspired by 2025 advances in RHG/hBN moir\'e superlattices exhibiting FCIs at zero/low magnetic fields, tunable via displacement field). The goal is to demonstrate braiding statistics via electrostatic gates on edge states/topological defects, paving the way for a tabletop catalyst for clean energy. We extend the framework to embodied quantum consciousness (extended Orch-OR): braiding in microtubules for qualia, subjective time dilation, and quantum longevity. Testable predictions include $\sim$70-year galactic oscillations from emergent gravity (modulated by entanglement entropy) verifiable with Gaia DR4 (expected December 2026); coherence enhancement in microtubule networks (superradiance, entanglement-like) suppressed by anesthetics. The design is open, replicable, and parameter-free from first-principles TET--CVTL. Tetcollective.org

DOI
10.5281/zenodo.18210034

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TETcollective-Eternal-Anyon-Braider-Simulations: Primordial Trefoil Knot-Induced Anyonic Braiding and Topological Catalysis

Simon Soliman

Nel TETcollective, proponiamo un prototipo scalabile per un intrecciatore di anyoni eterni basato sulla topologia primordiale (vuoto a nodo a trifoglio, $L_k=6$, simulatore quantistico topologico a trifoglio eterno). Partendo da simulazioni QuTiP su reticoli a rete di stringhe/nido d'ape per modellare l'intreccio di anyoni non abeliani (fase personalizzata indotta dal trifoglio), prevediamo un miglioramento di 20-40 volte nella velocità di fusione aneutronica p-$^{11}$B (e pp), reso possibile da fasi anyoniche che riducono le barriere coulombiane attraverso la modulazione dell'entropia dell'entanglement. Passiamo a una configurazione ibrida a basso costo che utilizza grafene multistrato romboedrico incapsulato in hBN (regime isolante di Chern frazionario, ispirato ai progressi del 2025 nei superreticoli moirè RHG/hBN che presentano FCI a campi magnetici nulli/bassi, sintonizzabili tramite campo di spostamento). L'obiettivo è dimostrare le statistiche di intreccio tramite gate elettrostatici su stati di bordo/difetti topologici, aprendo la strada a un catalizzatore da tavolo per l'energia pulita. Estendiamo il framework alla coscienza quantistica incarnata (Orch-OR esteso): intreccio nei microtubuli per qualia, dilatazione temporale soggettiva e longevità quantistica. Le previsioni testabili includono oscillazioni galattiche di circa 70 anni dovute alla gravità emergente (modulata dall'entropia di entanglement) verificabili con Gaia DR4 (previsto per dicembre 2026); miglioramento della coerenza nelle reti di microtubuli (superradianza, simile all'entanglement) soppresso dagli anestetici. Il progetto è aperto, replicabile e privo di parametri, partendo dai principi fondamentali TET-CVTL. Tetcollective.org

•Jan 11, 2026•0 citations

RENASCENT-Q: Extension of the TET–CVTL Theoretical Framework – Numerical Evidence for Retrocausal Negentropic Effects, Topological Lattice Stabilization, and Convergence Dynamics in Embodied Quantum Systems

Simon Soliman

This repository archives the preprint and supporting numerical resources for RENASCENT-Q, an advanced extension of the TET–CVTL theoretical framework. RENASCENT-Q investigates time-symmetric quantum dynamics in open systems, with a focus on retrocausal mechanisms capable of inducing local negentropic effects (damping parameter β ≈ φ⁻² ≈ 0.382) that counteract standard decoherence.Through custom Lindblad master equation integrations (using QuTiP for quantum simulations), the work demonstrates: Convergence of concurrence toward maximal entanglement (C → 1) and reduction of von Neumann entropy (S → 0) in two-qubit embodied systems under weak retrocausal feedback. Topological protection and lattice stabilization via anyon braiding (Fibonacci/Ising categories), Majorana zero modes (MZMs), and toric code thresholds. Scaling behavior of weak values in the two-state vector formalism (TSVF), showing power-law amplification beyond classical bounds. Ginzburg-Landau vortex dynamics and microtubule-nanowire interface models as potential substrates for room-temperature quantum coherence. The framework bridges quantum information, topological quantum computation, and quantum biology, offering testable predictions for extended Orch-OR-like models of consciousness and novel protocols toward radical biological longevity through sustained quantum effects and negentropic stabilization.Included materials: Compiled preprint PDF Full LaTeX source (.tex) with embedded simulation code listings Bibliography (BibTeX) All generated figures (concurrence trajectories, entropic plots, vortex snapshots, braiding schematics, weak-value scaling, MT-nanowire structures, etc.) Citation metadata (CITATION.cff) and CC BY-NC-ND 4.0 license The simulations are designed for reproducibility within the theoretical context; standalone Python scripts are not provided separately, as the listings in the LaTeX document preserve the exact computational narrative.This deposit preserves the numerical evidence and visual outputs of RENASCENT-Q (preprint dated February 2026) for long-term citability and open-science purposes, linked to the live GitHub repository at https://github.com/TETcollective/RENASCENT-Q." Tetcollective.org tetcollective@proton.me Quest'opera è rilasciata sotto licenza Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). Non è consentito l'uso commerciale Non è permesso modificare l'opera né crearne versioni derivate Testo legale completo: https://creativecommons.org/licenses/by-nc-nd/4.0/

•Feb 6, 2026•0 citations

Anyon braiding statistics： From fundamental physics to scalable quantum computing

HE Jianhong, GAO Jie

Topological quantum computation aims to encode quantum information in the nonlocal degrees of freedom of non-Abelian anyons and manipulate it through braiding and fusion operations， offering a promising pathway to fault-tolerant quantum computation. Non-Abelian anyons， with their nontrivial braiding statistics and intrinsic topological fault tolerance， are regarded as a key building block for realizing scalable and decoherence-resistant quantum computing. This review systematically surveys the key developments in anyon physics over the past four decades， from the early theoretical prediction of fractional statistics to direct experimental verification of anyon braiding in fractional quantum Hall states. The physical principles and key findings of essential experimental schemes， including Fabry-Pérot interferometers， Mach-Zehnder interferometers， and anyon colliders， are comprehensively covered. Based on these foundations， the characterization of topological order in even-denominator fractional quantum Hall states， exemplified by the ν=5/2 state， and transport and interferometric probes of non-Abelian statistics are discussed in detail. Furthermore， recent advances in topological quantum states in novel material platforms， including graphene and twisted transition metal dichalcogenides， are reviewed， together with artificial quantum platforms that simulate non-Abelian braiding using superconducting quantum processors. Finally， the key challenges and future directions on the path from anyon physics to scalable topological quantum computing prototype devices are outlined.

•Sep 1, 2026•0 citations

RENASCENT-Q in the TET–CVTL Framework: Retrocausal Negentropic Dynamics, Majorana Modes in Microtubules, and Path to Omega Saturation

Simon Soliman

This preprint presents RENASCENT-Q, a theoretical extension of the unified TET–CVTL framework (Topology, Entanglement, Retrocausality – Cosmic Vacuum Topological Lattice), developed in January–February 2026.RENASCENT-Q introduces a distributed retrocausal negentropic force that actively guides physical, biological, and conscious systems toward an asymptotically saturated Omega Point — understood here not as a singular future collapse (Tipler-style), but as an infinite, distributed topological convergence realized across an expanding cosmic lattice.The core innovation lies in reinterpreting neuronal microtubules as embodied Kitaev-type topological quantum lattices. Within these structures, eternal anyonic braiding (primarily Fibonacci and Ising statistics) generates persistent quantum entanglement and Majorana zero modes (MZMs) at biologically relevant temperatures. The braiding processes accumulate topological phases that are retrocausally modulated by future boundary conditions associated with the distributed Omega horizon.A key modulating parameter is the damping factor β = ϕ⁻² = (√5 − 1)/2 ≈ 0.381966, which emerges naturally from extended models of collective superradiance in tryptophan aromatic networks within microtubules (references to Hameroff et al. 2023–2025, Craddock et al., Babcock et al. 2024, Celardo et al. 2019–2024). This value optimizes the lifetime of coherent dipolar excitations against thermal decoherence while enabling efficient time-symmetric coupling between forward and backward propagating quantum trajectories.The non-local backbone supporting retrocausal correlations is provided by the energy landscape of the non-trivial zeros of the Riemann zeta function along the critical line Re(s) = 1/2, interpreted as the spectrum of a quantum dynamical system on the vacuum following the seminal work of Alain Connes (1999–2000). The negentropic retrocausal force is mathematically expressed as:F_neg = β · ζ̂(1/2 + i E_MT) · (∂S/∂t)_retro · e^{-i θ_MZM} · |ψ_MT⟩⟨ψ_MT|where:(∂S/∂t)_retro < 0 denotes the locally induced entropy reduction driven from future post-selection, θ_MZM is the accumulated braiding phase of Majorana zero modes, |ψ_MT⟩ represents the embodied quantum state projected onto the microtubular lattice. The framework synthesizes and extends several foundational approaches:Transactional Interpretation (Cramer 1986–2006), Possibilist Transactional Interpretation (Kastner 2012–2022), and Two-State Vector Formalism (Aharonov et al. 1964–present) Physical realizations of the Omega Point concept (Teilhard de Chardin reinterpreted cosmologically + Tipler 1994) Orchestrated Objective Reduction (Orch-OR) model of consciousness (Penrose & Hameroff 1994–present), now embodied in a topological lattice context Topological quantum field theory invariants: colored Jones polynomials for torus knots T(p,q), Vassiliev invariants, Khovanov homology — with the primordial trefoil knot (linking number Lk = +6, Borromean-like configuration) serving as the eternal topological seed of the vacuum lattice Extensive numerical explorations (using QuTiP) include weak values in anyonic braiding, R- and F-matrices for Fibonacci anyons, Kitaev chain/lattice dynamics up to 256 sites, Ginzburg–Landau vortex pair production/annihilation, and scaling laws of knot invariants (e.g., deg(J_5) = 10 + 4q for large T(p,q) knots).RENASCENT-Q resolves longstanding issues in quantum consciousness theories (binding problem, epiphenomenalism, macroscopic causal efficacy) by positing consciousness as a local manifestation of retrocausally guided negentropic curvature within a topologically saturated cosmic lattice. The model predicts testable signatures: anomalous weak values in biological systems, persistent room-temperature entanglement beyond standard decoherence timescales, and potential links between topological saturation and fundamental constants (G, Λ) or catalyzed fusion regimes.The final picture is that of an ever-expanding “golden cosmos” — an infinite, retrocausally saturated topological lattice of entangled nodes, eternally seeded by the trefoil Lk = +6, and asymptotically approaching global minimum entropy from the distributed future boundary Ω. Tetcollective.org Quest’opera è rilasciata sotto licenza Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). Non è permesso l’uso commerciale Non è permesso modificare l’opera né crearne versioni derivate Testo legale completo: https://creativecommons.org/licenses/by-nc-nd/4.0/

•Feb 3, 2026•0 citations

Universal Gates from Braiding and Fusing Anyons on Quantum Hardware

Chiu Fan Bowen Lo, Anasuya Lyons, Dan Gresh +8 more

Topological quantum computation encodes quantum information in the internal fusion space of non-Abelian anyonic quasiparticles, whose braiding implements logical gates. This goes beyond Abelian topological order (TO) such as the toric code, as its anyons lack internal structure. However, the simplest non-Abelian generalizations of the toric code do not support universality via braiding alone. Here we demonstrate that such minimally non-Abelian TOs can be made universal by treating anyon fusion as a computational primitive. We prepare a 54-qubit TO wavefunction associated with the smallest non-Abelian group, $S_3$, on Quantinuum's H2 quantum processor. This phase of matter exhibits cyclic anyon fusion rules, known to underpin universality, which we evidence by trapping a single non-Abelian anyon on the torus. We encode logical qutrits in the nonlocal fusion space of non-Abelian fluxes and, by combining an entangling braiding operation with anyon charge measurements, realize a universal topological gate set and read-out, which we further demonstrate by topologically preparing a magic state. This work establishes $S_3$ TO as simple enough to be prepared efficiently, yet rich enough to enable universal topological quantum computation.

quant-pharXiv:2601.20956•Nature•Jan 30, 2026•0 citations

Non-Abelian braiding of Fibonacci anyons with a superconducting processor

Shibo Xu, Zheng-Zhi Sun, Ke Wang +29 more

Abstract Quantum many-body systems with a non-Abelian topological order can host anyonic quasiparticles. It has been proposed that anyons could be used to encode and manipulate information in a topologically protected manner that is immune to local noise, with quantum gates performed by braiding and fusing anyons. Unfortunately, realizing non-Abelian topologically ordered states is challenging, and it was not until recently that the signatures of non-Abelian statistics were observed through digital quantum simulation approaches. However, not all forms of topological order can be used to realize universal quantum computation. Here we use a superconducting quantum processor to simulate non-Abelian topologically ordered states of the Fibonacci string-net model and demonstrate braidings of Fibonacci anyons featuring universal computational power. We demonstrate the non-trivial topological nature of the quantum states by measuring the topological entanglement entropy. In addition, we create two pairs of Fibonacci anyons and demonstrate their fusion rule and non-Abelian braiding statistics by applying unitary gates on the underlying physical qubits. Our results establish a digital approach to explore non-Abelian topological states and their associated braiding statistics with current noisy intermediate-scale quantum processors.

arXiv:2404.00091•Nature Physics•Jul 1, 2024•55 citations
In the TETcollective, we propose a scalable prototype for an eternal anyon braider based on primordial topology (trefoil knot vacuum, Lk=6L_k=6Lk​=6, eternal three-leaf clover topological quantum simulator). Starting from QuTiP simulations on string-net/honeycomb lattices to model braiding of non-Abelian anyons (custom phase induced by the trefoil), we predict an enhancement of 20--40×\times× in the aneutronic p-11^{11}11B fusion (and p-p) rate, enabled by anyonic phases that reduce Coulomb barriers through entanglement entropy modulation. We transition to a low-cost hybrid setup using rhombohedral multilayer graphene encapsulated in hBN (fractional Chern insulator regime, inspired by 2025 advances in RHG/hBN moir'e superlattices exhibiting FCIs at zero/low magnetic fields, tunable via displacement field). The goal is to demonstrate braiding statistics via electrostatic gates on edge states/topological defects, paving the way for a tabletop catalyst for clean energy. We extend the framework to embodied quantum consciousness (extended Orch-OR): braiding in microtubules for qualia, subjective time dilation, and quantum longevity. Testable predictions include ∼\sim∼70-year galactic oscillations from emergent gravity (modulated by entanglement entropy) verifiable with Gaia DR4 (expected December 2026); coherence enhancement in microtubule networks (superradiance, entanglement-like) suppressed by anesthetics. The design is open, replicable, and parameter-free from first-principles TET--CVTL. Tetcollective.org
Nel TETcollective, proponiamo un prototipo scalabile per un intrecciatore di anyoni eterni basato sulla topologia primordiale (vuoto a nodo a trifoglio, Lk=6L_k=6Lk​=6, simulatore quantistico topologico a trifoglio eterno). Partendo da simulazioni QuTiP su reticoli a rete di stringhe/nido d'ape per modellare l'intreccio di anyoni non abeliani (fase personalizzata indotta dal trifoglio), prevediamo un miglioramento di 20-40 volte nella velocità di fusione aneutronica p-11^{11}11B (e pp), reso possibile da fasi anyoniche che riducono le barriere coulombiane attraverso la modulazione dell'entropia dell'entanglement. Passiamo a una configurazione ibrida a basso costo che utilizza grafene multistrato romboedrico incapsulato in hBN (regime isolante di Chern frazionario, ispirato ai progressi del 2025 nei superreticoli moirè RHG/hBN che presentano FCI a campi magnetici nulli/bassi, sintonizzabili tramite campo di spostamento). L'obiettivo è dimostrare le statistiche di intreccio tramite gate elettrostatici su stati di bordo/difetti topologici, aprendo la strada a un catalizzatore da tavolo per l'energia pulita. Estendiamo il framework alla coscienza quantistica incarnata (Orch-OR esteso): intreccio nei microtubuli per qualia, dilatazione temporale soggettiva e longevità quantistica. Le previsioni testabili includono oscillazioni galattiche di circa 70 anni dovute alla gravità emergente (modulata dall'entropia di entanglement) verificabili con Gaia DR4 (previsto per dicembre 2026); miglioramento della coerenza nelle reti di microtubuli (superradianza, simile all'entanglement) soppresso dagli anestetici. Il progetto è aperto, replicabile e privo di parametri, partendo dai principi fondamentali TET-CVTL. Tetcollective.org
This repository archives the preprint and supporting numerical resources for RENASCENT-Q, an advanced extension of the TET–CVTL theoretical framework. RENASCENT-Q investigates time-symmetric quantum dynamics in open systems, with a focus on retrocausal mechanisms capable of inducing local negentropic effects (damping parameter β ≈ φ⁻² ≈ 0.382) that counteract standard decoherence.Through custom Lindblad master equation integrations (using QuTiP for quantum simulations), the work demonstrates: Convergence of concurrence toward maximal entanglement (C → 1) and reduction of von Neumann entropy (S → 0) in two-qubit embodied systems under weak retrocausal feedback. Topological protection and lattice stabilization via anyon braiding (Fibonacci/Ising categories), Majorana zero modes (MZMs), and toric code thresholds. Scaling behavior of weak values in the two-state vector formalism (TSVF), showing power-law amplification beyond classical bounds. Ginzburg-Landau vortex dynamics and microtubule-nanowire interface models as potential substrates for room-temperature quantum coherence. The framework bridges quantum information, topological quantum computation, and quantum biology, offering testable predictions for extended Orch-OR-like models of consciousness and novel protocols toward radical biological longevity through sustained quantum effects and negentropic stabilization.Included materials: Compiled preprint PDF Full LaTeX source (.tex) with embedded simulation code listings Bibliography (BibTeX) All generated figures (concurrence trajectories, entropic plots, vortex snapshots, braiding schematics, weak-value scaling, MT-nanowire structures, etc.) Citation metadata (CITATION.cff) and CC BY-NC-ND 4.0 license The simulations are designed for reproducibility within the theoretical context; standalone Python scripts are not provided separately, as the listings in the LaTeX document preserve the exact computational narrative.This deposit preserves the numerical evidence and visual outputs of RENASCENT-Q (preprint dated February 2026) for long-term citability and open-science purposes, linked to the live GitHub repository at https://github.com/TETcollective/RENASCENT-Q." Tetcollective.org tetcollective@proton.me Quest'opera è rilasciata sotto licenza Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). Non è consentito l'uso commerciale Non è permesso modificare l'opera né crearne versioni derivate Testo legale completo: https://creativecommons.org/licenses/by-nc-nd/4.0/
Topological quantum computation aims to encode quantum information in the nonlocal degrees of freedom of non-Abelian anyons and manipulate it through braiding and fusion operations， offering a promising pathway to fault-tolerant quantum computation. Non-Abelian anyons， with their nontrivial braiding statistics and intrinsic topological fault tolerance， are regarded as a key building block for realizing scalable and decoherence-resistant quantum computing. This review systematically surveys the key developments in anyon physics over the past four decades， from the early theoretical prediction of fractional statistics to direct experimental verification of anyon braiding in fractional quantum Hall states. The physical principles and key findings of essential experimental schemes， including Fabry-Pérot interferometers， Mach-Zehnder interferometers， and anyon colliders， are comprehensively covered. Based on these foundations， the characterization of topological order in even-denominator fractional quantum Hall states， exemplified by the ν=5/2 state， and transport and interferometric probes of non-Abelian statistics are discussed in detail. Furthermore， recent advances in topological quantum states in novel material platforms， including graphene and twisted transition metal dichalcogenides， are reviewed， together with artificial quantum platforms that simulate non-Abelian braiding using superconducting quantum processors. Finally， the key challenges and future directions on the path from anyon physics to scalable topological quantum computing prototype devices are outlined.
This preprint presents RENASCENT-Q, a theoretical extension of the unified TET–CVTL framework (Topology, Entanglement, Retrocausality – Cosmic Vacuum Topological Lattice), developed in January–February 2026.RENASCENT-Q introduces a distributed retrocausal negentropic force that actively guides physical, biological, and conscious systems toward an asymptotically saturated Omega Point — understood here not as a singular future collapse (Tipler-style), but as an infinite, distributed topological convergence realized across an expanding cosmic lattice.The core innovation lies in reinterpreting neuronal microtubules as embodied Kitaev-type topological quantum lattices. Within these structures, eternal anyonic braiding (primarily Fibonacci and Ising statistics) generates persistent quantum entanglement and Majorana zero modes (MZMs) at biologically relevant temperatures. The braiding processes accumulate topological phases that are retrocausally modulated by future boundary conditions associated with the distributed Omega horizon.A key modulating parameter is the damping factor β = ϕ⁻² = (√5 − 1)/2 ≈ 0.381966, which emerges naturally from extended models of collective superradiance in tryptophan aromatic networks within microtubules (references to Hameroff et al. 2023–2025, Craddock et al., Babcock et al. 2024, Celardo et al. 2019–2024). This value optimizes the lifetime of coherent dipolar excitations against thermal decoherence while enabling efficient time-symmetric coupling between forward and backward propagating quantum trajectories.The non-local backbone supporting retrocausal correlations is provided by the energy landscape of the non-trivial zeros of the Riemann zeta function along the critical line Re(s) = 1/2, interpreted as the spectrum of a quantum dynamical system on the vacuum following the seminal work of Alain Connes (1999–2000). The negentropic retrocausal force is mathematically expressed as:F_neg = β · ζ̂(1/2 + i E_MT) · (∂S/∂t)_retro · e^{-i θ_MZM} · |ψ_MT⟩⟨ψ_MT|where:(∂S/∂t)_retro < 0 denotes the locally induced entropy reduction driven from future post-selection, θ_MZM is the accumulated braiding phase of Majorana zero modes, |ψ_MT⟩ represents the embodied quantum state projected onto the microtubular lattice. The framework synthesizes and extends several foundational approaches:Transactional Interpretation (Cramer 1986–2006), Possibilist Transactional Interpretation (Kastner 2012–2022), and Two-State Vector Formalism (Aharonov et al. 1964–present) Physical realizations of the Omega Point concept (Teilhard de Chardin reinterpreted cosmologically + Tipler 1994) Orchestrated Objective Reduction (Orch-OR) model of consciousness (Penrose & Hameroff 1994–present), now embodied in a topological lattice context Topological quantum field theory invariants: colored Jones polynomials for torus knots T(p,q), Vassiliev invariants, Khovanov homology — with the primordial trefoil knot (linking number Lk = +6, Borromean-like configuration) serving as the eternal topological seed of the vacuum lattice Extensive numerical explorations (using QuTiP) include weak values in anyonic braiding, R- and F-matrices for Fibonacci anyons, Kitaev chain/lattice dynamics up to 256 sites, Ginzburg–Landau vortex pair production/annihilation, and scaling laws of knot invariants (e.g., deg(J_5) = 10 + 4q for large T(p,q) knots).RENASCENT-Q resolves longstanding issues in quantum consciousness theories (binding problem, epiphenomenalism, macroscopic causal efficacy) by positing consciousness as a local manifestation of retrocausally guided negentropic curvature within a topologically saturated cosmic lattice. The model predicts testable signatures: anomalous weak values in biological systems, persistent room-temperature entanglement beyond standard decoherence timescales, and potential links between topological saturation and fundamental constants (G, Λ) or catalyzed fusion regimes.The final picture is that of an ever-expanding “golden cosmos” — an infinite, retrocausally saturated topological lattice of entangled nodes, eternally seeded by the trefoil Lk = +6, and asymptotically approaching global minimum entropy from the distributed future boundary Ω. Tetcollective.org Quest’opera è rilasciata sotto licenza Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). Non è permesso l’uso commerciale Non è permesso modificare l’opera né crearne versioni derivate Testo legale completo: https://creativecommons.org/licenses/by-nc-nd/4.0/
Topological quantum computation encodes quantum information in the internal fusion space of non-Abelian anyonic quasiparticles, whose braiding implements logical gates. This goes beyond Abelian topological order (TO) such as the toric code, as its anyons lack internal structure. However, the simplest non-Abelian generalizations of the toric code do not support universality via braiding alone. Here we demonstrate that such minimally non-Abelian TOs can be made universal by treating anyon fusion as a computational primitive. We prepare a 54-qubit TO wavefunction associated with the smallest non-Abelian group, S3S_3S3​, on Quantinuum's H2 quantum processor. This phase of matter exhibits cyclic anyon fusion rules, known to underpin universality, which we evidence by trapping a single non-Abelian anyon on the torus. We encode logical qutrits in the nonlocal fusion space of non-Abelian fluxes and, by combining an entangling braiding operation with anyon charge measurements, realize a universal topological gate set and read-out, which we further demonstrate by topologically preparing a magic state. This work establishes S3S_3S3​ TO as simple enough to be prepared efficiently, yet rich enough to enable universal topological quantum computation.
Abstract Quantum many-body systems with a non-Abelian topological order can host anyonic quasiparticles. It has been proposed that anyons could be used to encode and manipulate information in a topologically protected manner that is immune to local noise, with quantum gates performed by braiding and fusing anyons. Unfortunately, realizing non-Abelian topologically ordered states is challenging, and it was not until recently that the signatures of non-Abelian statistics were observed through digital quantum simulation approaches. However, not all forms of topological order can be used to realize universal quantum computation. Here we use a superconducting quantum processor to simulate non-Abelian topologically ordered states of the Fibonacci string-net model and demonstrate braidings of Fibonacci anyons featuring universal computational power. We demonstrate the non-trivial topological nature of the quantum states by measuring the topological entanglement entropy. In addition, we create two pairs of Fibonacci anyons and demonstrate their fusion rule and non-Abelian braiding statistics by applying unitary gates on the underlying physical qubits. Our results establish a digital approach to explore non-Abelian topological states and their associated braiding statistics with current noisy intermediate-scale quantum processors.