Open Schools Journal for Open Science

Anyon qubits and quantum AI beyond interstellar

Viktoras Giannikopoulos

Published Jan 12, 2026• 0 citations

Abstract

Interstellar probes must operate for decades with long communication delays and limited opportunities for repair. This study explains why anyon qubits—topological qubits built from non‑Abelian anyons—are promising for deep‑space autonomy. We describe how braiding encodes information non‑locally, providing intrinsic robustness against local noise, and how this can support quantum artificial intelligence (AI) for onboard decision‑making. We also discuss why deep space may help: low vibration, high vacuum, and strong passive cooling can reduce decoherence channels. We conclude that anyon qubits combined with quantum AI provide a credible route to secure, autonomous communication beyond the Solar System.

DOI: 10.12681/osj.44022

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Open Schools Journal for Open Science

Anyon qubits and quantum AI beyond interstellar

Viktoras Giannikopoulos

Published Jan 12, 2026• 0 citations

Publisher

Abstract

DOI: 10.12681/osj.44022

Related papers

Topological Quantum Computing with Non-Abelian Anyons and Braid Group Operations — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Topological quantum computing uses non-Abelian anyons (Majorana zero modes) to encode qubits in braiding operations, immune to local decoherence. | MATH: Braid group $B_n$ generators $\sigma_i$ satisfy $\sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1}$ ; anyon fusion rules: $\sigma \times \sigma = 1 + \psi$ (Ising model); Majorana operators $\gamma_i$ with $\{\gamma_i, \gamma_j\} = 2\delta_{ij}$ ; topological qubit encoded in parity $i\gamma_1\gamma_2 = \pm 1$ . | CONNECTION: Braid group is related to the Fibonacci sequence via the Burau representation; the golden ratio $\phi = 1.618$ appears in the quantum dimension of Fibonacci anyons: $d_\tau = \phi$ . The Ising anyon quantum dimension is $\sqrt{2}$ , linking to $\sqrt{2} \approx 1.414$ , close to 1.4142 (no direct golden ratio). Crystallographic symmetry: Anyon braiding corresponds to the mapping class group of a punctured surface, related to root systems of Lie alge Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Topological quantum computing uses non-Abelian anyons (Majorana zero modes) to encode qubits in braiding operations, immune to local decoherence. | MATH: Braid group $ B_n $ generators $ \sigma_i $ satisfy $ \sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1} $; anyon fusion rules: $ \sigma \times \sigma = 1 + \psi $ (Ising model); Majorana operators $ \gamma_i $ with $ \{\gamma_i, \gamma_j\} = 2\delta_{ij} $; topological qubit encoded in parity $ i\gamma_1\gamma_2 = \pm 1 $. | CONNECTION: Braid group is related to the Fibonacci sequence via the Burau representation; the golden ratio $ \phi = 1.618 $ appears in the quantum dimension of Fibonacci anyons: $ d_\tau = \phi $. The Ising anyon quantum dimension is $ \sqrt{2} $, linking to $ \sqrt{2} \approx 1.414 $, close to 1.4142 (no direct golden ratio). Crystallographic symmetry: Anyon braiding corresponds to the mapping class group of a punctured surface, related to root systems of Lie alge Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Topological Qubits via Non-Abelian Anyons: Braiding for Error-Resistant Quantum Computing — E8 Intelligence Research

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基于拓扑量子计算的容错编码设计

Jincheng Zhang

This paper explores the design of a fault-tolerant encoding scheme specifically tailored for topological quantum computing. The central premise is to leverage the inherent robustness of topological protection against decoherence, a primary challenge in realizing practical quantum computers. We propose a scheme utilizing non-Abelian anyons, exotic quasiparticles found in topological superconductors, to construct a robust quantum code. The core concept involves encoding quantum information within the braiding operations of these anyons, where the resulting topological transformations inherently protect against local errors. The scheme's efficacy relies on the topological protection mechanism, effectively mitigating errors arising from environmental noise and imperfections in qubit control. This work provides a theoretical foundation for utilizing topological quantum computing to achieve high-fidelity quantum computation. The key mathematical elements explored include qubit states, braiding operations, and the mathematical description of the topological protection effect.This paper explores the design of a fault-tolerant encoding scheme specifically tailored for topological quantum computing. The central premise is to leverage the inherent robustness of topological protection against decoherence, a primary challenge in realizing practical quantum computers. We propose a scheme utilizing non-Abelian anyons, exotic quasiparticles found in topological superconductors, to construct a robust quantum code. The core concept involves encoding quantum information within the braiding operations of these anyons, where the resulting topological transformations inherently protect against local errors. The scheme's efficacy relies on the topological protection mechanism, effectively mitigating errors arising from environmental noise and imperfections in qubit control. This work provides a theoretical foundation for utilizing topological quantum computing to achieve high-fidelity quantum computation. The key mathematical elements explored include qubit states, braiding operations, and the mathematical description of the topological protection effect.

Sep 7, 20260 citations

Topological Quantum Computing with Majorana Zero Modes and Beyond

Christina Knapp

Topological quantum computing seeks to store and manipulate information in a protected manner using topological phases of matter. Information encoded in the degenerate state space of pairs of non-Abelian anyons or defects is robust to local perturbations, reducing its susceptiblity to environmental errors and potentially providing a scalable approach to quantum computing. However, topological quantum computing faces significant challenges, not least of which is identifying an experimentally accessible platform supporting non-Abelian topological physics. In this thesis, we critically analyze topological quantum computing with Majorana zero modes, non-Abelian defects of a topological superconductor. We identify intrinsic error sources for Majorana-based systems and propose quantum computing architectures that minimize their effects. Additionally, we consider a new approach for realizing and detecting non-Abelian topological defects in fractional Chern insulators. 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This momentum difference can be used to selectively contact the different edge states, thereby allowing detection of topological defects in the bulk with a standard four terminal measurement. Our proposal could be implemented in graphene subject to an artificially patterned lattice.Topological quantum computing seeks to store and manipulate information in a protected manner using topological phases of matter. Information encoded in the degenerate state space of pairs of non-Abelian anyons or defects is robust to local perturbations, reducing its susceptiblity to environmental errors and potentially providing a scalable approach to quantum computing. However, topological quantum computing faces significant challenges, not least of which is identifying an experimentally accessible platform supporting non-Abelian topological physics. In this thesis, we critically analyze topological quantum computing with Majorana zero modes, non-Abelian defects of a topological superconductor. We identify intrinsic error sources for Majorana-based systems and propose quantum computing architectures that minimize their effects. Additionally, we consider a new approach for realizing and detecting non-Abelian topological defects in fractional Chern insulators. Topological quantum computing is predicated on the idea that braiding non-Abelian anyons adiabatically can implement quantum gates fault tolerantly. However, any braiding experiment will necessarily depart from the strict adiabatic limit. We begin by analyzing the nature of diabatic errors for anyon braiding, paying particular attention to how such errors scale with braiding time. We find that diabatic errors are unfavorably large and worryingly sensitive to details of the time evolution. We present a measurement-based correction protocol for such errors, and illustrate its application in a particular Majorana-based qubit design. We next propose designs for Majorana-based qubits operated entirely by a measurement-based protocol, thereby avoiding the diabatic errors discussed above. Our designs can be scaled into large two dimensional arrays amenable to long-term quantum computing goals, whose core components are testable in near-term devices. These qubits are robust to quasiparticle poisoning, anticipated to be one of the dominant error sources coupling to Majorana zero modes. We demonstrate that our designs support topologically protected Clifford operations and can be augmented to a universal gate set without requiring additional control parameters.While topological protection greatly suppresses errors, residual coupling to noise limits the lifetimes of our proposed Majorana-based qubits. We analyze the dephasing times for our quasiparticle-poisoning-protected qubits by calculating their charge distribution using a particle number-conserving formalism. We find that fluctuations in the electromagnetic environment couple to an exponentially suppressed topological dipole moment. We estimate dephasing times due to $1/f$ noise, thermal quasiparticle excitations, and phonons for different qubit sizes.The residual errors discussed above will necessarily require error correction for a sufficiently long quantum computation. We develop physically motivated noise models for Majorana-based qubits that can be used to analyze the performance of a quantum error correcting code. We apply this noise model to estimate pseudo-thresholds for a small subsystem code, identifying the relative importance of difference error processes from a fault tolerance perspective. Our results emphasize the necessity of suppressing long-lived quasiparticle excitations that can spread across the code.Finally, we turn our attention to a different platform that could host non-Abelian topological defects: fractional Chern insulators in graphene. We study the edge states of fractional Chern insulators using the field theory of fractional quantum Hall edges supplemented with a symmetry action. We find that lattice symmetries impose a quantized momentum difference for edge electrons in a fractional state of a $C=2$ Chern band. This momentum difference can be used to selectively contact the different edge states, thereby allowing detection of topological defects in the bulk with a standard four terminal measurement. Our proposal could be implemented in graphene subject to an artificially patterned lattice.

Jan 1, 20192 citations

FINDING: Topological quantum computing uses non-Abelian anyons (Majorana zero modes) to encode qubits in braiding operations, immune to local decoherence. | MATH: Braid group

B_n

generators

\sigma_i

satisfy

\sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1}

; anyon fusion rules:

\sigma \times \sigma = 1 + \psi

(Ising model); Majorana operators

\gamma_i

with

\{\gamma_i, \gamma_j\} = 2\delta_{ij}

; topological qubit encoded in parity

i\gamma_1\gamma_2 = \pm 1

. | CONNECTION: Braid group is related to the Fibonacci sequence via the Burau representation; the golden ratio

\phi = 1.618

appears in the quantum dimension of Fibonacci anyons:

d_\tau = \phi

. The Ising anyon quantum dimension is

\sqrt{2}

, linking to

\sqrt{2} \approx 1.414

, close to 1.4142 (no direct golden ratio). Crystallographic symmetry: Anyon braiding corresponds to the mapping class group of a punctured surface, related to root systems of Lie alge Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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.

1/f

noise, thermal quasiparticle excitations, and phonons for different qubit sizes.The residual errors discussed above will necessarily require error correction for a sufficiently long quantum computation. We develop physically motivated noise models for Majorana-based qubits that can be used to analyze the performance of a quantum error correcting code. We apply this noise model to estimate pseudo-thresholds for a small subsystem code, identifying the relative importance of difference error processes from a fault tolerance perspective. Our results emphasize the necessity of suppressing long-lived quasiparticle excitations that can spread across the code.Finally, we turn our attention to a different platform that could host non-Abelian topological defects: fractional Chern insulators in graphene. We study the edge states of fractional Chern insulators using the field theory of fractional quantum Hall edges supplemented with a symmetry action. We find that lattice symmetries impose a quantized momentum difference for edge electrons in a fractional state of a

C=2

Chern band. This momentum difference can be used to selectively contact the different edge states, thereby allowing detection of topological defects in the bulk with a standard four terminal measurement. Our proposal could be implemented in graphene subject to an artificially patterned lattice.