Topological Qubits via Non-Abelian Anyons: Majorana Braiding and Microsoft's Majorana 1 — E8 Intelligence Research

Q: What does this research mean for the field?

Topological quantum computing achieves fault-tolerant braiding operations through non-Abelian anyons (Majorana zero modes), whose algebraic structure is governed by braid group relations and the Yang-Baxter equation. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22075665

August 24, 2026Open Access

Topological Qubits via Non-Abelian Anyons: Majorana Braiding and Microsoft's Majorana 1 — E8 Intelligence Research

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Key Points

To analyze the mathematical framework of non-Abelian anyon braiding operations and evaluate their application to fault-tolerant topological qubits in emerging quantum hardware.
Evaluated algebraic representations of the braid group governed by the Yang–Baxter equation.
Modeled Majorana operator anticommutation relations and parity-encoded qubit state transformations.
Calculated unitary matrices, fusion rules, and quantum dimensions for Ising and Fibonacci anyon models.
Demonstrated that non-Abelian anyon exchange produces unitary braiding matrices satisfying Yang–Baxter relations linked to two-dimensional crystallographic root systems.
Derived the golden ratio quantum dimension for Fibonacci anyons from the fusion rule yielding the characteristic dimension polynomial.
Characterized the algebraic parity state encoding underlying fault-tolerant operations in topological qubit hardware architectures.

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Implication

Theoretical analysis demonstrates fault-tolerant quantum computing via non-Abelian anyon braiding in Majorana systems, indicating pathways toward robust hardware like Microsoft's Majorana 1.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a8e9b92451774b83f3b459b https://doi.org/10.5281/zenodo.22075665

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Topological Qubits via Non-Abelian Anyons: Majorana Braiding and Microsoft's Majorana 1 — E8 Intelligence Research

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Topological Qubits via Non-Abelian Anyons: Majorana Braiding and Microsoft's Majorana 1 — E8 Intelligence Research

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