Numerical simulation of non-Abelian anyons

By braiding non-Abelian anyons it is possible to realize fault-tolerant quantum algorithms through the computation of Jones polynomials. So far, this has been an experimentally formidable task. In this Letter, a photonic quantum system employing two-photon correlations and nondissipative imaginary-time evolution is utilized to simulate two inequivalent braiding operations of Majorana zero modes. The resulting amplitudes are shown to be mathematically equivalent to Jones polynomials. The high fidelity of our optical platform allows us to distinguish between a wide range of links, such as Hopf links, Solomon links, Trefoil knots, Figure Eight knots and Borromean rings, through determining their corresponding Jones polynomials. Our photonic quantum simulator represents a significant step towards executing fault-tolerant quantum algorithms based on topological quantum encoding and manipulation. Published by the American Physical Society 2024

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What ChatGPT Has to Say About Its Topological Structure: The Anyon Hypothesis

Planat,

Amaral

2024

MAKE

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Large language models (LLMs) achieve remarkable predictive capabilities but remain opaque in their internal reasoning, creating a pressing need for more interpretable artificial intelligence. Here, we propose bridging this explanatory gap by drawing on concepts from topological quantum computing (TQC), specifically the anyonic frameworks arising from SU(2)k theories. Anyons interpolate between fermions and bosons, offering a mathematical language that may illuminate the latent structure and decision-making processes within LLMs. By examining how these topological constructs relate to token interactions and contextual dependencies in neural architectures, we aim to provide a fresh perspective on how meaning and coherence emerge. After eliciting insights from ChatGPT and exploring low-level cases of SU(2)k models, we argue that the machinery of modular tensor categories and topological phases could inform more transparent, stable, and robust AI systems. This interdisciplinary approach suggests that quantum-theoretic principles may underpin a novel understanding of explainable AI.

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Numerical simulation of non-Abelian anyons

Cited by 3 publications

References 77 publications

Characterizing the entanglement of anyonic systems using the anyonic partial transpose

Characterizing the entanglement of anyonic systems using the anyonic partial transpose

Photonic Simulation of Majorana-Based Jones Polynomials

What ChatGPT Has to Say About Its Topological Structure: The Anyon Hypothesis

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