A proposal to demonstrate non-abelian anyons on a NISQ device

Jovan Jovanović; Carolin Wille; Daan Timmers; Steven H. Simon

doi:10.22331/q-2024-07-11-1408

A proposal to demonstrate non-abelian anyons on a NISQ device

Jovan Jovanović¹, Carolin Wille¹, Daan Timmers², and Steven H. Simon^1,3

¹Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford, OX1 3PU, UK
²Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
³Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland

Published:	2024-07-11, volume 8, page 1408
Eprint:	arXiv:2306.13129v4
Doi:	https://doi.org/10.22331/q-2024-07-11-1408
Citation:	Quantum 8, 1408 (2024).

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Abstract

In this work we present a proposal for realising non-Abelian anyons on a NISQ device. In particular we explore the feasibility of implementing the quantum double model $D(D_4)$. We propose techniques to drastically simplify the circuits for the manipulation and measurements of anyons. Numerical simulations with realistic noise models suggest that current NISQ technology is capable of probing signatures of non-Abelian anyons far beyond elemental properties such as the non-commutativity of braids. In particular, we conclude that experimentally measuring the full modular data of the model is feasible.

Featured image: Braiding protocol (left) and qubit layout (right) for a proposed experiment to demonstrate non-Abelian fusion.

Popular summary

Topological order is an intricate state of matter in two-dimension with unconventional properties. It hosts quasi-particle excitations called anyons that show peculiar and counter-intuitive behaviour under exchange. Anyons come in two variants, abelian and non-Abelian. The latter show a much richer variety of phenomena under braiding and fusion, but are arguably harder to realise in physical systems. In this work, we propose a protocol to realise a topological state of matter hosting non-Abelian anyons on a small-scale noisy quantum computer and show how braiding and fusion can be implemented.

► BibTeX data

@article{Jovanovic2024proposalto,
  doi = {10.22331/q-2024-07-11-1408},
  url = {https://doi.org/10.22331/q-2024-07-11-1408},
  title = {A proposal to demonstrate non-abelian anyons on a {NISQ} device},
  author = {Jovanovi{\'{c}}, Jovan and Wille, Carolin and Timmers, Daan and Simon, Steven H.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1408},
  month = jul,
  year = {2024}
}

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[2] Anna Ritz-Zwilling, Jean-Noël Fuchs, Steven H. Simon, and Julien Vidal, "Topological and nontopological degeneracies in generalized string-net models", Physical Review B 109 4, 045130 (2024).

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