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Cited by 5,245Quantum many-body systemsTopological Materials and PhenomenaAdvanced Condensed Matter Physics

Anyons in an exactly solved model and beyond

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Kitaev, Alexei·2006·Annals of Physics
DOI 10.1016/j.aop.2005.10.005
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  • In Kitaev's code, the value of non-trivial loop operators l1, l2 are fixed to +1, that is, measuring them will give +1 outcome.

    “Namely, in Kitaev's code, the value of non-trivial loop operators ℓ1, ℓ2 are fixed to +1, that is, measuring them will give +1 outcome.”

    From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [118]

    In the introductory square-lattice code example (p. 5), the paper defines its vortex-free state as a superposition of all spin configurations with plaquette values +1, not as a state selected by setting non-trivial loop measurements to +1. Section 2.3 (p. 13) defines Wilson loops but does not impose that outcome on them. The cited text therefore does not support the asserted fixed measurement result. (LLM, conf=0.76)

    Checked by a reasoning model — may be wrong.

    Experimental — accuracy not yet measured

  • The stabilizer group S of Kitaev's honeycomb code is generated by 6-qubit Pauli operators on the hexagonal faces and two Pauli operators along two loops around the horizontal and vertical directions on the torus.

    “The stabilizer group S is generated by 6-qubit Pauli operators on the hexagonal faces and two Pauli operators along two loops around the horizontal and vertical directions on the torus”

    From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [118]

    Section 2.2 (p. 13) defines flux operators around hexagonal plaquettes, and Section 2.3 (p. 13) defines spin-based Wilson loop operators. These passages support the face-and-loop description, but they do not say that those operators generate a stabilizer group or specify two horizontal and vertical torus loops as its generators. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

  • In Kitaev's honeycomb code, the gauge group G is generated by two-qubit Pauli measurements on the edges, with edge color determining the Pauli observable, and plaquette colors determine the type of 6-qubit stabilizer on that plaquette.

    “This code has a gauge group G generated by two-qubit Pauli measurements on the edges of the lattice where the edge color determines its corresponding Pauli observable, while the plaquette colors determine the type of 6-qubit stabilizer on that plaquette10.”

    From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [118]

    Section 1, “The model,” defines x-, y-, and z-links and assigns each a corresponding two-qubit Pauli term; Section 2.3 (p. 13) discusses plaquette loop operators. The copy does not describe these edge terms as generators of a code gauge group, or say that plaquette colors determine different types of six-qubit stabilizer. (LLM, conf=0.85)

    Experimental — accuracy not yet measured

  • Kitaev's honeycomb code is a qubit subsystem stabilizer code defined on a hexagonal lattice on the surface of a torus where qubits are placed on the vertices.

    “This is the case with Kitaev's honeycomb code [118], which is a qubit subsystem stabilizer code defined on a hexagonal lattice on the surface of a torus where qubits are placed on the vertices”

    From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [118]

    Section 1, p. 10, describes spin-1/2 degrees of freedom at the vertices of a honeycomb lattice, and the discussion accompanying Fig. 11 considers that lattice on a torus. Our copy does not identify the model as a subsystem stabilizer code, so it does not support that part of the description. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

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References 103 · Cited by 5,245

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Authors
Kitaev, A.
Affiliations
California Institute of Technology (US)
Corresponding author
Kitaev, Alexei
ORCID
Kitaev, Alexei
Venue
Annals of Physics
Publisher
Elsevier BV
Published
2006-01
Volume
321
Issue
1
Pages
2-111
ISSN
0003-4916 (ISSN-L)
DOI
10.1016/j.aop.2005.10.005
OpenAlex
W2141708961
Cited by
5,245
References
103
Citations by year
2026: 266 · 2025: 462 · 2024: 468 · 2023: 494 · 2022: 420 · 2021: 457 · 2020: 441 · 2019: 354 · 2018: 304 · 2017: 285 · 2016: 254 · 2015: 180 · 2014: 169 · 2013: 137 · 2012: 130
FWCI
46.46
Type
journal article
Language
en
Open access
Licence
www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations
  • Annals of Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CaltechAUTHORS (California Institute of Technology) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
Keywords
anyons, honeycomb lattice, spin-1/2 model, exactly solvable models, free fermions, Z2 gauge field, non-Abelian anyons, Abelian anyons, Chern number, phase diagram

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