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PreprintCC BY 4.0arXiv

Entangling gates for the SU(N) anyons

  • Sergey Mironov
  • Andrey Morozov
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Abstract

The model of a topological quantum computer is a promising one due to its natural resistance to noise and other errors. Operations in such a computer are implemented by braiding the trajectories of anyons. While it is easy to understand how to build one-qubit operations, two-qubit operations are more difficult. In arXiv:2412.20931 we suggested an approach to build such operations for a topological quantum computer based on SU(2) Chern-Simons theory with arbitrary level using cabling of knots. In this paper we discuss how this approach should be generalized to the SU(N) case, what the differences are, and which new problems arise.

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Cite

BibTeXRIS
BibTeX
@misc{mironov2026entangling,
  title = {{Entangling gates for the SU(N) anyons}},
  author = {Sergey Mironov and Andrey Morozov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.04016},
  eprint = {2605.04016},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.04016},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Entangling gates for the SU(N) anyons
AU  - Sergey Mironov
AU  - Andrey Morozov
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2605.04016
UR  - https://arxiv.org/abs/2605.04016
AB  - The model of a topological quantum computer is a promising one due to its natural resistance to noise and other errors. Operations in such a computer are implemented by braiding the trajectories of anyons. While it is easy to understand how to build one-qubit operations, two-qubit operations are more difficult. In arXiv:2412.20931 we suggested an approach to build such operations for a topological quantum computer based on SU(2) Chern-Simons theory with arbitrary level using cabling of knots. In this paper we discuss how this approach should be generalized to the SU(N) case, what the differences are, and which new problems arise.
ER  -