Skip to content
DraconiticResearch
Search Sources API
201,818 studies31 sourcesUpdated 24 min ago
PreprintCC BY 4.0arXiv

Protected Logical Qudits in Kitaev Quantum Double Models via Stable Representations

  • Naihong Hu
  • Futao Wang
Open at sourcePDFDOICite

Abstract

Fault-tolerant quantum computation requires robust protection of encoded quantum information. In this work, we develop a representation-theoretic framework for constructing protected logical qudits in finite-group Kitaev quantum double models. By introducing ε-stable irreducible representations, we establish a necessary and sufficient existence criterion and derive ribbon--projector commutation relations that yield a d-dimensional protected logical subspace. We apply this construction to symmetric and alternating groups, obtaining logical qubits for Sn (n≥ 3) and a logical qutrit for A4. Moreover, the family (ℤ2)drtimesℤd realizes protected logical qudits of arbitrary dimension d≥ 2. Finally, for D(A4), we describe a scheme for universal logical qutrit computation using ribbon-based logical operations.

Related

  1. Simultaneous Reduction of Observables and Measured Qudits in Entanglement-Assisted Quantum Local Recovery
    Ryutaroh Matsumoto
    arXivPreprintarXiv licenceFull textGeneral mathematicsQuantum physics & quantum informationarXiv
  2. The quantum-classical bipartite universe and the logical emergence of ℏ from classical temporality
    Vincenzo Chilla
    arXivPreprintCC BY 4.0Full textMathematical physicsQuantum physics & quantum informationarXiv
  3. Code-Visible Liouvillian Modes and Coherent Logical Errors in Quantum Codes
    Marina Gordeychuk, Oleg Kiselev
    arXivPreprintarXiv licenceFull textMathematical physicsQuantum physics & quantum informationarXiv
  4. Some finite dimensional representations of shifted quantum affine algebras of type A
    Ryosuke Kodera, Kentaro Wada
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Representations of shifted quantum affine algebras and cluster algebras II: Non simply-laced types and cluster expansions
    Christof Geiss, David Hernandez, Bernard Leclerc
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{hu2026protected,
  title = {{Protected Logical Qudits in Kitaev Quantum Double Models via Stable Representations}},
  author = {Naihong Hu and Futao Wang},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.31011},
  eprint = {2608.31011},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.31011},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Protected Logical Qudits in Kitaev Quantum Double Models via Stable Representations
AU  - Naihong Hu
AU  - Futao Wang
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.31011
UR  - https://arxiv.org/abs/2608.31011
AB  - Fault-tolerant quantum computation requires robust protection of encoded quantum information. In this work, we develop a representation-theoretic framework for constructing protected logical qudits in finite-group Kitaev quantum double models. By introducing ε-stable irreducible representations, we establish a necessary and sufficient existence criterion and derive ribbon--projector commutation relations that yield a d-dimensional protected logical subspace. We apply this construction to symmetric and alternating groups, obtaining logical qubits for S_n (n≥ 3) and a logical qutrit for A_4. Moreover, the family (ℤ_2)^drtimesℤ_d realizes protected logical qudits of arbitrary dimension d≥ 2. Finally, for D(A_4), we describe a scheme for universal logical qutrit computation using ribbon-based logical operations.
ER  -