Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 18 min ago
PreprintarXiv licencearXiv

Self-Correcting 3D Surface Code with Growing Local Dimension

  • Jinkang Guo
Open at sourcePDFDOICite

Abstract

We construct self-correcting 3D surface codes over ℤq with local dimension q growing with system size. The model preserves the local geometry and stabilizer support of the ordinary 3D surface code and remains translation invariant in the bulk, while modifying only the stabilizer Pauli powers. We use the Lee metric to characterize error weight and consider local Metropolis dynamics with single-qudit X±1 and Z±1 updates, each changing the energy by at most a constant independent of q and system size N. We prove that, below the critical temperature, when the local dimension scales as q=Θ(N), the memory times in both error sectors grow at least as exp[Ω(N1/3)]. Our numerical results further support these analytical results. Together, these results establish growing local Hilbert-space dimension as a new resource for designing self-correcting quantum memories while retaining simple local geometry and local thermal dynamics.

Related

  1. Stabilizer entropy cones as self-dual slices of linear rank cones: a five-party gap and dependence on the local dimension
    Xidan Song, Ruifeng Cao
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsQuantum physics & quantum informationarXiv
  2. Self-testing of logical subspaces of quantum error-correcting codes
    Li-Yi Hsu, En-Jui Kuo
    New Journal of PhysicsPeer-reviewedCC BY 4.0Full textAtomic, molecular & optical physicsCrossref
  3. Universally Certifying Partially Self-Correcting Quantum Memories in 3D Translation-Invariant Stabilizer Codes
    Chong-Yuan Xu, Yong Xu
    arXivPreprintarXiv licenceFull textQuantum physics & quantum informationarXiv
  4. Approximating Local Properties by Tensor Network States With Constant Bond Dimension
    Yichen Huang
    IEEE Transactions on Information TheoryPeer-reviewedLicence not statedFull text17 citedAtomic, molecular & optical physicsOpenAlex
  5. The Quantum Hamming Bound in Arbitrary Local Dimension
    Yu-Xuan Zhang, Jing-Ling Chen
    arXivPreprintCC BY 4.0Full textQuantum physics & quantum informationarXiv

Cite

BibTeXRIS
BibTeX
@misc{guo2026selfcorrecting,
  title = {{Self-Correcting 3D Surface Code with Growing Local Dimension}},
  author = {Jinkang Guo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35099},
  eprint = {2610.35099},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35099},
}
RIS
TY  - UNPB
TI  - Self-Correcting 3D Surface Code with Growing Local Dimension
AU  - Jinkang Guo
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35099
UR  - https://arxiv.org/abs/2610.35099
AB  - We construct self-correcting 3D surface codes over ℤ_q with local dimension q growing with system size. The model preserves the local geometry and stabilizer support of the ordinary 3D surface code and remains translation invariant in the bulk, while modifying only the stabilizer Pauli powers. We use the Lee metric to characterize error weight and consider local Metropolis dynamics with single-qudit X^±1 and Z^±1 updates, each changing the energy by at most a constant independent of q and system size N. We prove that, below the critical temperature, when the local dimension scales as q=Θ(N), the memory times in both error sectors grow at least as exp[Ω(N^1/3)]. Our numerical results further support these analytical results. Together, these results establish growing local Hilbert-space dimension as a new resource for designing self-correcting quantum memories while retaining simple local geometry and local thermal dynamics.
ER  -