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PreprintCC BY 4.0arXiv

High-Rank Encoding Can Improve Approximate Quantum Error Correction

  • Bikun Li
  • Liang Jiang
Open at sourcePDFDOICite

Abstract

Conventional quantum-code constructions encode pure logical states as pure code states, but this restriction can sacrifice performance. We show that intrinsic encoding randomness can improve optimal entanglement fidelity. We bound the loss from imposing a rank-one encoder and prove it is at most quadratic near perfect recovery after joint optimization. The optimized advantage survives small noise perturbations. An explicit noise family requires higher-rank encoders arbitrarily close to perfect recovery, with every optimal encoder mapping pure inputs to mixed code states.

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Cite

BibTeXRIS
BibTeX
@misc{li2026highrank,
  title = {{High-Rank Encoding Can Improve Approximate Quantum Error Correction}},
  author = {Bikun Li and Liang Jiang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00778},
  eprint = {2609.00778},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00778},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - High-Rank Encoding Can Improve Approximate Quantum Error Correction
AU  - Bikun Li
AU  - Liang Jiang
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00778
UR  - https://arxiv.org/abs/2609.00778
AB  - Conventional quantum-code constructions encode pure logical states as pure code states, but this restriction can sacrifice performance. We show that intrinsic encoding randomness can improve optimal entanglement fidelity. We bound the loss from imposing a rank-one encoder and prove it is at most quadratic near perfect recovery after joint optimization. The optimized advantage survives small noise perturbations. An explicit noise family requires higher-rank encoders arbitrarily close to perfect recovery, with every optimal encoder mapping pure inputs to mixed code states.
ER  -