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Good Quantum Locally Testable Codes from Product Expansion

  • Mitali Bafna
  • Anqi Li
  • Quynh T. Nguyen
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Abstract

We construct quantum locally testable codes (LTCs) with constant rate, distance, soundness and locality under a variant of a product expansion conjecture of Bafna and Vyas about Reed-Solomon codes. In particular, we use the high-dimensional expansion framework of Dinur, Lin and Vidick for constructing quantum LTCs, instantiated with the non-Abelian cubical complexes of Rungtanapirom, Stix and Vdovina. Our code is obtained by equipping the complex with carefully chosen Reed-Solomon local codes whose symmetries are compatible with those of the complex.

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Cite

BibTeXRIS
BibTeX
@misc{bafna2026good,
  title = {{Good Quantum Locally Testable Codes from Product Expansion}},
  author = {Mitali Bafna and Anqi Li and Quynh T. Nguyen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26735},
  eprint = {2609.26735},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26735},
}
RIS
TY  - UNPB
TI  - Good Quantum Locally Testable Codes from Product Expansion
AU  - Mitali Bafna
AU  - Anqi Li
AU  - Quynh T. Nguyen
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26735
UR  - https://arxiv.org/abs/2609.26735
AB  - We construct quantum locally testable codes (LTCs) with constant rate, distance, soundness and locality under a variant of a product expansion conjecture of Bafna and Vyas about Reed-Solomon codes. In particular, we use the high-dimensional expansion framework of Dinur, Lin and Vidick for constructing quantum LTCs, instantiated with the non-Abelian cubical complexes of Rungtanapirom, Stix and Vdovina. Our code is obtained by equipping the complex with carefully chosen Reed-Solomon local codes whose symmetries are compatible with those of the complex.
ER  -