Good Quantum Locally Testable Codes from Product Expansion

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.

Quantum Physics (quant-ph); Computational Complexity (cs.CC); Information Theory (cs.IT)

arXiv:2609.26735 [quant-ph]

(or arXiv:2609.26735v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.26735 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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