Good Quantum Locally Testable Codes from Product Expansion

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.

Source: arXiv:2609.26735v1 - http://arxiv.org/abs/2609.26735v1 PDF: https://arxiv.org/pdf/2609.26735v1 Original Link: http://arxiv.org/abs/2609.26735v1