Asymptotically Good Quantum and Locally Testable Classical LDPC Codes

Pavel Panteleev; Gleb Kalachev

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arXiv · 2111.03654

Asymptotically Good Quantum and Locally Testable Classical LDPC Codes

Pavel Panteleev·Gleb Kalachev

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Abstract

We study classical and quantum LDPC codes of constant rate obtained by the lifted product construction over non-abelian groups. We show that the obtained families of quantum LDPC codes are asymptotically good, which proves the qLDPC conjecture. Moreover, we show that the produced classical LDPC codes are also asymptotically good and locally testable with constant query and soundness parameters, which proves a well-known conjecture in the field of locally testable codes.

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Pavel Panteleev, Gleb Kalachev. 2021-11-05. Asymptotically Good Quantum and Locally Testable Classical LDPC Codes. https://arxiv.org/abs/2111.03654

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