Quantum LDPC Codes

Pavel Panteleev, Gleb Vyacheslavovich Kalachev

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.

Ivan B. Djordjević

Pavel Panteleev, Gleb Vyacheslavovich Kalachev

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.

Joschka Roffe

Kenta Kasai, Kenta Kasai

Gleb Vyacheslavovich Kalachev, Pavel Panteleev

In this paper we study classical and quantum LDPC codes with constant rate obtained using tensor product operation over noncommutative group algebra for chain complexes. It is shown that these families of quantum LDPC codes are asymptotically good, which proves the qLDPC conjecture. The existence of asymptotically good families of locally testable codes with constant parameters of locality and soundness is also shown, which gives the solution of the known conjecture in the field of classical locally testable codes.