Shannon's determination of the capacity of the linear Gaussian channel has posed a
magnificent challenge to succeeding generations of researchers. This paper surveys how …

Low-density parity-check (LDPC) codes have attracted much attention over the past two
decades since they can asymptotically approach the Shannon capacity in a variety of data …

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 …

Quantum error correction is an indispensable ingredient for scalable quantum computing. In
this Perspective we discuss a particular class of quantum codes called “quantum low-density …

Tanner codes are long error correcting codes obtained from short codes and a graph, with
bits on the edges and parity-check constraints from the short codes enforced at the vertices …

We construct a new explicit family of good quantum low-density parity-check codes which
additionally have linear time decoders. Our codes are based on a three-term chain (2 m× m) …

This work provides the first explicit and non-random family of [[N, K, D]] LDPC quantum
codes which encode K∈ Θ (N 4/5) logical qubits with distance D∈ Ω (N 3/5). The family is …

We give a construction of quantum LDPC codes of dimension and distance as the code
length. Using a product of chain complexes this construction also provides a family of …

The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings posits that
there exist families of Hamiltonians with all low energy states of non-trivial complexity (with …

A locally testable code (LTC) is an error correcting code that has a property-tester. The tester
reads q bits that are randomly chosen, and rejects words with probability proportional to their …