Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of codes called low-density parity-check (LDPC) codes. The are alternatives to the surface code, which currently leading candidate implement fault-tolerance. We introduce zoo LDPC and their potential making computers robust against noise. particular, explain ...

Low Density Parity Check Codes originally invented by Gallagher and subsequently rediscovered by multiple groups 30 years later has become the best known error correcting code in a variety of situations. In this paper, we review regular and irregular LDPC codes. We describe a number of message passing decoders for decoding these codes and explain their operation via examples. Density evolution,...

A low-density parity-check code is a code specified by a parity-check matrix with the following properties : each column contains a small fixed numberj > 3 of I’s and each row contains a small fixed number k > j of 1’s. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed j. When used with maximum likelihood decoding on a snfhciently quiet ...