Knowledge tree for codes related to higher-dimensional quantum hypergraph product codes

In classical information processing, the capacity-approaching codes can be constructed through lower-density-parity-check(LDPC) codes with random matrices. These include the protocols used in 4G and 5G technologies. Its quantum analog is a promising substitute for quantum topological code, where the former has finite code rate but the latter encodes zero qubit asymptotically. Precious few examples of quantum LDPC codes were known which gives finite rate and also satisfies the fault tolerant condition. Our result on higher-dimensional quantum hypergraph product codes generalizes several known constructions. It relates to many common CSS codes as shown in the map.

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