Designing entanglement-assisted quantum low-density parity-check codes

This paper develops a general theory for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum error-correcting codes (EAQECCs) with many desirable properties. These properties include the requirement of only one initial entanglement bit, high error correction performance, high rates, and low decoding complexity. These methods are flexible and can be used to produce codes with a wide variety of parameters and entanglement requirements. As far as the authors are aware, this is the first framework for constructing EAQECCs requiring prescribed mounts of entanglement. Combinatorial design theory is the primary tool used in these constructions. Results include many new codes, as well as minimum distances for several classical codes.