Qudit low-density parity-check codes

Researchers generalized quantum low-density parity-check codes to qudit architectures. Qudits provide advantages over qubits that include more efficient gate compilation and reduced resource requirements. Prior LDPC codes had remained largely limited to qubits. A general framework was introduced for identifying qudit LDPC codes. The formalism extends to bivariate bicycle codes including coprime variants. Hypergraph product codes such as La-cross codes also fall under the generalization. Subsystem hypergraph product codes receive the same extension. High-dimensional expander codes that rely on Ramanujan complexes and fiber bundle codes complete the list of covered families. Numerical searches yielded several new qudit codes compatible with near-term hardware. Decoding followed for those codes.