# Qudit low-density parity-check codes

_Friday, June 26, 2026 at 8:04 PM EDT · science · Latest · Tier 2 — Notable_

![Qudit low-density parity-check codes — Primary](https://quantum-journal.org/wp-content/uploads/2026/03/cover_figure-1-1.png)

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.

## Sources

- [Quantum Journal](https://quantum-journal.org/papers/q-2026-03-13-2023/)

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Retrieved: 2026-06-27T04:57:58.988Z
Publisher: Tech & Business (techandbusiness.org)