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  "path": "/papers/q-2026-03-13-2023/",
  "publishedAt": "2026-03-13T11:25:50.000Z",
  "site": "https://quantum-journal.org",
  "tags": [
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    "https://doi.org/10.22331/q-2026-03-13-2023"
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  "textContent": "Quantum 10, 2023 (2026).\n\nhttps://doi.org/10.22331/q-2026-03-13-2023\n\nQudits offer significant advantages over qubit-based architectures, including more efficient gate compilation, reduced resource requirements, improved error-correction primitives, and enhanced capabilities for quantum communication and cryptography. Yet, one of the most promising families of quantum error correction codes, namely quantum low-density parity-check (LDPC) codes, have so far been mostly restricted to qubits. Here, we generalize recent advancements in LDPC codes from qubits to qudits. We introduce a general framework for finding qudit LDPC codes and apply our formalism to several promising types of LDPC codes. We generalize bivariate bicycle codes, including their coprime variant; hypergraph product codes, including the recently proposed La-cross codes; subsystem hypergraph product (SHYPS) codes; high-dimensional expander codes, which make use of Ramanujan complexes; and fiber bundle codes. Using the qudit generalization formalism, we then numerically search for and decode several novel qudit codes compatible with near-term hardware. Our results highlight the potential of qudit LDPC codes as a versatile and hardware-compatible pathway toward scalable quantum error correction.",
  "title": "Qudit low-density parity-check codes"
}