Qudit low-density parity-check codes

• URL: http://arxiv.org/abs/2510.06495v1
• Date: Tue, 07 Oct 2025 22:25:28 GMT
• Title: Qudit low-density parity-check codes
• Authors: Daniel J. Spencer, Andrew Tanggara, Tobias Haug, Derek Khu, Kishor Bharti,
• Abstract summary: We introduce a general framework for finding qudit LDPC codes and apply our formalism to several promising types of LDPC codes.<n>We then numerically search for and decode several novel qudit codes compatible with near-term hardware.
• Score: 0.4053073794503683
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Qudits 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 family of quantum error correction codes, namely quantum low-density parity-check (LDPC) codes, have been so far 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.

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