Qudit low-density parity-check codes
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912970128228352 |
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| author | Spencer, Daniel J. Tanggara, Andrew Haug, Tobias Khu, Derek Bharti, Kishor |
| author_facet | Spencer, Daniel J. Tanggara, Andrew Haug, Tobias Khu, Derek Bharti, Kishor |
| contents | 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06495 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Qudit low-density parity-check codes Spencer, Daniel J. Tanggara, Andrew Haug, Tobias Khu, Derek Bharti, Kishor Quantum Physics 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 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 |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.06495 |