Research
Quantum error-correcting codes that combine explicit structure, useful rate, large girth, and practical decoding.
Useful quantum computation requires many reliable logical qubits, yet present systems need large numbers of physical qubits to protect a much smaller logical space. Engineering constraints matter, but code design itself also faces fundamental limitations.
Quantum low-density parity-check codes are attractive because sparse checks can support scalable syndrome processing. The central challenge is to obtain several desirable properties at once: useful coding rate, large girth, strong finite-length performance, controlled error floors, and low-complexity decoding.
Explicit CSS constructions that control commutativity without forcing all of the graph structure into restrictive orthogonality patterns. The work emphasizes regular sparse matrices, large girth, and reproducible finite-length instances.
Kasai codes →Constructions and decoding over larger finite fields, expanded to binary CSS codes on qubits. The aim is to use algebraic structure and degeneracy-aware decoding to improve the low-error-rate regime.
Non-binary codes →Large-girth regular CSS LDPC constructions designed around a controlled orthogonality barrier.
Details →Pair-partition constructions with CPM-based verification records and explicit instances.
Details →Affine-coset, finite-field two-branch, and high-rate constructions maintained separately from the two main families.
Details →The site separates conceptual explanations from computational evidence. Construction pages describe the code families; the software and data page records reusable implementations and archives; the distance pages state what is known through benchmarks, lower bounds, and explicit upper-bound witnesses.
The decoding experiments use sum-product BP formulations that retain the local correlation between Pauli error components, together with lightweight post-processing where stated. Decoder labels and assumptions are given on the relevant paper, software, or data page.