Fast computational primitives for La-cross qLDPC codes
Abstract
Quantum LDPC codes promise to reduce the overhead of fault-tolerant quantum computation, but their practical use requires efficient logical gates, measurements, and access to non-Clifford resources. Here, we develop a complete set of computational primitives for La-cross hypergraph product codes. For a subclass of these codes, we show that seed automorphisms together with fold-transversal gates generate the full logical Clifford group up to Pauli corrections. We further prove that every rank one logical operator admits D pairwise disjoint physical representatives, enabling parallel gauging and a space--time tradeoff for logical measurements. Finally, we construct an addressable surface code interface for injecting externally prepared resource states into selected logical qubits. Together, these results establish La-cross codes as a simple, low-connectivity generalisation of surface code computation, retaining analogous computational primitives while providing a complete Clifford+T instruction set across multiple encoded qubits.
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BibTeX
@misc{fini2026fast,
title = {{Fast computational primitives for La-cross qLDPC codes}},
author = {Andrea Di Fini and Tom Hartweg and Laura Pecorari and Guido Pupillo and Samuel Crew},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12685},
eprint = {2610.12685},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12685},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Fast computational primitives for La-cross qLDPC codes
AU - Andrea Di Fini
AU - Tom Hartweg
AU - Laura Pecorari
AU - Guido Pupillo
AU - Samuel Crew
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12685
UR - https://arxiv.org/abs/2610.12685
AB - Quantum LDPC codes promise to reduce the overhead of fault-tolerant quantum computation, but their practical use requires efficient logical gates, measurements, and access to non-Clifford resources. Here, we develop a complete set of computational primitives for La-cross hypergraph product codes. For a subclass of these codes, we show that seed automorphisms together with fold-transversal gates generate the full logical Clifford group up to Pauli corrections. We further prove that every rank one logical operator admits D pairwise disjoint physical representatives, enabling parallel gauging and a space--time tradeoff for logical measurements. Finally, we construct an addressable surface code interface for injecting externally prepared resource states into selected logical qubits. Together, these results establish La-cross codes as a simple, low-connectivity generalisation of surface code computation, retaining analogous computational primitives while providing a complete Clifford+T instruction set across multiple encoded qubits.
ER -