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.

arXiv:2610.12685 [quant-ph]

(or arXiv:2610.12685v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.12685 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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