Full Extractors for Logical Processing in Hypergraph Product Codes

Abstract:Quantum low-density parity-check (QLDPC) codes are promising candidates for practical low-overhead quantum memories. For large-scale fault-tolerant quantum computation, we further need logical processing methods for QLDPC codes. In this work, we construct full extractors---surgery systems capable of measuring arbitrary logical Pauli operators on a code block---for several hypergraph product (HGP) codes. These extractors enable logical processing via Pauli-based computation (PBC) without the compilation overhead observed in prior works. Moreover, our extractors have sizes between $47\%$ and $80\%$ of the base HGP codes, and the extractor-augmented codes can be supported on fixed-connectivity hardware with maximum qubit degree ten. Our approach involves assembling many partial extractors with verifiable fault tolerance into a single full extractor. For a distance $10$ HGP code, circuit-level noise simulations yield logical measurement error rates of approximately $10^{-6}$ at a physical error rate of $0.1\%$. These results demonstrate that extractor architectures, when designed in the fixed-connectivity setting, can achieve the space efficiency of QLDPC codes without introducing compilation overhead compared to surface-code PBC architectures.

arXiv:2606.03507 [quant-ph]

(or arXiv:2606.03507v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.03507 Focus to learn more arXiv-issued DOI via DataCite

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