Full Extractors for Logical Processing in Hypergraph Product Codes

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 50% 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.