Single-Shot Decoding of Biased-Tailored Quantum LDPC Codes
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Abstract
Quantum processors often exhibit biased noise (dominant $Z$ errors) and noisy readout, both of which degrade reliability and reproducibility. This work unifies two complementary strategies: bias tailoring, which realigns stabilizers to the dominant error basis, and single-shot (SS) decoding, which leverages metachecks to identify measurement faults from a single noisy round. We instantiate this in a four-dimensional lifted hypergraph-product (4D-LHP) LDPC code built from quasi-cyclic protograph seeds. Simulations show that tailoring reduces word-error rate (WER) by 20-60% across realistic $Z: X$ bias ratios (1:1 to 103:1), with the largest gains at moderate bias. Under realistic $q=4 \%$ measurement noise, a single SS round recovers $\sim 33 \%$ of the performance lost to readout faults; metachecks detect > 99.8% of faulty syndromes, ffering near-complete fault visibility despite modest correction capability. These results indicate that 4D-LHP codes offer practical resilience under realistic noise, making them well-suited for integration into orchestrated QPU-CPU workflows.