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This research introduces a rank-based search method that efficiently certifies quantum code distances for systems up to 31,200 qubits, correcting overestimated resilience figures in recent literature. By expressing distances as tropical partition functions, the approach significantly outperforms existing solvers while enabling more accurate resource estimates and schedule optimizations for fault-tolerant quantum computing.
Rank-based search certifies quantum code distances at scale
Code and circuit distances characterize how strongly quantum error correction suppresses logical errors and guide code comparisons, schedule choices and resource estimates. The authors certify distances for codes with up to 31,200 qubits and for memory circuits with up to 8× 10^5 fault mechanisms, identifying overestimated distances in 10 recent papers.
Bin Cheng, Naixu Guo, and Feng Pan have certified a circuit distance of 16 for IBM’s two-gross memory circuits using a standard schedule, a finding that corrects the previously assumed distance of 18. Their new method, which evaluates quantum code distances as tropical partition functions, also revealed discrepancies in 10 of 26 recent papers, finding overestimated distances with a maximum difference of at least eight. The work certifies distances for codes with up to 31,200 qubits and memory circuits with up to 800,000 fault mechanisms, demonstrating a significant improvement…
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