Flag Proxy Networks: Tackling the Architectural, Scheduling, and Decoding Obstacles of Quantum LDPC codes
<|reference_start|>Flag Proxy Networks: Tackling the Architectural, Scheduling, and Decoding Obstacles of Quantum LDPC codes: Quantum error correction is necessary for achieving exponential speedups on important applications. The planar surface code has remained the most studied error-correcting code for the last two decades because of its relative simplicity. However, encoding a singular logical qubit with the planar surface code requires physical qubits quadratic in the code distance~($d$), making it space-inefficient for the large-distance codes necessary for promising applications. Thus, {\em Quantum Low-Density Parity-Check (QLDPC)} have emerged as an alternative to the planar surface code but require a higher degree of connectivity. Furthermore, the problems of fault-tolerant syndrome extraction and decoding are understudied for these codes and also remain obstacles to their usage.   In this paper, we consider two under-studied families of QLDPC codes: hyperbolic surface codes and hyperbolic color codes. We tackle the three challenges mentioned above as follows. {\em First}, we propose {\em Flag-Proxy Networks (FPNs)}, a generalizable architecture for quantum codes that achieves low connectivity through flag and proxy qubits. {\em Second}, we propose a {\em greedy syndrome extraction scheduling} algorithm for general quantum codes and further use this algorithm for fault-tolerant syndrome extraction on FPNs. {\em Third}, we present two decoders that leverage flag measurements to decode the hyperbolic codes accurately. Our work finds that degree-4 FPNs of the hyperbolic surface and color codes are respectively $2.9\times$ and $5.5\times$ more space-efficient than the $d = 5$ planar surface code, and become even more space-efficient when considering higher distances. The hyperbolic codes also have error rates comparable to their planar counterparts.<|reference_end|>
@article{vittal2024flag,
    title={Flag Proxy Networks: Tackling the Architectural, Scheduling, and
  Decoding Obstacles of Quantum LDPC codes},
    author={Suhas Vittal, Ali Javadi-Abhari, Andrew W. Cross, Lev S. Bishop,
  Moinuddin Qureshi},
    journal={arXiv preprint arXiv:2409.14283},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.14283},
    primaryClass={quant-ph cs.AR}
}