Flag Proxy Networks: Tackling the Architectural, Scheduling, and Decoding Obstacles of Quantum LDPC codes

• URL: http://arxiv.org/abs/2409.14283v1
• Date: Sun, 22 Sep 2024 01:08:58 GMT
• Title: Flag Proxy Networks: Tackling the Architectural, Scheduling, and Decoding Obstacles of Quantum LDPC codes
• Authors: Suhas Vittal, Ali Javadi-Abhari, Andrew W. Cross, Lev S. Bishop, Moinuddin Qureshi,
• Abstract summary: In this paper, we consider two under-studied families of QLDPC codes: hyperbolic surface codes and hyperbolic color codes. degree-4 FPNs of the hyperbolic surface and color codes are respectively $2.9times$ and $5.5times$ more space-efficient than the $d = 5$ planar surface code. The hyperbolic codes also have error rates comparable to their planar counterparts.
• Score: 1.870400753080051
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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