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

arXiv: https://arxiv.org/abs/2409.14283 · HTML: https://mlsanity.com/paper/2409.14283/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2024.

## Built on by (most cited first, 1 of 1)

- [Are LLMs Good For Quantum Software, Architecture, and System Design?](https://mlsanity.com/paper/2603.26904/) (2026)

## Abstract (arXiv)

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× and 5.5× 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.