Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
153 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Toward a Union-Find decoder for quantum LDPC codes (2103.08049v1)

Published 14 Mar 2021 in quant-ph, cs.IT, and math.IT

Abstract: Quantum LDPC codes are a promising direction for low overhead quantum computing. In this paper, we propose a generalization of the Union-Find decoder as adecoder for quantum LDPC codes. We prove that this decoder corrects all errors with weight up to An{\alpha} for some A, {\alpha} > 0 for different classes of quantum LDPC codes such as toric codes and hyperbolic codes in any dimension D \geq 3 and quantum expander codes. To prove this result, we introduce a notion of covering radius which measures the spread of an error from its syndrome. We believe this notion could find application beyond the decoding problem. We also perform numerical simulations, which show that our Union-Find decoder outperforms the belief propagation decoder in the low error rate regime in the case of a quantum LDPC code with length 3600.

Citations (37)

Summary

We haven't generated a summary for this paper yet.