On the Logical Error Rate of Sparse Quantum Codes
On the Logical Error Rate of Sparse Quantum Codes
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DOI：
10.1109/tqe.2022.3196609
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发表时间：
2021-08
影响因子：
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通讯作者：
Patricio Fuentes;Josu Etxezarreta Martinez;P. Crespo;J. Garcia-Frías
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文献类型：
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作者：
Patricio Fuentes;Josu Etxezarreta Martinez;P. Crespo;J. Garcia-Frías
量子范式呈现出一种被称为简并的现象，它有可能提高量子纠错码的性能。然而，在评估稀疏量子码的性能时，这种机制的影响有时会被忽略，并且逻辑错误率并非总是能被正确报告。在本文中，我们讨论了先前已有的计算逻辑错误率的方法，并且受经典编码策略的启发，提出了一种基于陪集的有效方法来估计简并错误并将其与逻辑错误区分开来。此外，我们表明所提出的方法对Calderbank - Shor - Steane码族具有计算优势。我们使用这种方法证明在一个特定的稀疏量子码族中简并错误频繁出现，这强调了准确报告其性能的重要性。我们的结果还表明，文献中提出的改进解码策略是提高稀疏量子码性能的重要工具。
The quantum paradigm presents a phenomenon known as degeneracy that can potentially improve the performance of quantum error correcting codes. However, the effects of this mechanism are sometimes ignored when evaluating the performance of sparse quantum codes and the logical error rate is not always correctly reported. In this article, we discuss previously existing methods to compute the logical error rate and we present an efficient coset-based method inspired by classical coding strategies to estimate degenerate errors and distinguish them from logical errors. Additionally, we show that the proposed method presents a computational advantage for the family of Calderbank–Shor–Steane codes. We use this method to prove that degenerate errors are frequent in a specific family of sparse quantum codes, which stresses the importance of accurately reporting their performance. Our results also reveal that the modified decoding strategies proposed in the literature are an important tool to improve the performance of sparse quantum codes.