量子比特间相关错误下的张量网络解码
Tensor Network decoding under inter-qubit correlated errors
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中文总结 AI 辅助
研究量子比特间相关错误下张量网络解码问题，通过引入额外二进制索引和变换构建多索引张量网络，并利用重新参数化等方法分解高维张量，所提方法实现的解码器比MWPM解码器有更高有限尺寸阈值。
中文摘要 AI 辅助
基于张量网络的最大似然解码器在二维表面码中取得了巨大成功，实现了最优解码成功率。然而，现有的张量网络解码器通常是为独立单量子比特错误模型设计的，其在量子比特间相关错误模型下的性能仍未得到探索。这是由于两个主要挑战。第一个挑战在于构建相关错误的张量网络，因为相同的最终泡利错误可能由许多不同的独立和相关错误组合产生，阻止了错误概率的直接分解。第二个挑战是，即使构建了张量网络，它通常包含高维张量，因此难以有效收缩。在这项工作中，为了解决第一个困难，我们引入了额外的二进制索引和两种变换来构建用于相关错误最大似然解码的多索引张量网络。为了解决第二个困难，我们使用重新参数化、消除和索引分类将高维张量分解为低维张量。这为满足本文推导的可处理性条件的错误模型产生了一个可有效收缩的张量网络。我们对一个代表性的相关错误模型进行了数值模拟，结果表明，用我们的多索引张量网络构建实现的最大似然解码器比广泛使用的MWPM解码器具有更高的有限尺寸阈值。
英文摘要
The maximum likelihood decoder based on tensor networks has proven highly successful for the 2D surface code, achieving the optimal decoding success rate. However, existing tensor network decoders are typically designed for independent single-qubit error models, and their performance under inter-qubit correlated error models remains unexplored. This is due to two major challenges. The first challenge lies in constructing the tensor network for correlated errors, since the same final Pauli error can arise from many different combinations of independent and correlated errors, preventing a direct factorization of the error probability. The second challenge is that even after a tensor network is constructed, it generally contains huge-dimensional tensors and is therefore not efficiently contractible. In this work, to address the first difficulty, we introduce additional binary indices and two transformations to construct a multi-index tensor network for maximum-likelihood decoding with correlated errors. To address the second difficulty, we use reparametrization, elimination, and index classification to decompose the huge-dimensional tensors into lower-dimensional tensors. This yields an efficiently contractible tensor network for error models satisfying the tractability conditions derived in this work. We perform numerical simulations for a representative correlated error model and show that the maximum-likelihood decoder implemented with our multi-index tensor network construction achieves a higher finite-size threshold than the widely used MWPM decoder.
