Farrelly Terry, Harris Robert J, McMahon Nathan A, Stace Thomas M
ARC Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St. Lucia, Queensland 4072, Australia.
Department of Physics, Friedrich-Alexander University Erlangen-Nürnberg (FAU), D-91058 Erlangen, Germany.
Phys Rev Lett. 2021 Jul 23;127(4):040507. doi: 10.1103/PhysRevLett.127.040507.
We introduce tensor-network stabilizer codes which come with a natural tensor-network decoder. These codes can correspond to any geometry, but, as a special case, we generalize holographic codes beyond those constructed from perfect or block-perfect isometries, and we give an example that corresponds to neither. Using the tensor-network decoder, we find a threshold of 18.8% for this code under depolarizing noise. We show that, for holographic codes, the exact tensor-network decoder (with no bond-dimension truncation) has polynomial complexity in the number of physical qubits, even for locally correlated noise, making this the first efficient decoder for holographic codes against Pauli noise and, also, a rare example of a decoder that is both efficient and exact.
我们引入了带有自然张量网络解码器的张量网络稳定器码。这些码可以对应任何几何结构，但作为一个特殊情况，我们将全息码推广到了那些由完美或块完美等距变换构建的全息码之外，并且给出了一个不属于这两者的例子。使用张量网络解码器，我们发现在去极化噪声下该码的阈值为18.8%。我们表明，对于全息码，精确的张量网络解码器（无键维度截断）在物理量子比特数量上具有多项式复杂度，即使对于局部相关噪声也是如此，这使得它成为针对泡利噪声的全息码的首个高效解码器，也是一个高效且精确的解码器的罕见例子。
