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arXiv · 2009.10329

Tensor-network codes

Terry Farrelly·Robert J. Harris·Nathan A. McMahon·Thomas M. Stace
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Abstract

Inspired by holographic codes and tensor-network decoders, 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 also show that for holographic codes the exact tensor-network decoder (with no bond-dimension truncation) is efficient with a complexity that is polynomial in the number of physical qubits, even for locally correlated noise.

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Terry Farrelly, Robert J. Harris, Nathan A. McMahon, Thomas M. Stace. 2020-09-22. Tensor-network codes. https://doi.org/10.1103/physrevlett.127.040507

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