Tensor-network codes

• URL: http://arxiv.org/abs/2009.10329v1
• Date: Tue, 22 Sep 2020 05:44:50 GMT
• Title: Tensor-network codes
• Authors: Terry Farrelly, Robert J. Harris, Nathan A. McMahon, Thomas M. Stace
• Abstract summary: We introduce tensor-network stabilizer codes which come with a natural tensor-network decoder. We generalize holographic codes beyond those constructed from perfect or block-perfect isometries. For holographic codes exact the tensor-network decoder is efficient with a complexity that is in the number of physical qubits.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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