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Tensor-network codes
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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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Cited by 1 Pith paper
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Tensor-network decoders for process tensor descriptions of non-Markovian noise
A tensor-network-based maximum likelihood decoder is constructed for quantum error correction under process-tensor noise, with an MPS approximation demonstrated on the five-qubit and Steane codes.
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