Tensor-network codes

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.

arXiv comment5 pages main body + 5 pages appendices; 6 figures

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Cited by in corpus (18)

• Holographic tensor network models and quantum error correction: A topical review
• Experimental benchmarking of an automated deterministic error suppression workflow for quantum algorithms
• Hyper-optimized approximate contraction of tensor networks with arbitrary geometry
• Universal Fault-Tolerant Quantum Computing with Stabiliser Codes
• Tensor networks for quantum computing
• Conformal Properties of Hyperinvariant Tensor Networks
• Simulating quantum circuits using efficient tensor network contraction algorithms with subexponential upper bound
• Local tensor-network codes
• Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations
• Tensor network decompositions for absolutely maximally entangled states
• Near-Term Spin-Qubit Architecture Design via Multipartite Maximally-Entangled States
• The resource theory of tensor networks
• Unifying non-Markovian characterisation with an efficient and self-consistent framework
• Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes
• Quantum Lego and XP Stabilizer Codes
• Dynamically generated concatenated codes and their phase diagrams
• Tensor network method for real-space topology in quasicrystal Chern mosaics
• Biased-Noise Thresholds of Zero-Rate Holographic Codes with Tensor-Network Decoding