Decoding Holographic Codes with an Integer Optimisation Decoder

Abstract

We develop a most likely error Pauli error decoding algorithm for stabiliser codes based on general purpose integer optimisation. Using this decoder we analyse the performance of holographic codes against Pauli errors and find numerical evidence for thresholds against Pauli errors for bulk qubits. We compare the performance of holographic code families of various code rates and find phenomenological Pauli error thresholds ranging from $7\%$ to $16\%$, depending on the code rate. Additionally we give numerical evidence that specific distance measures of the codes we consider scales polynomially with number of physical qubits.

arXiv comment7 pages, 6 figures

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• Universal Fault-Tolerant Quantum Computing with Stabiliser Codes
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• Conformal Properties of Hyperinvariant Tensor Networks
• Engineering holography with stabilizer graph codes
• Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes
• Biased-Noise Thresholds of Zero-Rate Holographic Codes with Tensor-Network Decoding