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• W3163123156 abstract "We give a broad generalisation of the mapping, originally due to Dennis, Kitaev, Landahl, and Preskill, from quantum error correcting codes to statistical mechanical models. We show how the mapping can be extended to arbitrary stabiliser or subsystem codes subject to correlated Pauli noise models, including models of fault tolerance. This mapping connects the error correction threshold of the quantum code to a phase transition in the statistical mechanical model. Thus, any existing method for finding phase transitions, such as Monte Carlo simulations, can be applied to approximate the threshold of any such code, without having to perform optimal decoding. By way of example, we numerically study the threshold of the surface code under mildly correlated bit-flip noise, showing that noise with bunching correlations causes the threshold to drop to $p{textup{corr}}=10.04(6)%$, from its known iid value of $p{text{iid}}=10.917(3)%$. Complementing this, we show that the mapping also allows us to utilise any algorithm which can calculate/approximate partition functions of classical statistical mechanical models to perform optimal/approximately optimal decoding. Specifically, for 2D codes subject to locally correlated noise, we give a linear-time tensor network-based algorithm for approximate optimal decoding which extends the MPS decoder of Bravyi, Suchara and Vargo." @default.
• W3163123156 created "2021-05-24" @default.
• W3163123156 creator A5007129549 @default.
• W3163123156 creator A5079839412 @default.
• W3163123156 date "2021-05-16" @default.
• W3163123156 modified "2023-10-02" @default.
• W3163123156 title "Statistical mechanical models for quantum codes with correlated noise" @default.
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• W3163123156 doi "https://doi.org/10.4171/aihpd/105" @default.
• W3163123156 hasPublicationYear "2021" @default.
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