A common approach to studying the performance of quantum error correcting codes is to assume independent and identically distributed single-qubit errors. However, the available experimental data shows that realistic errors in modern multi-qubit devices are typically neither independent nor identical across qubits. In this work, we develop and investigate the properties of topological surface codes adapted to a known noise structure by Clifford conjugations. We show that the surface code locally tailored to non-uniform single-qubit noise in conjunction with a scalable matching decoder yields an increase in error thresholds and exponential suppression of sub-threshold failure rates when compared to the standard surface code. Furthermore, we study the behaviour of the tailored surface code under local two-qubit noise and show the role that code degeneracy plays in correcting such noise. The proposed methods do not require additional overhead in terms of the number of qubits or gates and use a standard matching decoder, hence come at no extra cost compared to the standard surface-code error correction.
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 Such an XXZZ code is reminiscent of the rotated XZZX code introduced in Ref.  that has the same structure of logical operators as in our XXZZ code and therefore also performs optimally on a squared rotated lattice.
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 In Eq. \eqrefeq:weights_mod, we only include the zeroth order terms in $p_1$ and $p_2$. In Ref. PhysRevA.89.042334, the probability of connecting two defects by a chain of single- and two-qubit errors has been calculated to the the higher order. That is, the authors have also included the possibility of creating connecting two defects with Manhattan distance $N$ by one single-qubit error and $N-1$ two-qubit errors when $p_1/p_2 \ll 1$ (by one two-qubit error and $N-1$ single-qubit errors when $p_2/p_1 \ll 1$). However, our simulations show that adding such higher-order terms has vahishingly small effect on the decoding fidelity.
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 The codes used for numerical simulations of the QECCs studied in this work are available at https://github.com/HQSquantumsimulations/non-iid-error-correction-published.
 The data obtained from numerical simulations and used for the plots in this work is available at https://github.com/peter-janderks/plots-and-data-non-iid-errors-with-surface-codes/.
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