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Clifford-Deformed Surface Codes



Arpit Dua, Aleksander Kubica, Liang Jiang, Steven Flammia, Michael Gullans


Kitaev's toric/surface code and its numerous variants provide promising approaches to practi- cal quantum error correction (QEC). As recently discovered, a careful choice of the code variant and lattice layout can dramatically reduce logical error rate for the biased Pauli noise, resulting in significantly improved thresholds. Attracted by potential gains, we study the performance of Clifford-deformed surface codes that are obtained from the surface code by deforming its stabilizer group via the application of single-qubit Clifford operators. We first analyze Clifford-deformed codes on the 3 × 3 layout and find that depending on the noise bias, their logical error rate can differ by orders of magnitude. Then, we focus on random Clifford-deformed codes and demonstrate that they can outperform the subthreshold logical error rate of the best known translationally-invariant codes, such as the XY and XZZX surface codes, while maintaining their high threshold values. We also conjecture a threshold phase diagram that describes the region of random codes with 50% threshold for infinite bias noise, which we support using percolation-theory arguments and tensor-network simulations.
PRX Quantum


Quantum error correction, surface code, quantum computing


Dua, A. , Kubica, A. , Jiang, L. , Flammia, S. and Gullans, M. (2024), Clifford-Deformed Surface Codes, PRX Quantum, [online],, (Accessed April 23, 2024)
Created March 19, 2024, Updated March 27, 2024