Error Correction of Transversal cnot Gates for Scalable Surface-Code Computation PRX Quantum 05/01/2025 10592927 10.1103/PRXQuantum.6.020326 PRX quantum 2691-3399 6 2 Kaavya SahayYingjia LinShilin HuangKenneth R BrownShruti Puri Recent experimental advances have made it possible to implement logical multiqubit transversal gates on surface codes in a multitude of platforms. A transversal controlled- (t) gate on two surface codes introduces correlated errors across the code blocks and thus requires modified decoding compared to established methods of decoding surface-code quantum memory (SCQM) or lattice-surgery operations. In this work, we examine and benchmark the performance of three different decoding strategies for the t for scalable fault-tolerant quantum computation. In particular, we present a low-complexity decoder based on minimum-weight perfect matching (MWPM) that achieves the same threshold as the SCQM MWPM decoder. We extend our analysis with a study of tailored decoding of a transversal-teleportation circuit, along with a comparison between the performance of lattice-surgery and transversal operations under Pauli- and erasure-noise models. Our investigation builds toward systematic estimation of the cost of implementing large-scale quantum algorithms based on transversal gates in the surface code.

Published by the American Physical Society2025]]>

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