Journal ArticleError Correction of Transversal cnot Gates for Scalable Surface-Code ComputationSahay, Kaavya; Lin, Yingjia; Huang, Shilin; Brown, Kenneth R; Puri, Shruti<p>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.</p> <sec><supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2025</copyright-year></permissions></supplementary-material></sec>PRX Quantum2025-05-0110592927PRX quantum622691-3399https://doi.org/10.1103/PRXQuantum.6.0203262120757National Science Foundation