Error Correction of Transversal cnot Gates for Scalable Surface-Code Computation
Kaavya Sahay, Yingjia Lin, Shilin Huang, Kenneth R. Brown, Shruti Puri
Abstract
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.