We realize a suite of logical operations on a distance-two logical qubit stabilized using repeated error detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch sphere, and a universal set of single-qubit gates. For each type of operation, we observe higher performance for fault-tolerant variants over non-fault-tolerant variants, and quantify the difference through detailed characterization. In particular, we demonstrate process tomography of logical gates, using the notion of a logical Pauli transfer matrix. This integration of high-fidelity logical operations with a scalable scheme for repeated stabilization is a milestone on the road to quantum error correction with higher-distance superconducting surface codes.
@article{arxiv.2102.13071,
title = {Logical-qubit operations in an error-detecting surface code},
author = {J. F. Marques and B. M. Varbanov and M. S. Moreira and H. Ali and N. Muthusubramanian and C. Zachariadis and F. Battistel and M. Beekman and N. Haider and W. Vlothuizen and A. Bruno and B. M. Terhal and L. DiCarlo},
journal= {arXiv preprint arXiv:2102.13071},
year = {2023}
}