Precise and robust quantum control is the key to emerging quantum technologies. We uncover the essential correspondence between driven noisy quantum evolution and geometric curves described with the Frenet-Serret formulas. In terms of the geometric correspondence, we develop an explicit quantum robust control theory. The theory gives necessary and sufficient conditions of the robust control for given errors, and also offers quantitative measure of control robustness. Based on the analytic theory, we propose and demonstrate a practical framework to construct universal robust quantum gates for realistic qubits. We establish the analytic-numerical hybrid protocol to obtain arbitrary robust control pulses with simplest waveforms and arbitrary gate time. We obtain universal quantum gates with high fidelities above the fault tolerance threshold over a broad range of error strength. These results are tested numerically for realistic semiconductor spin qubits and superconducting transmon qubits, demonstrating the experimental feasibility of our theory.
Xiu-Hao Deng is an associate researcher (assistant professor, PI) of Shenzhen Institute of Quantum Science and Engineering, SUSTech, and the Shenzhen branch of Hefei Lab. He obtains B.S. from the Department of Modern Physics, University of Science and Technology of China (USTC). He continued with the graduate study of quantum information and quantum error correction at USTC. He went to the University of California, Merced to study superconducting qubits and got his Ph.D. in 2015. After he finished a short-term research associate at UC Merced he joined Sophia and Ed Barnes's joint group in VirginiaTech as a postdoctoral associate, to pursue the research in quantum control theory and quantum dynamics. He returned to China in late 2018 and started his position in the institute till now.