Universal Robust Quantum Gates by Geometric Correspondence

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, and develop a quantum robust control theory with a systematic, explicit, and geometric intuitive framework to construct universal quantum gates that are robust to generic errors. We propose conditions for dynamically correcting errors and quantitative robustness measures for any control pulses, and establish an analytic-numerical hybrid protocol to search for robust control pulses with the simplest waveforms and any given gate time. The resulting universal robust quantum gates are demonstrated with numerical tests for realistic semiconductor spin qubits and superconducting transmon qubits. The theory is ready to assist the future leap of quantum computing.