Universal robust quantum gates by geometric correspondence of noisy quantum evolution

A key to the next leap in quantum technologies and quantum computing relies on precise and robust control over noisy quantum systems. For the first time, our theory uncovers an essential correspondence between the driven noisy quantum evolution and multiplex space curves relating to various noises. Each two-sate system's noisy dynamics correspond to a diagram formed of the curves. The curve's properties provide a quantitative geometric metric of evolution error. On the other hand, the geometric correspondence is an explicit model to engineer quantum gates robust against various noises. It further gives the criteria to identify whether a noisy quantum system's evolution could be controlled robustly. Our analytic-numerical hybrid protocol enables the construction of universal robust quantum gates with very simple and smooth pulses for any given gate time. Based on realistic models of semiconductor spin qubits and superconducting transmons, our numerical simulations demonstrate plateaus of gate fidelity above the fault-tolerance threshold over a broad range of noise strength. These solid and promising results prove that our universal robust control pulses are ready for experiments. Therefore, this work shines some light on resolving the general robust quantum control problems.