We experimentally demonstrate fast and high-fidelity geometric control of a quantum system with the most brachistochrone method on hybrid spin registers in diamond. Based on the time-optimal universal geometric control, single geometric gates with the fidelities over 99.2% on the spin state of nitrogen-vacancy center are realized with average durations shortened by 74.9%, comparing with conventional geometric method. The fidelity of the fast geometric two-qubit gate exceeds 96.5% on the hybrid spin registers. With these fast high-fidelity gates available, we implement quantum entanglement-enhanced phase estimation algorithm and demonstrate the Heisenberg quantum limit at room-temperature. By comparing with the conventional geometric circuit, the measurement bandwidth and sensitivity is enhanced by 3.5 and 2.9 times. Hence, our results show that high-fidelity quantum control based on a fast geometric route will be a versatile tool for broad applications of quantum information processing in practice.
@article{arxiv.2105.05481,
title = {Fast high-fidelity geometric quantum control with quantum brachistochrones},
author = {Yang Dong and Ce Feng and Yu Zheng and Xiang-Dong Chen and Guang-Can Guo and Fang-Wen Sun},
journal= {arXiv preprint arXiv:2105.05481},
year = {2021}
}