The Hamiltonian, which determines the evolution of a quantum system, is fundamental in quantum physics. Therefore, it is crucial to implement high-precision generation and measurement of the Hamiltonian in a practical quantum system. Here, we experimentally demonstrate ultrahigh-precision Hamiltonian parameter estimation with a significant quantum advantage in a superconducting circuit via sequential control. We first observe the commutation relation for noncommuting operations determined by the system Hamiltonian, both with and without adding quantum control, verifying the commuting property of controlled noncommuting operations. Based on this control-induced commuting property, we further demonstrate Hamiltonian parameter estimation for polar and azimuth angles in superconducting circuits, achieving ultrahigh metrological gains in measurement precision exceeding the standard quantum limit by up to 16.0 and 16.1 dB at 𝑁=100, respectively.

Sai Li1,2,*, De-Jian Pan1,*, Yuan-Ke Zhu1,*, Jia-Lang Zhou1, Wen-Cui Liao1, Wei-Xin Zhang1, Zhen-Tao Liang1,2, Qing-Xian Lv1,2, Haifeng Yu3,4, Zheng-Yuan Xue1,2,4,†, Hui Yan1,2,4,‡, and Shi-Liang Zhu1,2,4,§

• 1Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, and School of Physics, South China Normal University, Guangzhou 510006, China

• 2Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, and Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China

• 3Beijing Academy of Quantum Information Sciences, Beijing 100193, China

• 4Hefei National Laboratory, Hefei 230088, China

• *These authors contributed equally to this work.

• †zyxue83@163.com

• ‡yanhui@scnu.edu.cn

• §slzhu@scnu.edu.cn