In recent years, superconducting quantum computing has developed rapidly, and the applications that everyone pays attention to generally have two directions, the implementation of quantum algorithms and the nature of quantum simulation multibody systems. The use of superconducting qubits to achieve multi-particle entanglement can demonstrate the ability of the system to control multiple qubits at the same time, and quantum entanglement as a useful resource for quantum computing, can be convenient to prepare will reduce the difficulty of implementing quantum algorithms, but for the use of quantum entanglement to break through the standard quantum limit of classical methods of measuring accuracy, and further approach the Heisenberg limit, this direction is the content of quantum metrology.
Quantum metrology has broad application prospects, the purpose of which is to use entangled states to achieve breakthroughs in the accuracy limit of classical technology, in order to achieve ultra-high-precision measurement of certain physical quantities. Life experience tells us that it is difficult to measure the thickness of a piece of paper directly with calipers, but measuring the thickness of a stack of paper by dividing the number of paper layers makes it easy to get the thickness of a piece of paper. Quantum metrology is based on this naïve idea, such as considering the measurement of phase information of light qubits, if these photons are independent of each other, according to the central limit theorem of statistics, the accuracy of multiple measurements can only reach the scattered noise limit, also known as the standard quantum limit, but if these photons are all entangled to form a special multi-particle entanglement state, its phase information is enlarged, just like multi-layer paper stacked, then the measurement of phase information can break through the standard quantum limit. And can be close to the final limit of accuracy limited by the uncertainty principle of quantum mechanics, generally called the Heisenberg limit, this property can be called the advantage of quantum metrology.
The degree of approximation of the Heisenberg limit is related to the degree of entanglement of the multiparticle state that enables the detection, but the measurement of the entanglement size of multiple particles is a complex problem and depends on the specific application of concern, and the advantages of quantum metrology can be measured with quantum Fisher information, which is also directly related to the size of the entanglement. Unfortunately, although the entanglement and quantum metrology advantages of Gaussian compressed states can be characterized by linear compression coefficients, for non-Gaussian entangled states in the overcompressed region, the linear compression coefficient cannot determine whether there is multibody entanglement. In recent years, it has been noted that the compression coefficient can be generalized from the original concept of linearity to a nonlinear compression coefficient, which can well characterize the entanglement of non-Gaussian states, and is directly related to the advantages of quantum metrology, but subject to the experimental difficulty of multi-qubit single-shot measurement, the measurement of nonlinear compression coefficient is not realized in various multi-particle entanglement systems.
Multiparticle entanglement can be achieved with superconducting qubits, can one obtain a special entanglement state with the advantages of high quantum metrology?
Recently, Xu Kai, Associate Researcher of Q03 Group, Laboratory of Solid State Quantum Information and Computing, Institute of Physics, Chinese Academy of Sciences/Beijing National Research Center for Condensed Matter Physics, Researcher Fan Juan, Researcher Zheng Dongning, Sc5 Group, State Key Laboratory of Superconductivity, and Collaborated with Professor Wang Haohua's team of Zhejiang University, and Dr. Zhang Yuran and Professor Nori of Japan's Riken Institute of Science, using devices with 20 superconducting qubits, a newly built superconducting quantum computing platform at the Institute of Physics. The preparation of entangled states of superconducting qubits and multiparticles was successfully realized, and the measurement of nonlinear compression coefficient was realized for the first time by combining the measurement advantages of the system.
Experiments show that the preparation of 19-bit non-Gaussian compressed state, can achieve very close to the Heisenberg limit accuracy, the quantum advantage obtained is the best in the experimental results of the year-on-year number of specials, see Figure 1, the achieved quantum metrology advantage can be compared with the entanglement system of thousands of particles in other systems, showing the advanced nature of superconducting quantum computing technology, related results were recently published in Phys. Rev. Lett. 128, 150501 (2022).
In addition, Sun Zhenghang, a researcher and doctoral student at the Institute of Physics of the Chinese Academy of Sciences, cooperated with the team of Professor Zhu Xiaobo and Professor Pan Jianwei of the University of Science and Technology of China to realize the quantum simulation of two different property models of one-dimensional XX and ladder XX based on the superconducting quantum device of the 24-bit ladder structure, and observed the dynamic characteristics of non-various states of quantum heating, information scrambling and integrable systems respectively, and the team of the Institute of Physics was responsible for the theoretical scheme. The results were recently published in Phys. Rev. Lett. 128, 160502 (2022).
Figure I. The asterisk pointed to by the arrow is the quantum metrology advantage achieved by this work, and the results show that the entangled state prepared using 19 superconducting quanta is closer to the Heisenberg limit shown by the shadow boundary than other experiments, and the figure above is the annex to the article.
Figure II. The device contains 19 qubit positions, which are coupled to each other for intensity information, as well as experimental procedures when measuring linear and nonlinear compression coefficients, quantum Fisher information.
Figure III. Linear and nonlinear compression coefficients of the entangled states of 10 superconducting qubits, as well as measurements of quantum Fisher information, distribution of qubits at different time points.
Figure IV. A circuit diagram of 19 qubits measuring quantum Fisher information, the results of which are shown as a function of distribution.
The above two tasks were supported by the Beijing Branch of Songshan Lake Materials Laboratory, the Center of Excellence for Topological Quantum Computing of the Chinese Academy of Sciences and the Pilot B Project, the Beijing Institute of Quantum Information Science, and the National Natural Science Foundation of China.
bibliography:
[1] Kai Xu#, Yu-Ran Zhang#, Zheng-Hang Sun#, Hekang Li, Pengtao Song, Zhongcheng Xiang, Kaixuan Huang, Hao Li, Yun-Hao Shi, Chi-Tong Chen, Xiaohui Song, Dongning Zheng, Franco Nori*, H. Wang*, and Heng Fan*.
Metrological characterization of non-Gaussian entangled states of superconducting qubits,
Physical Review Letters 128, 150501 (2022).
[2] Qingling Zhu#, Zheng-Hang Sun#, Ming Gong#, Fusheng Chen, Yu-Ran Zhang, Yulin Wu, Yangsen Ye, Chen Zha, Shaowei Li, Shaojun Guo, Haoran Qian, He-Liang Huang, Jiale Yu, Hui Deng, Hao Rong, Jin Lin, Yu Xu, Lihua Sun, Cheng Guo, Na Li, Futian Liang, Cheng-Zhi Peng, Heng Fan*, Xiaobo Zhu*, Jian-Wei Pan*,
Observation of thermalization and information scrambling in a superconducting quantum processor.
EDIT: just_iu