The first experiment of USTC realizes the optimal quantum gate test based on local operation

Academician Guo guangcan's team has made important progress in the measurement and inspection of quantum gates. Li Chuanfeng and Xiang Guoyong of the team cooperated with Zhu huangjun of Fudan University and Shang Jiangwei of Beijing University of technology to realize the optimal quantum gate test based on local operation for the first time. The research results were published online in the international well-known journal physics review express on January 14, 2022, and were selected into the articles recommended by the editor.

Quantum gate is the basic unit of constructing quantum computer. Realizing high fidelity quantum gate operation is a necessary condition for fault-tolerant quantum computing. How to check whether the fidelity of the actually prepared quantum gate meets the requirements is the first problem to be solved in the implementation of fault-tolerant quantum computing. As the number of parameters in the quantum gate increases exponentially with the size of the quantum system, the traditional quantum process tomography scheme increases exponentially with the size of the quantum gate. For the quality characterization of large-scale quantum gates and quantum circuits in the future, the traditional quantum process tomography method does not have practical operability. Quantum gate test, a new theoretical method developed recently in the world, has brought dawn to solve the above problems. It can achieve the optimal sample complexity for most quantum gates and only use local operation. However, this method has difficulties in practical application. It is not robust to experimental errors and quantum gate defects.

Xiang Guoyong's group and collaborators combined the idea of quantum gate test with the multi parameter quantum precision measurement platform developed by the group in recent years [NAT. Commun. 9,1 (2018); PRL 124060502 (2020); PRL 125020501 (2020); PRL 126070503 (2021)] to improve the data processing algorithm of quantum gate test, The quantum gate test improves the robustness to errors while retaining high efficiency. The improved quantum gate test estimates the upper bound ∈ of the distortion of the quantum gate by multiple local projection measurements of the quantum gate output. The experimental results show that the estimated value of ∈ is nearly inversely proportional to the number of samples n, that is, the estimation accuracy of 1 / n. This means that the quantum gate test with the optimal sample complexity of 1 / ∈ is realized. More importantly, the sample complexity required by this method does not increase with the increase of the size of the quantum gate.

Figure 1. Schematic diagram of optimal quantum gate inspection scheme

Using the optimal quantum gate test, the research group tested the two bit CNOT gate and the three bit Toffoli gate respectively. On average, only 1600 and 2600 measurements are needed to check whether the fidelity reaches more than 99% and 97%, and only 20 and 32 measurement base items are used. In contrast, using quantum process tomography to characterize their distortion requires 324 and 4096 measurement bases and millions of measurements. Therefore, the quantum gate test is of great significance for the verification of large-scale quantum gates and quantum circuits.

figure 2. Inspection results of CNOT door. (a) Significance level (b) distortion upper bound

Zhang Ruiqi, a graduate student of the Key Laboratory of quantum information of the Chinese Academy of Sciences, and Hou Zhibo, an associate researcher, are the co first authors of the work. The work was supported by the Ministry of science and technology, the National Natural Science Foundation of China, the Chinese Academy of Sciences, the Ministry of education and Anhui Province.

Paper link:https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.020502