Progress in superconducting quantum computing series made by the Institute of Physics, Chinese Academy of Sciences
The core of artificial intelligence is machine learning. In recent years, a new star has risen in the field of machine learning, Generative Adversarial Networks (GAN, Generative Adversarial Networks), proposed by Goodfellow et al. in 2014. It is currently in the field of image identification. There are a large number of application examples in areas such as video generation and video generation. The basic idea of GAN is derived from the zero-sum game of game theory. Participants are composed of a generator G (Generator) and a discriminator D (Discriminator), and they are trained by the method of adversarial learning. The purpose of G is to learn the data distribution of the real data set R as much as possible, and the purpose of D is to correctly determine whether the input data comes from R or G. In order to win the game, these two game participants need to continuously optimize their own strategies and improve their generation and discrimination capabilities. The entire learning optimization process is to find a Nash equilibrium between the two.
However, like other algorithms of machine learning, the biggest problem GAN faces is the so-called "curse of dimensionality", that is, the number of training sets required for learning increases exponentially with the dimensionality. If the data we face exists in a high-dimensional space, then classical computers will soon be unable to process it effectively. Fortunately, we have a new computing method dominated by the laws of quantum mechanics, that is, quantum computing, which can solve many problems that classical computers cannot solve or are too complex. A clear application is that quantum computers can crack the RSA public key cryptosystem commonly used in the Internet and financial systems by using the Shor quantum algorithm. In terms of practicality, quantum search algorithms can be expected to be applied to big data retrieval; quantum annealing algorithms can be applied to optimization problems, such as logistics and transportation optimization; quantum simulation can be applied to quantum multi-body physics and quantum chemistry research, such as biosynthesis And drug screening. Compared with other systems, the technical route of superconducting quantum computing has an advantageous position in the direction of practical quantum computing.
So, can we combine GAN with quantum computing to design a more efficient Quantum Generative Adversarial Networks (QGAN, Quantum Generative Adversarial Networks) algorithm? This concept was first proposed by Dallaire-Demers and others. Its basic principle is similar to GAN. The difference is that G and D are composed of quantum circuits or quantum networks. The training data set can also be quantum data (such as quantum states, etc.) . So far, the display of QGAN on the superconducting quantum computing platform is limited to the learning of single-bit quantum states, and its gradient calculation is still a classic difference method, so that the calculation accuracy is affected by the inherent difference error, which in turn affects the convergence of the final training. At the same time, quantum entanglement, which can embody quantum properties and is an important resource for realizing quantum hegemony, has not been reflected in existing research.
Recently, the Institute of Physics of the Chinese Academy of Sciences/Beijing National Research Center for Condensed Matter Physics Fan Heng, Xu Kai's group, and Zheng Dongning's group have joined forces with Nankai University's Tian Jianguo and Liu Zhibo's groups, Zhejiang University's Wang Haohua's group and Tsinghua University's Deng Dongling's group, For the first time, the QGAN algorithm was extended to more bit categories and multi-body entanglement was introduced, and for the first time, QGAN training guided by quantum gradients was realized in a superconducting quantum computing platform.
In this experiment, a quantum chip with a full-connected architecture containing 20 qubits was used. On this chip, some high-level tasks including preparation of 20-bit Schrodinger cat states and simulation of dynamic phase transitions have been implemented. This experiment uses 5 qubits. The corresponding quantum algorithm is shown in Figure 1. It includes multiple single-bit quantum gates, multiple multi-bit entanglement gates, and multiple two-bit control gates. The line depth exceeds 20. In the experiment, it is necessary to continuously optimize the parameters of the single-bit quantum gate according to the quantum gradient guidance. In order to test the feasibility of the quantum gradient, the researchers first tried to train an arbitrary single-bit mixed state. After about 140 steps of training, the fidelity of the generated quantum state was 0.999 relative to the real situation, as shown in Figure 2. On this basis, they changed the learning goal to a more complex two-bit XOR gate. After about 190 steps of training, the researchers reproduced the truth table of the XOR gate with a fidelity of 0.927, as shown in Figure 3. This shows that QGAN has great potential in the learning of complex quantum processes. As the scale of the system increases, it can be directly extended to areas such as optimal control and self-guided quantum tomography.
This work has recently been published in npj Quantum Information 7, 165 (2021). Nankai University co-trained doctoral student Huang Kaixuan, Q03 group doctoral student Wang Zhengan, and Zhejiang University Song Chao distinguished professor as the co-first authors of the paper. The cooperation team also includes Zhejiang University postdoctoral fellow Li Hekang (quantum chip preparation), Zhejiang University distinguished professor Wang Zhen, Zhejiang University Hangzhou International Science and Innovation Center Researcher Guo Qiujiang, Zhejiang University master student Song Zixuan, etc.
In addition, Associate Research Fellow Xu Kai, Researcher Fan Hang, Researcher Zheng Dongning of the Institute of Physics of the Chinese Academy of Sciences, etc. cooperated with the research group of Professor Zheng Shibiao and Professor Yang Zhenbiao of Fuzhou University to achieve non-Abelian geometric control using two superconducting qubits and their auxiliary energy levels. Not gate, related results were published on Optica 8, 972 (2021).
Researcher Fan Hang and doctoral student Sun Zhenghang of the Institute of Physics of the Chinese Academy of Sciences collaborated with Professor Xiaobo Zhu, Professor Jianwei Pan of the University of Science and Technology of China, etc., using 12 superconducting qubits arranged in one dimension to prepare different initial states corresponding to different temperatures. The experimental observations of the phenomena of different degrees of thermalization are presented, and the relevant results are published in Phys. Rev. Lett. 127, 020602 (2021).
References:
[1] Kaixuan Huang#, Zheng-An Wang#, Chao Song#, Kai Xu, Hekang Li, Zhen Wang, Qiujiang Guo, Zixuan Song, Zhi-Bo Liu*, Dongning Zheng, Dong-Ling Deng*, H. Wang, Jian-Guo Tian, Heng Fan*, Quantum generative adversarial networks with multiple superconducting qubits, npj Quantum Information 7, 165 (2021).
[2] Kai Xu, Wen Ning, Xin-Jie Huang, Pie-Rong Han , Hekang Li, Zhen-Biao Yang*, Dongning Zheng, Heng Fan*, Shi-Biao Zheng*, Demonstration of a non-Abelian geometric controlled-NOT gate in a superconducting circuit, Optica 8, 972-976 (2021).
[3] Fusheng Chen#, Zheng-Hang Sun#, Ming Gong#, Qingling Zhu, 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 strong and weak thermalization in a superconducting quantum processor, Phys. Rev. Lett. 127, 020602 (2021).
(a) QGAN flow chart. (B) Simple schematic diagram of Quan Unicom's sample chip. (C) QGAN actual algorithm circuit diagram, in which the magenta part is the quantum gradient calculation circuit.
(a) The result of arbitrary single-qubit mixed state training. (B) Compared with the real density matrix obtained by training, the fidelity can reach 0.999.
(a) XOR gate training results. The fidelity of the trained truth table is 0.927. (B) Changes in the parameters of the two characteristic single-bit quantum gates during the training process.
