Generation of genuine entanglement up to 51 superconducting qubits

Sirui Cao; Bujiao Wu; Fusheng Chen; Ming Gong; Yulin Wu; Yangsen Ye; Chen Zha; Haoran Qian; Chong Ying; Shaojun Guo; Qingling Zhu; He-Liang Huang; Youwei Zhao; Shaowei Li; Shiyu Wang; Jiale Yu; Daojin Fan; Dachao Wu; Hong Su; Hui Deng; Hao Rong; Yuan Li; Kaili Zhang; Tung-Hsun Chung; Futian Liang; Jin Lin; Yu Xu; Lihua Sun; Cheng Guo; Na Li; Yong-Heng Huo; Cheng-Zhi Peng; Chao-Yang Lu; Xiao Yuan; Xiaobo Zhu; Jian-Wei Pan

doi:10.1038/s41586-023-06195-1

Generation of genuine entanglement up to 51 superconducting qubits

Nature. 2023 Jul;619(7971):738-742. doi: 10.1038/s41586-023-06195-1. Epub 2023 Jul 12.

Authors

Sirui Cao^#^{1

2

3}, Bujiao Wu^#^{4

5}, Fusheng Chen^#^{1

2

3}, Ming Gong^#^{1

2

3}, Yulin Wu^{1

2

3}, Yangsen Ye^{1

2

3}, Chen Zha^{1

2

3}, Haoran Qian^{1

2

3}, Chong Ying^{1

2

3}, Shaojun Guo^{1

2

3}, Qingling Zhu^{1

2

3}, He-Liang Huang^{1

2

3}, Youwei Zhao^{1

2

3}, Shaowei Li^{1

2

3}, Shiyu Wang^{1

2

3}, Jiale Yu^{1

2

3}, Daojin Fan^{1

2

3}, Dachao Wu^{1

2

3}, Hong Su^{1

2

3}, Hui Deng^{1

2

3}, Hao Rong^{1

2

3}, Yuan Li^{1

2

3}, Kaili Zhang^{1

2

3}, Tung-Hsun Chung^{1

2

3}, Futian Liang^{1

2

3}, Jin Lin^{1

2

3}, Yu Xu^{1

2

3}, Lihua Sun^{1

2

3}, Cheng Guo^{1

2

3}, Na Li^{1

2

3}, Yong-Heng Huo^{1

2

3}, Cheng-Zhi Peng^{1

2

3}, Chao-Yang Lu^{1

2

3}, Xiao Yuan^{6

7

8}, Xiaobo Zhu^{9

10

11}, Jian-Wei Pan^{12

13

14}

Affiliations

¹ Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China.
² Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China.
³ Hefei National Laboratory, University of Science and Technology of China, Hefei, China.
⁴ Center on Frontiers of Computing Studies, Peking University, Beijing, China.
⁵ School of Computer Science, Peking University, Beijing, China.
⁶ Hefei National Laboratory, University of Science and Technology of China, Hefei, China. xiaoyuan@pku.edu.cn.
⁷ Center on Frontiers of Computing Studies, Peking University, Beijing, China. xiaoyuan@pku.edu.cn.
⁸ School of Computer Science, Peking University, Beijing, China. xiaoyuan@pku.edu.cn.
⁹ Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China. xbzhu16@ustc.edu.cn.
¹⁰ Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China. xbzhu16@ustc.edu.cn.
¹¹ Hefei National Laboratory, University of Science and Technology of China, Hefei, China. xbzhu16@ustc.edu.cn.
¹² Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China. pan@ustc.edu.cn.
¹³ Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China. pan@ustc.edu.cn.
¹⁴ Hefei National Laboratory, University of Science and Technology of China, Hefei, China. pan@ustc.edu.cn.

^# Contributed equally.

PMID: 37438533
DOI: 10.1038/s41586-023-06195-1

Abstract

Scalable generation of genuine multipartite entanglement with an increasing number of qubits is important for both fundamental interest and practical use in quantum-information technologies^1,2. On the one hand, multipartite entanglement shows a strong contradiction between the prediction of quantum mechanics and local realization and can be used for the study of quantum-to-classical transition^3,4. On the other hand, realizing large-scale entanglement is a benchmark for the quality and controllability of the quantum system and is essential for realizing universal quantum computing^5-8. However, scalable generation of genuine multipartite entanglement on a state-of-the-art quantum device can be challenging, requiring accurate quantum gates and efficient verification protocols. Here we show a scalable approach for preparing and verifying intermediate-scale genuine entanglement on a 66-qubit superconducting quantum processor. We used high-fidelity parallel quantum gates and optimized the fidelitites of parallel single- and two-qubit gates to be 99.91% and 99.05%, respectively. With efficient randomized fidelity estimation⁹, we realized 51-qubit one-dimensional and 30-qubit two-dimensional cluster states and achieved fidelities of 0.637 ± 0.030 and 0.671 ± 0.006, respectively. On the basis of high-fidelity cluster states, we further show a proof-of-principle realization of measurement-based variational quantum eigensolver¹⁰ for perturbed planar codes. Our work provides a feasible approach for preparing and verifying entanglement with a few hundred qubits, enabling medium-scale quantum computing with superconducting quantum systems.