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Digital Simulation of Projective Non-Abelian Anyons with 68 Superconducting Qubits |
| Shibo Xu1†, Zheng-Zhi Sun2†, Ke Wang1†, Liang Xiang1, Zehang Bao1, Zitian Zhu1, Fanhao Shen1, Zixuan Song1, Pengfei Zhang1, Wenhui Ren1, Xu Zhang1, Hang Dong1, Jinfeng Deng1, Jiachen Chen1, Yaozu Wu1, Ziqi Tan1, Yu Gao1, Feitong Jin1, Xuhao Zhu1, Chuanyu Zhang1, Ning Wang1, Yiren Zou1, Jiarun Zhong1, Aosai Zhang1, Weikang Li2, Wenjie Jiang2, Li-Wei Yu3, Yunyan Yao1, Zhen Wang1,4, Hekang Li1, Qiujiang Guo1,4, Chao Song1,4*, H. Wang1,4*, and Dong-Ling Deng2,4,5* |
1School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
2Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, China
3Theoretical Physics Division, Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
4Hefei National Laboratory, Hefei 230088, China
5Shanghai Qi Zhi Institute, Shanghai 200232, China
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Shibo Xu, Zheng-Zhi Sun, Ke Wang et al 2023 Chin. Phys. Lett. 40 060301 |
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Abstract Non-Abelian anyons are exotic quasiparticle excitations hosted by certain topological phases of matter. They break the fermion-boson dichotomy and obey non-Abelian braiding statistics: their interchanges yield unitary operations, rather than merely a phase factor, in a space spanned by topologically degenerate wavefunctions. They are the building blocks of topological quantum computing. However, experimental observation of non-Abelian anyons and their characterizing braiding statistics is notoriously challenging and has remained elusive hitherto, in spite of various theoretical proposals. Here, we report an experimental quantum digital simulation of projective non-Abelian anyons and their braiding statistics with up to 68 programmable superconducting qubits arranged on a two-dimensional lattice. By implementing the ground states of the toric-code model with twists through quantum circuits, we demonstrate that twists exchange electric and magnetic charges and behave as a particular type of non-Abelian anyons, i.e., the Ising anyons. In particular, we show experimentally that these twists follow the fusion rules and non-Abelian braiding statistics of the Ising type, and can be explored to encode topological logical qubits. Furthermore, we demonstrate how to implement both single- and two-qubit logic gates through applying a sequence of elementary Pauli gates on the underlying physical qubits. Our results demonstrate a versatile quantum digital approach for simulating non-Abelian anyons, offering a new lens into the study of such peculiar quasiparticles.
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Received: 06 May 2023
Express Letter
Published: 09 May 2023
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