Exploring nontrivial topology at quantum criticality in a superconducting processor

• URL: http://arxiv.org/abs/2501.04679v1
• Date: Wed, 08 Jan 2025 18:39:44 GMT
• Title: Exploring nontrivial topology at quantum criticality in a superconducting processor
• Authors: Ziqi Tan, Ke Wang, Sheng Yang, Fanhao Shen, Feitong Jin, Xuhao Zhu, Yujie Ji, Shibo Xu, Jiachen Chen, Yaozu Wu, Chuanyu Zhang, Yu Gao, Ning Wang, Yiren Zou, Aosai Zhang, Tingting Li, Zehang Bao, Zitian Zhu, Jiarun Zhong, Zhengyi Cui, Yihang Han, Yiyang He, Han Wang, Jianan Yang, Yanzhe Wang, Jiayuan Shen, Gongyu Liu, Zixuan Song, Jinfeng Deng, Hang Dong, Pengfei Zhang, Shao-Kai Jian, Hekang Li, Zhen Wang, Qiujiang Guo, Chao Song, Xue-Jia Yu, H. Wang, Hai-Qing Lin, Fei Wu,
• Abstract summary: We present an experimental exploration of the critical cluster Ising model by preparing its low-lying critical states on a superconducting processor with up to $100$ qubits. We develop an efficient method to probe the boundary $g$-function based on prepared low-energy states, which allows us to uniquely identify the nontrivial topology of the critical systems under study. Our results demonstrate the low-lying critical states as useful quantum resources for investigating the interplay between topology and quantum criticality.
• Score: 23.278631632470628
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• Abstract: The discovery of nontrivial topology in quantum critical states has introduced a new paradigm for classifying quantum phase transitions and challenges the conventional belief that topological phases are typically associated with a bulk energy gap. However, realizing and characterizing such topologically nontrivial quantum critical states with large particle numbers remains an outstanding experimental challenge in statistical and condensed matter physics. Programmable quantum processors can directly prepare and manipulate exotic quantum many-body states, offering a powerful path for exploring the physics behind these states. Here, we present an experimental exploration of the critical cluster Ising model by preparing its low-lying critical states on a superconducting processor with up to $100$ qubits. We develop an efficient method to probe the boundary $g$-function based on prepared low-energy states, which allows us to uniquely identify the nontrivial topology of the critical systems under study. Furthermore, by adapting the entanglement Hamiltonian tomography technique, we recognize two-fold topological degeneracy in the entanglement spectrum under periodic boundary condition, experimentally verifying the universal bulk-boundary correspondence in topological critical systems. Our results demonstrate the low-lying critical states as useful quantum resources for investigating the interplay between topology and quantum criticality.

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