Magic Class and the Convolution Group
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916118510174208 |
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| author | Bu, Kaifeng Jaffe, Arthur Wei, Zixia |
| author_facet | Bu, Kaifeng Jaffe, Arthur Wei, Zixia |
| contents | The classification of many-body quantum states plays a fundamental role in the study of quantum phases of matter. In this work, we propose an approach to classify quantum states by introducing the concept of magic class. In addition, we introduce an efficient coarse-graining procedure to extract the magic feature of states, which we call the ``convolution group (CG).'' We classify quantum states into different magic classes using the fixed points of the CG and circuit equivalence. We also show that magic classes can be characterized by symmetries and the quantum entropy of the CG fixed points. Finally, we discuss the connection between the CG and the renormalization group. These results may provide new insight into the study of the state classification and quantum phases of matter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05780 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Magic Class and the Convolution Group Bu, Kaifeng Jaffe, Arthur Wei, Zixia Quantum Physics Statistical Mechanics High Energy Physics - Theory Mathematical Physics The classification of many-body quantum states plays a fundamental role in the study of quantum phases of matter. In this work, we propose an approach to classify quantum states by introducing the concept of magic class. In addition, we introduce an efficient coarse-graining procedure to extract the magic feature of states, which we call the ``convolution group (CG).'' We classify quantum states into different magic classes using the fixed points of the CG and circuit equivalence. We also show that magic classes can be characterized by symmetries and the quantum entropy of the CG fixed points. Finally, we discuss the connection between the CG and the renormalization group. These results may provide new insight into the study of the state classification and quantum phases of matter. |
| title | Magic Class and the Convolution Group |
| topic | Quantum Physics Statistical Mechanics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2402.05780 |