Quon Classical Simulation: Unifying Cliffords, Matchgates and Entanglement
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908481773109248 |
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| author | Feng, Zixuan Liu, Zhengwei Lu, Fan Wang, Ningfeng |
| author_facet | Feng, Zixuan Liu, Zhengwei Lu, Fan Wang, Ningfeng |
| contents | We propose a new framework of topological complexity to study the computational complexity of quantum circuits and tensor networks. Within this framework, we establish the Quon Classical Simulation (QCS) for hybrid Clifford-Matchgate circuits, which is efficient for both Clifford circuits and Matchgate circuits, therefore answering a long standing open question on unifying efficient classical simulations. This framework is built upon the Quon language, a 2+1D topological quantum field theory with space-time boundary and defects. Its exponential computation complexity is captured by Magic holes, a topological feature capturing the global long-range entanglement. Both Clifford circuits and Matchgate circuits are free of Magic holes. Efficient classical simulations of Cliffords and Matchgates are implemented by two parallel operations, generalized surgery theory of 3-manifolds and Yang-Baxter relations on the 2D boundary respectively, with additional binary arithmetic properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quon Classical Simulation: Unifying Cliffords, Matchgates and Entanglement Feng, Zixuan Liu, Zhengwei Lu, Fan Wang, Ningfeng Quantum Physics Computational Complexity Mathematical Physics 81P45 We propose a new framework of topological complexity to study the computational complexity of quantum circuits and tensor networks. Within this framework, we establish the Quon Classical Simulation (QCS) for hybrid Clifford-Matchgate circuits, which is efficient for both Clifford circuits and Matchgate circuits, therefore answering a long standing open question on unifying efficient classical simulations. This framework is built upon the Quon language, a 2+1D topological quantum field theory with space-time boundary and defects. Its exponential computation complexity is captured by Magic holes, a topological feature capturing the global long-range entanglement. Both Clifford circuits and Matchgate circuits are free of Magic holes. Efficient classical simulations of Cliffords and Matchgates are implemented by two parallel operations, generalized surgery theory of 3-manifolds and Yang-Baxter relations on the 2D boundary respectively, with additional binary arithmetic properties. |
| title | Quon Classical Simulation: Unifying Cliffords, Matchgates and Entanglement |
| topic | Quantum Physics Computational Complexity Mathematical Physics 81P45 |
| url | https://arxiv.org/abs/2505.07804 |