Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
We investigate operator dynamics and entanglement growth in dual-unitary circuits, a class of locally scrambled quantum systems that enables efficient simulation beyond the exponential complexity of the Hilbert space. By mapping the operator evolution to a classical Markov process, we perform Monte...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-04-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-04-01-1681/pdf/ |
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| _version_ | 1849337727509594112 |
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| author | Menghan Song Zhaoyi Zeng Ting-Tung Wang Yi-Zhuang You Zi Yang Meng Pengfei Zhang |
| author_facet | Menghan Song Zhaoyi Zeng Ting-Tung Wang Yi-Zhuang You Zi Yang Meng Pengfei Zhang |
| author_sort | Menghan Song |
| collection | DOAJ |
| description | We investigate operator dynamics and entanglement growth in dual-unitary circuits, a class of locally scrambled quantum systems that enables efficient simulation beyond the exponential complexity of the Hilbert space. By mapping the operator evolution to a classical Markov process, we perform Monte Carlo simulations to access the time evolution of local operator density and entanglement with polynomial computational cost. Our results reveal that the operator density converges exponentially to a steady-state value, with analytical bounds that match our simulations. Additionally, we observe a volume-law scaling of operator entanglement across different subregions, and identify a critical transition from maximal to sub-maximal entanglement growth, governed by the circuit’s gate parameter. This transition, confirmed by both mean-field theory and Monte Carlo simulations, provides new insights into operator entanglement dynamics in quantum many-body systems. Our work offers a scalable computational framework for studying long-time operator evolution and entanglement, paving the way for deeper exploration of quantum information dynamics. |
| format | Article |
| id | doaj-art-7a0ca9d99e214d20a1c12fe94a2abc39 |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-7a0ca9d99e214d20a1c12fe94a2abc392025-08-20T03:44:36ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-04-019168110.22331/q-2025-04-01-168110.22331/q-2025-04-01-1681Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary CircuitsMenghan SongZhaoyi ZengTing-Tung WangYi-Zhuang YouZi Yang MengPengfei ZhangWe investigate operator dynamics and entanglement growth in dual-unitary circuits, a class of locally scrambled quantum systems that enables efficient simulation beyond the exponential complexity of the Hilbert space. By mapping the operator evolution to a classical Markov process, we perform Monte Carlo simulations to access the time evolution of local operator density and entanglement with polynomial computational cost. Our results reveal that the operator density converges exponentially to a steady-state value, with analytical bounds that match our simulations. Additionally, we observe a volume-law scaling of operator entanglement across different subregions, and identify a critical transition from maximal to sub-maximal entanglement growth, governed by the circuit’s gate parameter. This transition, confirmed by both mean-field theory and Monte Carlo simulations, provides new insights into operator entanglement dynamics in quantum many-body systems. Our work offers a scalable computational framework for studying long-time operator evolution and entanglement, paving the way for deeper exploration of quantum information dynamics.https://quantum-journal.org/papers/q-2025-04-01-1681/pdf/ |
| spellingShingle | Menghan Song Zhaoyi Zeng Ting-Tung Wang Yi-Zhuang You Zi Yang Meng Pengfei Zhang Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits Quantum |
| title | Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits |
| title_full | Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits |
| title_fullStr | Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits |
| title_full_unstemmed | Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits |
| title_short | Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits |
| title_sort | monte carlo simulation of operator dynamics and entanglement in dual unitary circuits |
| url | https://quantum-journal.org/papers/q-2025-04-01-1681/pdf/ |
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