Quantum and Classical Dynamics with Random Permutation Circuits
Understanding thermalization in quantum many-body systems is among the most enduring problems in modern physics. A particularly interesting question concerns the role played by quantum mechanics in this process, i.e., whether thermalization in quantum many-body systems is fundamentally different fro...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-01-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.15.011015 |
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| _version_ | 1832583376527163392 |
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| author | Bruno Bertini Katja Klobas Pavel Kos Daniel Malz |
| author_facet | Bruno Bertini Katja Klobas Pavel Kos Daniel Malz |
| author_sort | Bruno Bertini |
| collection | DOAJ |
| description | Understanding thermalization in quantum many-body systems is among the most enduring problems in modern physics. A particularly interesting question concerns the role played by quantum mechanics in this process, i.e., whether thermalization in quantum many-body systems is fundamentally different from that in classical many-body systems and, if so, which of its features are genuinely quantum. Here, we study this question in minimally structured many-body systems that are only constrained to have local interactions, i.e., local random circuits. In particular, we introduce random permutation circuits (RPCs), which are circuits comprising gates that locally permute basis states, as a counterpart to random unitary circuits (RUCs), a standard toy model for generic quantum dynamics. RPCs represent a model for generic microscopic classical reversible dynamics but, interestingly, can be interpreted both as classical or as quantum dynamics. We show that, upon averaging over all circuit realizations, RPCs permit the analytical computation of several key quantities such as out-of-time-order correlators (OTOCs) and entanglement entropies. In the classical setting, we obtain similar exact results relating (quantum) purity to (classical) growth of mutual information and (quantum) OTOCs to (classical) decorrelators. We, thus, discover a series of exact relations, connecting quantities in RUC and (quantum or classical) RPCs. Our results indicate that, despite the fundamental differences between quantum and classical systems, their many-body dynamics exhibits remarkably similar behaviors. |
| format | Article |
| id | doaj-art-cc1699a99db443dbb2c195eb7e941955 |
| institution | Kabale University |
| issn | 2160-3308 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj-art-cc1699a99db443dbb2c195eb7e9419552025-01-28T16:49:38ZengAmerican Physical SocietyPhysical Review X2160-33082025-01-0115101101510.1103/PhysRevX.15.011015Quantum and Classical Dynamics with Random Permutation CircuitsBruno BertiniKatja KlobasPavel KosDaniel MalzUnderstanding thermalization in quantum many-body systems is among the most enduring problems in modern physics. A particularly interesting question concerns the role played by quantum mechanics in this process, i.e., whether thermalization in quantum many-body systems is fundamentally different from that in classical many-body systems and, if so, which of its features are genuinely quantum. Here, we study this question in minimally structured many-body systems that are only constrained to have local interactions, i.e., local random circuits. In particular, we introduce random permutation circuits (RPCs), which are circuits comprising gates that locally permute basis states, as a counterpart to random unitary circuits (RUCs), a standard toy model for generic quantum dynamics. RPCs represent a model for generic microscopic classical reversible dynamics but, interestingly, can be interpreted both as classical or as quantum dynamics. We show that, upon averaging over all circuit realizations, RPCs permit the analytical computation of several key quantities such as out-of-time-order correlators (OTOCs) and entanglement entropies. In the classical setting, we obtain similar exact results relating (quantum) purity to (classical) growth of mutual information and (quantum) OTOCs to (classical) decorrelators. We, thus, discover a series of exact relations, connecting quantities in RUC and (quantum or classical) RPCs. Our results indicate that, despite the fundamental differences between quantum and classical systems, their many-body dynamics exhibits remarkably similar behaviors.http://doi.org/10.1103/PhysRevX.15.011015 |
| spellingShingle | Bruno Bertini Katja Klobas Pavel Kos Daniel Malz Quantum and Classical Dynamics with Random Permutation Circuits Physical Review X |
| title | Quantum and Classical Dynamics with Random Permutation Circuits |
| title_full | Quantum and Classical Dynamics with Random Permutation Circuits |
| title_fullStr | Quantum and Classical Dynamics with Random Permutation Circuits |
| title_full_unstemmed | Quantum and Classical Dynamics with Random Permutation Circuits |
| title_short | Quantum and Classical Dynamics with Random Permutation Circuits |
| title_sort | quantum and classical dynamics with random permutation circuits |
| url | http://doi.org/10.1103/PhysRevX.15.011015 |
| work_keys_str_mv | AT brunobertini quantumandclassicaldynamicswithrandompermutationcircuits AT katjaklobas quantumandclassicaldynamicswithrandompermutationcircuits AT pavelkos quantumandclassicaldynamicswithrandompermutationcircuits AT danielmalz quantumandclassicaldynamicswithrandompermutationcircuits |