Temporal Entanglement in Chaotic Quantum Circuits
The concept of space evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. The basic idea involves exchanging the roles of space and time, evolving the system using a space transfer matrix rather than the time evolution operator. The infinite-volume lim...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-10-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.13.041008 |
| _version_ | 1797661537611022336 |
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| author | Alessandro Foligno Tianci Zhou Bruno Bertini |
| author_facet | Alessandro Foligno Tianci Zhou Bruno Bertini |
| author_sort | Alessandro Foligno |
| collection | DOAJ |
| description | The concept of space evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. The basic idea involves exchanging the roles of space and time, evolving the system using a space transfer matrix rather than the time evolution operator. The infinite-volume limit is then described by the fixed points of the latter transfer matrix, also known as influence matrices. To establish the potential of this method as a bona fide computational scheme, it is important to understand whether the influence matrices can be efficiently encoded in a classical computer. Here we begin this quest by presenting a systematic characterization of their entanglement—dubbed temporal entanglement—in chaotic quantum systems. We consider the most general form of space evolution, i.e., evolution in a generic spacelike direction, and present two fundamental results. First, we show that temporal entanglement always follows a volume law in time. Second, we identify two marginal cases—(i) pure space evolution in generic chaotic systems and (ii) any spacelike evolution in dual-unitary circuits—where Rényi entropies with index larger than one are sublinear in time while the von Neumann entanglement entropy grows linearly. We attribute this behavior to the existence of a product state with large overlap with the influence matrices. This unexpected structure in the temporal entanglement spectrum might be the key to an efficient computational implementation of the space evolution. |
| first_indexed | 2024-03-11T18:47:07Z |
| format | Article |
| id | doaj.art-c4bb3d0e25a14031802843ac04f15a06 |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-03-11T18:47:07Z |
| publishDate | 2023-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-c4bb3d0e25a14031802843ac04f15a062023-10-11T17:55:33ZengAmerican Physical SocietyPhysical Review X2160-33082023-10-0113404100810.1103/PhysRevX.13.041008Temporal Entanglement in Chaotic Quantum CircuitsAlessandro FolignoTianci ZhouBruno BertiniThe concept of space evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. The basic idea involves exchanging the roles of space and time, evolving the system using a space transfer matrix rather than the time evolution operator. The infinite-volume limit is then described by the fixed points of the latter transfer matrix, also known as influence matrices. To establish the potential of this method as a bona fide computational scheme, it is important to understand whether the influence matrices can be efficiently encoded in a classical computer. Here we begin this quest by presenting a systematic characterization of their entanglement—dubbed temporal entanglement—in chaotic quantum systems. We consider the most general form of space evolution, i.e., evolution in a generic spacelike direction, and present two fundamental results. First, we show that temporal entanglement always follows a volume law in time. Second, we identify two marginal cases—(i) pure space evolution in generic chaotic systems and (ii) any spacelike evolution in dual-unitary circuits—where Rényi entropies with index larger than one are sublinear in time while the von Neumann entanglement entropy grows linearly. We attribute this behavior to the existence of a product state with large overlap with the influence matrices. This unexpected structure in the temporal entanglement spectrum might be the key to an efficient computational implementation of the space evolution.http://doi.org/10.1103/PhysRevX.13.041008 |
| spellingShingle | Alessandro Foligno Tianci Zhou Bruno Bertini Temporal Entanglement in Chaotic Quantum Circuits Physical Review X |
| title | Temporal Entanglement in Chaotic Quantum Circuits |
| title_full | Temporal Entanglement in Chaotic Quantum Circuits |
| title_fullStr | Temporal Entanglement in Chaotic Quantum Circuits |
| title_full_unstemmed | Temporal Entanglement in Chaotic Quantum Circuits |
| title_short | Temporal Entanglement in Chaotic Quantum Circuits |
| title_sort | temporal entanglement in chaotic quantum circuits |
| url | http://doi.org/10.1103/PhysRevX.13.041008 |
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