Phase transitions in the classical simulability of open quantum systems
Abstract We introduce a Langevin unravelling of the density matrix evolution of an open quantum system over matrix product states, which we term the time-dependent variational principle-Langevin equation. This allows the study of entanglement dynamics as a function of both temperature and coupling t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-05-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-35336-9 |
| _version_ | 1797811527718273024 |
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| author | F. Azad A. Hallam J. Morley A. G. Green |
| author_facet | F. Azad A. Hallam J. Morley A. G. Green |
| author_sort | F. Azad |
| collection | DOAJ |
| description | Abstract We introduce a Langevin unravelling of the density matrix evolution of an open quantum system over matrix product states, which we term the time-dependent variational principle-Langevin equation. This allows the study of entanglement dynamics as a function of both temperature and coupling to the environment. As the strength of coupling to and temperature of the environment is increased, we find a transition where the entanglement of the individual trajectories saturates, permitting a classical simulation of the system for all times. This is the Hamiltonian open system counterpart of the saturation in entanglement found in random circuits with projective or weak measurements. If a system is open, there is a limit to the advantage in simulating its behaviour on a quantum computer, even when that evolution harbours important quantum effects. Moreover, if a quantum simulator is in this phase, it cannot simulate with quantum advantage. |
| first_indexed | 2024-03-13T07:25:02Z |
| format | Article |
| id | doaj.art-215cfa7a781d4013ac5a539c43128859 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-13T07:25:02Z |
| publishDate | 2023-05-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-215cfa7a781d4013ac5a539c431288592023-06-04T11:25:56ZengNature PortfolioScientific Reports2045-23222023-05-011311910.1038/s41598-023-35336-9Phase transitions in the classical simulability of open quantum systemsF. Azad0A. Hallam1J. Morley2A. G. Green3London Centre for Nanotechnology, University College LondonSchool of Physics and Astronomy, University of LeedsLondon Centre for Nanotechnology, University College LondonLondon Centre for Nanotechnology, University College LondonAbstract We introduce a Langevin unravelling of the density matrix evolution of an open quantum system over matrix product states, which we term the time-dependent variational principle-Langevin equation. This allows the study of entanglement dynamics as a function of both temperature and coupling to the environment. As the strength of coupling to and temperature of the environment is increased, we find a transition where the entanglement of the individual trajectories saturates, permitting a classical simulation of the system for all times. This is the Hamiltonian open system counterpart of the saturation in entanglement found in random circuits with projective or weak measurements. If a system is open, there is a limit to the advantage in simulating its behaviour on a quantum computer, even when that evolution harbours important quantum effects. Moreover, if a quantum simulator is in this phase, it cannot simulate with quantum advantage.https://doi.org/10.1038/s41598-023-35336-9 |
| spellingShingle | F. Azad A. Hallam J. Morley A. G. Green Phase transitions in the classical simulability of open quantum systems Scientific Reports |
| title | Phase transitions in the classical simulability of open quantum systems |
| title_full | Phase transitions in the classical simulability of open quantum systems |
| title_fullStr | Phase transitions in the classical simulability of open quantum systems |
| title_full_unstemmed | Phase transitions in the classical simulability of open quantum systems |
| title_short | Phase transitions in the classical simulability of open quantum systems |
| title_sort | phase transitions in the classical simulability of open quantum systems |
| url | https://doi.org/10.1038/s41598-023-35336-9 |
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