Circuit complexity in quantum field theory
Abstract Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of Gaussian states, in particular the ground state, in a free scalar field theory for general dimensions. Appl...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP10(2017)107 |
| _version_ | 1819028355413966848 |
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| author | Robert A. Jefferson Robert C. Myers |
| author_facet | Robert A. Jefferson Robert C. Myers |
| author_sort | Robert A. Jefferson |
| collection | DOAJ |
| description | Abstract Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of Gaussian states, in particular the ground state, in a free scalar field theory for general dimensions. Applying the geometric approach of Nielsen to this quantum circuit model, the complexity of the state becomes the length of the shortest geodesic in the space of circuits. We compare the complexity of the ground state of the free scalar field to the analogous results from holographic complexity, and find some surprising similarities. |
| first_indexed | 2024-12-21T05:57:03Z |
| format | Article |
| id | doaj.art-9fe0ce1a6d8f4232afb70afc56d9304e |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T05:57:03Z |
| publishDate | 2017-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-9fe0ce1a6d8f4232afb70afc56d9304e2022-12-21T19:13:50ZengSpringerOpenJournal of High Energy Physics1029-84792017-10-0120171018110.1007/JHEP10(2017)107Circuit complexity in quantum field theoryRobert A. Jefferson0Robert C. Myers1Perimeter Institute for Theoretical PhysicsPerimeter Institute for Theoretical PhysicsAbstract Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of Gaussian states, in particular the ground state, in a free scalar field theory for general dimensions. Applying the geometric approach of Nielsen to this quantum circuit model, the complexity of the state becomes the length of the shortest geodesic in the space of circuits. We compare the complexity of the ground state of the free scalar field to the analogous results from holographic complexity, and find some surprising similarities.http://link.springer.com/article/10.1007/JHEP10(2017)107AdS-CFT CorrespondenceEffective Field TheoriesBlack Holes in String TheoryLattice Quantum Field Theory |
| spellingShingle | Robert A. Jefferson Robert C. Myers Circuit complexity in quantum field theory Journal of High Energy Physics AdS-CFT Correspondence Effective Field Theories Black Holes in String Theory Lattice Quantum Field Theory |
| title | Circuit complexity in quantum field theory |
| title_full | Circuit complexity in quantum field theory |
| title_fullStr | Circuit complexity in quantum field theory |
| title_full_unstemmed | Circuit complexity in quantum field theory |
| title_short | Circuit complexity in quantum field theory |
| title_sort | circuit complexity in quantum field theory |
| topic | AdS-CFT Correspondence Effective Field Theories Black Holes in String Theory Lattice Quantum Field Theory |
| url | http://link.springer.com/article/10.1007/JHEP10(2017)107 |
| work_keys_str_mv | AT robertajefferson circuitcomplexityinquantumfieldtheory AT robertcmyers circuitcomplexityinquantumfieldtheory |