Quantum Computation as Gravity
We formulate Nielsen's geometric approach to circuit complexity in the context of two-dimensional conformal field theories, where series of conformal transformations are interpreted as "unitary circuits" built from energy-momentum tensor gates. We show that the complexity functional i...
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| Published in: | Physical review letters Vol. 122; no. 23; p. 231302 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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American Physical Society
14.06.2019
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| ISSN: | 0031-9007, 1079-7114, 1079-7114 |
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| Abstract | We formulate Nielsen's geometric approach to circuit complexity in the context of two-dimensional conformal field theories, where series of conformal transformations are interpreted as "unitary circuits" built from energy-momentum tensor gates. We show that the complexity functional in this setup can be written as the Polyakov action of two-dimensional gravity or, equivalently, as the geometric action on the coadjoint orbits of the Virasoro group. This way, we argue that gravity sets the rules for optimal quantum computation in conformal field theories. |
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| AbstractList | We formulate Nielsen's geometric approach to circuit complexity in the context of two-dimensional conformal field theories, where series of conformal transformations are interpreted as "unitary circuits" built from energy-momentum tensor gates. We show that the complexity functional in this setup can be written as the Polyakov action of two-dimensional gravity or, equivalently, as the geometric action on the coadjoint orbits of the Virasoro group. This way, we argue that gravity sets the rules for optimal quantum computation in conformal field theories.We formulate Nielsen's geometric approach to circuit complexity in the context of two-dimensional conformal field theories, where series of conformal transformations are interpreted as "unitary circuits" built from energy-momentum tensor gates. We show that the complexity functional in this setup can be written as the Polyakov action of two-dimensional gravity or, equivalently, as the geometric action on the coadjoint orbits of the Virasoro group. This way, we argue that gravity sets the rules for optimal quantum computation in conformal field theories. We formulate Nielsen's geometric approach to circuit complexity in the context of two-dimensional conformal field theories, where series of conformal transformations are interpreted as "unitary circuits" built from energy-momentum tensor gates. We show that the complexity functional in this setup can be written as the Polyakov action of two-dimensional gravity or, equivalently, as the geometric action on the coadjoint orbits of the Virasoro group. This way, we argue that gravity sets the rules for optimal quantum computation in conformal field theories. |
| ArticleNumber | 231302 |
| Author | Magan, Javier M. Caputa, Paweł |
| Author_xml | – sequence: 1 givenname: Paweł surname: Caputa fullname: Caputa, Paweł – sequence: 2 givenname: Javier M. surname: Magan fullname: Magan, Javier M. |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/31298880$$D View this record in MEDLINE/PubMed |
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| Snippet | We formulate Nielsen's geometric approach to circuit complexity in the context of two-dimensional conformal field theories, where series of conformal... |
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| SubjectTerms | Complexity Computation Conformal mapping Gates (circuits) Gravitation Tensors |
| Title | Quantum Computation as Gravity |
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