Cayley graphs and complexity geometry
Abstract The basic idea of quantum complexity geometry is to endow the space of unitary matrices with a metric, engineered to make complex operators far from the identity, and simple operators near. By restricting our attention to a finite subgroup of the unitary group, we observe that this idea can...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-02-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP02(2019)063 |
| Summary: | Abstract The basic idea of quantum complexity geometry is to endow the space of unitary matrices with a metric, engineered to make complex operators far from the identity, and simple operators near. By restricting our attention to a finite subgroup of the unitary group, we observe that this idea can be made rigorous: the complexity geometry becomes what is known as a Cayley graph. This connection allows us to translate results from the geometrical group theory literature into statements about complexity. For example, the notion of δ-hyperbolicity makes precise the idea that complexity geometry is negatively curved. We report an exact (in the large N limit) computation of the average complexity as a function of time in a random circuit model. |
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| ISSN: | 1029-8479 |