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摘要
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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 -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.
Keyword:
AdS-CFT Correspondence
Random Systems
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期刊
IF:
5.5
论文数:
4.0W
被引数:
13.7W
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