期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 7, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP07(2018)139
关键词
AdS-CFT Correspondence; Effective Field Theories
资金
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Research Innovation
- Frymoyer fellowship
- Mebus fellowship
- National Science Foundation [PHY-1404204, NSF PHY17-48958]
- Natural Sciences and Engineering Research Council of Canada
- Simons Foundation through the It from Qubit collaboration
We study circuit complexity for free fermionic field theories and Gaussian states. Our definition of circuit complexity is based on the notion of geodesic distance on the Lie group of special orthogonal transformations equipped with a right-invariant metric. After analyzing the differences and similarities to bosonic circuit complexity, we develop a comprehensive mathematical framework to compute circuit complexity between arbitrary fermionic Gaussian states. We apply this framework to the free Dirac field in four dimensions where we compute the circuit complexity of the Dirac ground state with respect to several classes of spatially unentangled reference states. Moreover, we show that our methods can also be applied to compute the complexity of excited energy eigenstates of the free Dirac field. Finally, we discuss the relation of our results to alternative approaches based on the Fubini-Study metric, the relevance to holography and possible extensions.
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