期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 4, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP04(2017)121
关键词
AdS-CFT Correspondence; Gauge-gravity correspondence; Random Systems; Holography and condensed matter physics (AdS/CMT)
资金
- Simons Foundation through the It from Qubit collaboration
- Fannie and John Hertz Foundation
- National Science Foundation [PHY-1606531]
- Paul Dirac Fund
- U.S. Department of Energy [DESC0012567]
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Research and Innovation
We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the frame potential, which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. Additionally, we prove that these 2k-point correlators for Pauli operators completely determine the k-fold channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.
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