In the large-Hilbert-space limit, Floquet chaotic dynamics with Haar random gates produce linear shot-noise scaling of quantum Fisher information, with super-linear advantages at finite sizes, while local random circuits asymptotically mimic global unitaries.
Reimann, Foundation of Statistical Mechanics under Exper- imentally Realistic Conditions, Physical Review Letters101, 190403 (2008)
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Asymptotic Metrological Scaling and Concentration in Chaotic Floquet Dynamics
In the large-Hilbert-space limit, Floquet chaotic dynamics with Haar random gates produce linear shot-noise scaling of quantum Fisher information, with super-linear advantages at finite sizes, while local random circuits asymptotically mimic global unitaries.