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We study the application of a new method for simulating nonlinear dynamics ofmany-body spin systems using quantum measurement and feedback [Mu\~noz-Arias etal., Phys. Rev. Lett. 124, 110503 (2020)] to a broad class of many-body modelsknown as $p$-spin Hamiltonians, which describe Ising-like models on acompletely connected graph with $p$-body interactions. The method simulates thedesired mean field dynamics in the thermodynamic limit by combiningnonprojective measurements of a component of the collective spin with a globalrotation conditioned on the measurement outcome. We apply this protocol tosimulate the dynamics of the $p$-spin Hamiltonians and demonstrate howdifferent aspects of criticality in the mean-field regime are readilyaccessible with our protocol. We study applications including properties ofdynamical phase transitions and the emergence of spontaneous symmetry breakingin the adiabatic dynamics of the collective spin for different values of theparameter $p$. We also demonstrate how this method can be employed to study thequantum-to-classical transition in the dynamics continuously as a function ofsystem size.

Simulation of complex dynamics of mean-field $p$-spin models using measurement-based quantum feedback control