  We study a method to simulate quantum many-body dynamics of spin ensembles
using measurement-based feedback. By performing a weak collective measurement
on a large ensemble of two-level quantum systems and applying global rotations
conditioned on the measurement outcome, one can simulate the dynamics of a
mean-field quantum kicked top, a standard paradigm of quantum chaos. We
analytically show that there exists a regime in which individual quantum
trajectories adequately recover the classical limit, and show the transition
between noisy quantum dynamics to full deterministic chaos described by
classical Lyapunov exponents. We also analyze the effects of decoherence, and
show that the proposed scheme represents a robust method to explore the
emergence of chaos from complex quantum dynamics in a realistic experimental
platform based on an atom-light interface.
