Quantum measurement-based feedback simulation of complex dynamics of mean-field $p$-spin models.

We study a method for simulating the nonlinear dynamics of many-body spin systems based on measurement-based feedback. We focus on $p$-spin models describing an Ising-like model on a completely connected graph with $p$-body interactions. These models exhibit diverse critical phenomena. For $p=2$ this recovers the Lipkin-Meshkov-Glick (LMG) model, exhibiting a continuous second-order phase transition between paramagnetic and ferromagnetic phases. For $p>2$, the phase transition is a first order and discontinuous. Our protocol considers the collective spin of an ensemble on $N$ qubits, and approximates the dynamics by weakly measuring one projection of the collective spin, followed by unitary evolution conditioned on the measurement outcome~\footnote{Munoz-Arias, et. al, PRL 124, 110503 (2020)}~\footnote{Munoz-Arias, et. al, PRA 102, 022610 (2020)}. We use our scheme to simulate dynamical quantum phase transitions of $p$-spin models, and explore a possible experimental implementation of these dynamical quantum simulations on an atom-light interface.