Description
One paradigmatic route to exploring states of matter in analog quantum simulators is to perform adiabatic parameter sweeps. However, the presence of small gaps along the sweep, either due to unavoidable quantum phase transitions or competing orders, generically poses an obstacle to preparing desired ground states. Recently, it was shown that the slightly non-equilibrium nature of dynamical sweeps can aid in the preparation of finite-size analogs of exotic states of matter (coined quantum puddles or lakes), even in the absence of a ground state with the desired order. Here, we show that going even further out of equilibrium can accelerate the preparation of these quantum lakes. In particular, we utilize insights from counter-diabatic driving to construct specific external drives that enable lake creation along systematically faster parameter sweeps. We give numerical evidence for these claims by simulating the preparation of $\mathbb{Z}_2$ quantum spin lakes both in a deformed toric code model and a model for Rydberg atoms. We conclude by exploring the construction of local Hamiltonians whose quench dynamics take product states to these quantum lakes, potentially eliminating limitations on the sweep rate and further accelerating state preparation.
