Quantum spin liquids are elusive long-range entangled states. Motivated by experiments in Rydberg quantum simulators, recent excitement has centered on the possibility of dynamically preparing a state with quantum spin-liquid correlations even when the ground-state phase diagram does not exhibit such a topological phase. Understanding the microscopic nature of such quantum spin “lake” states and their relationship to equilibrium spin-liquid order remains an essential question. Here, we extend the use of approximately symmetric neural quantum states for real-time evolution and directly simulate the dynamical preparation in systems of up to $N=384$ atoms. We analyze a variety of spin-liquid diagnostics as a function of the preparation protocol and optimize the extent of the quantum spin lake thus obtained. In the optimal case, the prepared state shows spin-liquid properties extending over half the system size, with a topological entanglement entropy plateauing close to $\gamma =\ln 2$. We extract two physical length scales, ${\lambda }_e$ and ${\xi }_m$, which constrain the extent of the quantum spin lake $\ell$ from above and below.

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• Quantum spin liquid
• Quantum state engineering
• Artificial neural networks