We introduce a method for digital preparation of ground states of a simulated Hamiltonians, inspired by cooling in nature and adapted to leverage the capabilities of digital quantum hardware. The cold bath is simulated by a single ancillary qubit, which is reset periodically and coupled to the system non-perturbatively. Studying this cooling method on a 1-qubit system toy model allows us to optimize two cooling protocols based on weak-coupling and strong-coupling approaches. Extending the insight from the 1-qubit system model, we develop two scalable protocols for larger systems. The LogSweep protocol extends the weak-coupling approach by sweeping energies to resonantly match any targeted transition. It demonstrates the ability to prepare an approximate ground state of tranverse-field Ising chains in the ferromangetic and critical phases, with an error that can be made polynomially small in time. The BangBang protocol extends the strong-coupling approach, and exploits a heuristics for local Hamiltonians to maximise the probability of de-exciting system transitions in the shortest possible time. Although this protocol does not promise long-time convergence, it allows for a rapid cooling to an approximation of the ground state, making this protocol appealing for near-term simulation applications.
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