  We propose a method based on deep reinforcement learning that efficiently
prepares a quantum many-body pure state in thermal or prethermal equilibrium.
The main physical intuition underlying the method is that the information on
the equilibrium states can be efficiently encoded/extracted by focusing on only
a few local observables, relying on the typicality of equilibrium states.
Instead of resorting to the expensive preparation protocol that adopts global
features such as the quantum state fidelity, we show that the equilibrium
states can be efficiently prepared only by learning the expectation values of
local observables. We demonstrate our method by preparing two illustrative
examples: Gibbs ensembles in non-integrable systems and generalized Gibbs
ensembles in integrable systems. Pure states prepared solely from local
observables are numerically shown to successfully encode the macroscopic
properties of the equilibrium states. Furthermore, we find that the preparation
errors, with respect to the system size, decay exponentially for Gibbs
ensembles and polynomially for generalized Gibbs ensembles, which are in
agreement with the finite-size fluctuation within thermodynamic ensembles. Our
method paves a path toward studying the thermodynamic and statistical
properties of quantum many-body systems in quantum hardware.
