  The fast and faithful preparation of the ground state of quantum systems is a
challenging task but crucial for several applications in the realm of
quantum-based technologies. Decoherence poses a limit to the maximum
time-window allowed to an experiment to faithfully achieve such desired states.
This is of particular significance in critical systems, where the vanishing
energy gap challenges an adiabatic ground state preparation. We show that a
bang-bang protocol, consisting of a time evolution under two different values
of an externally tunable parameter, allows for a high-fidelity ground state
preparation in evolution times no longer than those required by the application
of standard optimal control techniques, such as the chopped-random basis
quantum optimization. In addition, owing to their reduced number of variables,
such bang-bang protocols are very well suited to optimization purposes,
reducing the increasing computational cost of other optimal control protocols.
We benchmark the performance of such approach through two paradigmatic models,
namely the Landau-Zener and the Lipkin-Meshkov-Glick model. Remarkably, the
critical ground state of the latter model can be prepared with a high fidelity
in a total evolution time that scales slower than the inverse of the vanishing
energy gap.
