  In the current era of noisy quantum devices, there is a need for quantum
algorithms that are efficient and robust against noise. Towards this end, we
introduce the projected cooling algorithm for quantum computation. The
projected cooling algorithm is able to construct the localized ground state of
any Hamiltonian with a translationally-invariant kinetic energy and
interactions that vanish at large distances. The term "localized" refers to
localization in position space. The method can be viewed as the quantum analog
of evaporative cooling. We start with an initial state with support over a
compact region of a large volume. We then drive the excited quantum states to
disperse and measure the remaining portion of the wave function left behind.
For the nontrivial examples we consider here, the improvement over other
methods is substantial. The only additional resource required is performing the
operations in a volume significantly larger than the size of the localized
state. These characteristics make the projected cooling algorithm a promising
tool for calculations of self-bound systems such as atomic nuclei.
