  We propose a quantum algorithm for projecting a quantum system to eigenstates
of any Hermitian operator, provided one can access the associated
control-unitary evolution for the ancilla and the system, as well as the
measurement of the controlling ancillary qubit. Such a Hadamard-test like
primitive is iterated so as to achieve the spectral projection, and the
distribution of the projected eigenstates obeys the Born rule. This algorithm
can be used as a subroutine in the quantum annealing procedure by measurement
to drive the system to the ground state of a final Hamiltonian, and we simulate
this for quantum many-body spin chains.

Quantum Physics