  We introduce a method to perform imaginary time evolution in a controllable
quantum system using measurements and conditional unitary operations. By
performing a sequence of weak measurements based on the desired Hamiltonian
constructed by a Suzuki-Trotter decomposition, an evolution approximating
imaginary time evolution can be realized. The randomness due to measurement is
corrected using conditional unitary operations, making the evolution
deterministic. Both the measurements required for the algorithm and the
conditional unitary operations can be constructed efficiently. We show that the
algorithm converges only below a specified energy threshold and the complexity
is estimated for some specific problem instances.
