An idea for an application of the quantum annealing mechanism to construct a projection measurement in a collective space is proposed. We use the annealing mechanism to drive the pointer degree of freedom associated with the measurement process. The parameters in its problem Hamiltonian is given not as classical variables but as quantum variables (states). By additionally introducing successive short interactions so that the back reaction to the quantum state (to be measured) can be controlled, we invent a quantum mechanically parametrized quantum annealing process. Applying to a particular problem of discrimination of two collective states , we find that the process by the quantum mechanically parametrized annealing arrives at projection measurement in the collective space when the parametrizing quantum variables themselves are orthogonal (or distinguishable).
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