In this short notes, we present the formulation of a kind of quantum algorithm, applicable to the polynomial optimization. The present algorithm introduces the quantum effect by means of the coordinate variables, the momentum variables, and the commutators, and the Plank constant, which shall establish the correspondence between the quantum and the classical cases. The formalism is an extension to the polynomial optimization in the ``classical'' sense; the relations among quantum mechanical values are represented by a semi-algebraic set ( by the set of polynomials and sign conditions), and the optimum is searched in this semi-algebraic set. In the context of this formalism, the optimization of the Ising model [QUBO model] will be a special case. However, the computational procedure proposed here is different from the quantum annealing which is now in vogue. We demonstrate the exemplary calculation through quantifier elimination (which is a kind of symbolic computation applicable to optimization and other problems).
Towards fast one-block quantifier elimination through generalised critical values
