Quantum optimization methods in water flow control

This paper examines the problem of optimizing water flow control in order to minimize costs, represented as the square of the water flow. This takes into account restrictions on this flow, such as the maximum flow value. To solve this problem, two optimization methods are used: the classical optimization method Sequential Least SQuares Programming (SLSQP) and the quantum optimization method Variational Quantum Eigensolver (VQE). First, the classical SLSQP method finds the optimal control (water flow) according to the given cost function and constraints. Then the obtained result is refined using the quantum VQE method. The quantum method uses an ansatz to represent the quantum circuit and a Hamiltonian to describe the system. The problem comes down to finding the minimum eigenvalue of the Hamiltonian, which makes it possible to determine the optimal parameters of the quantum circuit that minimize the cost of controlling the water flow. Thus, the proposed approach combines the strengths of classical and quantum optimization to effectively solve the water flow control optimization problem.