A computer (such as a classical computer, a quantum computer, or a hybrid quantum-classical computer) which performs PDE-constrained optimization of problems in cases in which, for a fixed set of design variables, there is an explicit expression for a set of state variables that is either optimal or an approximation to the optimal solution. This enables embodiments of the present invention to eliminate the state variables from the optimization problem and to formulate the optimization as a polynomial unconstrained binary optimization (PUBO) problem.
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