Abstract: A computer-implemented method for solving a computational problem comprises receiving information about a target function associated an object or a process having an input variable of domain X, the information including a differential equation comprising one or more derivatives of the target function and associated boundary conditions; using a functional relation defining that a derivative of a surrogate function G with respect to the input variable equals a product of a kernel function k and the target function; training a neural network so that the trained neural network represents the surrogate function; and, computing the solution, the computing including providing at least a first integral limit and a second integral limit of the input variable to the input to obtain a first function value and a second function value of the surrogate function respectively and, determining the integral transform based on the first function value and the second function value.

Abstract: Methods and systems determine a solution for an optimization problem using a quantum computer and a classical computer. The method comprises: receiving or determining, by the classical computer, a description of the problem; receiving or determining, by the classical computer, one or more quantum circuits defining gate operations to be executed by the quantum computer; determining, by the classical computer, an optimized first parametric quantum circuit comprising execution, by the quantum computer, of the gate operations; determining, using the quantum computer, an optimized input value in the input space; and determining, by the classical computer, the solution to the optimization problem based on the optimized input value and/or an output value corresponding to that optimized input value.