Learning adiabatic quantum algorithms over optimization problems

An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem, and an evolution schedule such that the adiabatic condition is satisfied. A correct choice of these elements is crucial for an efficient adiabatic quantum computation. In this paper, we propose a hybrid quantum-classical algorithm that, by solving optimization problems with an adiabatic machine, determines a problem Hamiltonian assuming restrictions on the class of available problem Hamiltonians. The scheme is based on repeated calls to the quantum machine into a classical iterative structure. In particular, we suggest a technique to estimate the encoding of a given optimization problem into a problem Hamiltonian and we prove the convergence of the algorithm.