Abstract: A hybrid computing system comprising a digital and an analog processor calculates the ground energy state of a non-diagonal Hamiltonian via diagonalization of the Hamiltonian in different bases and reverse annealing. A first basis is rotated to render part of the Hamiltonian diagonal, then the quantum processor evolves backwards until a value s* of the normalized evolution coefficient. Another basis is rotated to render another part of the Hamiltonian diagonal and the quantum processor evolves backwards again until s*. The bases can be rotated via discrete Fourier transform. The quantum processor may pause for a time t after each backward evolution. The ground state energy is calculated using the final ground states.

Abstract: A hybrid computing system comprising a digital and an analog processor calculates the ground energy state of a non-diagonal Hamiltonian via diagonalization of the Hamiltonian in different bases and reverse annealing. A first basis is rotated to render part of the Hamiltonian diagonal, then the quantum processor evolves backwards until a value s* of the normalized evolution coefficient. Another basis is rotated to render another part of the Hamiltonian diagonal and the quantum processor evolves backwards again until s*. The bases can be rotated via discrete Fourier transform. The quantum processor may pause for a time t after each backward evolution. The ground state energy is calculated using the final ground states.