Various adaptations to adiabatic quantum computation and quantum annealing are described. These adaptations generally involve tailoring an initial Hamiltonian so that a local minimum is avoided when a quantum processor is evolved from the initial Hamiltonian to a problem Hamiltonian. The initial Hamiltonian may represent a mixed Hamiltonian that includes both diagonal and off-diagonal terms, where the diagonal terms at least partially define a center point of a first computation space that is at least partially contained within a second computation space. A problem Hamiltonian may be evolved into a low energy state by inhomogeneously inducing disorder in the qubits of the quantum processor. A higher degree of disorder may be induced in a subset of qubits predicted to contribute to a local minimum of the problem Hamiltonian.