  In quantum adiabatic evolution algorithms, the quantum computer follows the
ground state of a slowly varying Hamiltonian. The ground state of the initial
Hamiltonian is easy to construct; the ground state of the final Hamiltonian
encodes the solution of the computational problem. These algorithms have
generally been studied in the case where the "straight line" path from initial
to final Hamiltonian is taken. But there is no reason not to try paths
involving terms that are not linear combinations of the initial and final
Hamiltonians. We give several proposals for randomly generating new paths.
Using one of these proposals, we convert an algorithmic failure into a success.
