  Adiabatic quantum computation (AQC) is a universal model for quantum
computation which seeks to transform the initial ground state of a quantum
system into a final ground state encoding the answer to a computational
problem. AQC initial Hamiltonians conventionally have a uniform superposition
as ground state. We diverge from this practice by introducing a simple form of
heuristics: the ability to start the quantum evolution with a state which is a
guess to the solution of the problem. With this goal in mind, we explain the
viability of this approach and the needed modifications to the conventional AQC
(CAQC) algorithm. By performing a numerical study on hard-to-satisfy 6 and 7
bit random instances of the satisfiability problem (3-SAT), we show how this
heuristic approach is possible and we identify that the performance of the
particular algorithm proposed is largely determined by the Hamming distance of
the chosen initial guess state with respect to the solution. Besides the
possibility of introducing educated guesses as initial states, the new strategy
allows for the possibility of restarting a failed adiabatic process from the
measured excited state as opposed to restarting from the full superposition of
states as in CAQC. The outcome of the measurement can be used as a more refined
guess state to restart the adiabatic evolution. This concatenated restart
process is another heuristic that the CAQC strategy cannot capture.
