Interesting problems in quantum computation take the form of finding
low-energy states of spin systems with engineered Hamiltonians that encode the
problem data. Motivated by the practical possibility of producing very
low-temperature spin systems, we propose and exemplify the possibility to
compute by coupling the computational spins to a non-Markovian bath of spins
that serve as a heat sink. We demonstrate both analytically and numerically
that this strategy can achieve quantum advantage in the Grover search problem.Comment: 6 figure