Abstract
A large class of optimisation problems can be mapped to the Ising model where all details are encoded in the coupling of spins. The task of the original mathematical optimisation is then equivalent to finding the ground state of the corresponding spin system which can be achieved via quantum annealing relying on the adiabatic theorem. Some of the inherent disadvantages of this procedure can be alleviated or resolved using a stochastic approach, and by coupling to the external environment. We show that careful engineering of the system-bath coupling at an individual spin level can further improve annealing.