FIG. 4. Plot of the success probability, averaged over a number of noise realisations, against computation speed for the | 00 〉 → | 00 〉 and | 11 〉 → | 10 〉 operations of the CNOT gate with an artificial noise source with a time-dependent amplitude and α = 10. that, in general, the success probability of the algorithm scaled polynomially as a function of computation speed and this scaling was independent of the amplitude of the noise. We demonstrate that when the effects of noise are taken in to account, the criteria used to select an initial configuration for the system may be relaxed and it is not necessary to avoid symmetries in the Hamiltonian. This is because, the presence of noise will break any degeneracies in the energy spectrum, crucially those that exist between the ground and first excited states. In these situations, the success probability at a given computation speed was found to increase linearly with noise amplitude. It was noted that this increase comes at the expense of the fidelity of the final state, but an optimal compromise between the two factors exists. The effects of an artificial noise source with a time-dependent noise amplitude were also investigated. This scheme was found to offer significantly higher success probabilities at relatively fast computation speeds and could be engineered in such a way that the fidelity 11