We investigate the effects of a generic noise source on a prototypical adiabatic quantum algorithm. We take an alternative eigenvalue dynamics viewpoint and derive a generalised, stochastic form of the Pechukas-Yukawa model. The distribution of avoided crossings in the energy spectra is then analysed in order to estimate the probability of level occupation.
We find that the probability of successfully finding the system in the solution state decreases polynomially with the computation speed and that this relationship is independent of the noise amplitude. The overall regularity of the eigenvalue dynamics is shown to be relatively unaffected by noise perturbations. These results imply that adiabatic quantum computation is a relatively stable process and possesses a degree of resistance against the effects of noise. We also show that generic noise will inherently break any symmetries, and therefore remove degeneracies, in the energy spectrum that might otherwise have impeded the computation process. This suggests that the conventional stipulation that the initial and final Hamiltonians do not commute is unnecessary in realistic physical systems. We explore the effects of an artificial noise source with a specifically engineered time-dependent amplitude and show that such a scheme could provide a significant enhancement to the performance of the computation.
Finally, we formulate an extended version of the Pechukas-Yukawa formalism. This provides a complete description of the dynamics of a quantum system by way of an exact mapping to a system of classical equations of motion.
A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University.