%0 Journal Article
%T The relationship between minimum gap and success probability in adiabatic quantum computing
%A M. Cullimore
%A M. J. Everitt
%A M. A. Ormerod
%A J. H. Samson
%A R. D. Wilson
%A A. M. Zagoskin
%J Mathematics
%D 2011
%I arXiv
%R 10.1088/1751-8113/45/50/505305
%X We explore the relationship between two figures of merit for an adiabatic quantum computation process: the success probability $P$ and the minimum gap $\Delta_{min}$ between the ground and first excited states, investigating to what extent the success probability for an ensemble of problem Hamiltonians can be fitted by a function of $\Delta_{min}$ and the computation time $T$. We study a generic adiabatic algorithm and show that a rich structure exists in the distribution of $P$ and $\Delta_{min}$. In the case of two qubits, $P$ is to a good approximation a function of $\Delta_{min}$, of the stage in the evolution at which the minimum occurs and of $T$. This structure persists in examples of larger systems.
%U http://arxiv.org/abs/1107.4034v2