Relationship between minimum gap and success probability in adiabatic quantum computing
M Cullimore, M. J. Everitt, M A Ormerod, John H. Samson, R D Wilson, Alexandre M. Zagoskin · Journal of Physics A Mathematical and Theoretical · 2012
We explore the relationship between two figures of merit for an adiabatic quantum computation process: the success probability P and the minimum gap Δ 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 Δ 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 Δ min . In the case of two qubits, P is to a good approximation a function of Δ min , of the stage in the evolution at which the minimum occurs and of T . This structure persists in examples of larger systems.