Relationship between minimum gap and success probability in adiabatic quantum computing
journal contributionposted on 31.01.2013, 14:43 by M. Cullimore, Mark EverittMark Everitt, M.A. Ormerod, John SamsonJohn Samson, Richard D. Wilson, Alexandre ZagoskinAlexandre Zagoskin
We explore the relationship between two figures of merit for an adiabatic quantum computation process: the success probability P and the minimum gap Δmin 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 Δmin and the computation time T. We study a generic adiabatic algorithm and show that a rich structure exists in the distribution of P and Δmin. In the case of two qubits, P is to a good approximation a function of Δmin, of the stage in the evolution at which the minimum occurs and of T. This structure persists in examples of larger systems.