Abstract
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.
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