The relationship between minimum gap and success probability in adiabatic quantum computing

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.

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