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We extend the work in New J. Phys. 19, 103015 (2017) by deriving a lowerbound for the minimum time necessary to implement a unitary transformation on ageneric, closed quantum system with an arbitrary number of classical controlfields. This bound is explicitly analyzed for a specific N-level system similarto those used to represent simple models of an atom, or the first excitationsector of a Heisenberg spin chain, both of which are of interest in quantumcontrol for quantum computation. Specifically, it is shown that the resultantbound depends on the dimension of the system, and on the number of controlsused to implement a specific target unitary operation. The value of the bounddetermined numerically, and an estimate of the true minimum gate time aresystematically compared for a range of system dimension and number of controls;special attention is drawn to the relationship between these two variables. Itis seen that the bound captures the scaling of the minimum time well for thesystems studied, and quantitatively is correct in the order of magnitude.

Dependence of the Quantum Speed Limit on System Size and Control Complexity