Efficient Realization of Unitary Transformation at the Quantum Speed Limit

We numerically investigate the minimum time required to implement a target unitary transformation in a qubit network in which each qubit can be locally controlled. The speed limits are explicitly analyzed for qubit graphs used to represent simple models of a Ising spin chain, or a central spin which describes electron-nuclear spin interactions in NV centers. We study the tightness of the obtained speed limits via comparing with the bound derived by Arenz et al. It is shown that the limits capture the coupling constant present in the graph dependence of the minimum evolution time remarkably well.