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We study the controllability of a central spin guided by a classical fieldand interacting with a spin bath, showing that the central spin is fullycontrollable independently of the number of bath spins. Additionally we findthat for unequal system-bath couplings even the bath becomes controllable byacting on the central spin alone. We then analyze numerically how the time toimplement gates on the central spin scales with the number of bath spins andconjecture that for equal system-bath couplings it reaches a saturation value.We provide evidence that sometimes noise can be effectively suppressed throughcontrol.

Control of open quantum systems: Case study of the central spin model