  We examine the circuit complexity of coherent states in a free scalar field
theory, applying Nielsen's geometric approach as in [1]. The complexity of the
coherent states have the same UV divergences as the vacuum state complexity and
so we consider the finite increase of the complexity of these states over the
vacuum state. One observation is that generally, the optimal circuits introduce
entanglement between the normal modes at intermediate stages even though our
reference state and target states are not entangled in this basis. We also
compare our results from Nielsen's approach with those found using the
Fubini-Study method of [2]. For general coherent states, we find that the
complexities, as well as the optimal circuits, derived from these two
approaches, are different.
