  It is known that several sub-universal quantum computing models, such as the
IQP model, the Boson sampling model, the one-clean qubit model, and the random
circuit model, cannot be classically simulated in polynomial time under certain
conjectures in classical complexity theory. Recently, these results have been
improved to "fine-grained" versions where even exponential-time classical
simulations are excluded assuming certain classical fine-grained complexity
conjectures. All these fine-grained results are, however, about the hardness of
strong simulations or multiplicative-error sampling. It was open whether any
fine-grained quantum supremacy result can be shown for additive-error sampling.
In this paper, we show the additive-error fine-grained quantum supremacy. As
examples, we consider the IQP model, a mixture of the IQP model and log-depth
Boolean circuits, and Clifford+$T$ circuits. Similar results should hold for
other sub-universal models.
