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It is known that several sub-universal quantum computing models, such as theIQP model, the Boson sampling model, the one-clean qubit model, and the randomcircuit model, cannot be classically simulated in polynomial time under certainconjectures in classical complexity theory. Recently, these results have beenimproved to "fine-grained" versions where even exponential-time classicalsimulations are excluded assuming certain classical fine-grained complexityconjectures. All these fine-grained results are, however, about the hardness ofstrong simulations or multiplicative-error sampling. It was open whether anyfine-grained quantum supremacy result can be shown for additive-error sampling.In this paper, we show the additive-error fine-grained quantum supremacy. Asexamples, we consider the IQP model, a mixture of the IQP model and log-depthBoolean circuits, and Clifford+$T$ circuits. Similar results should hold forother sub-universal models.

Additive-error fine-grained quantum supremacy