Fine-grained quantum supremacy and stabilizer rank

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It is known that several sub-universal quantum computing models cannot be classically simulated unless the polynomial-time
hierarchy collapses. However, these results exclude only polynomial-time classical simulations. In this talk, based on fine-grained
complexity conjectures, I show more ``fine-grained" quantum supremacy results that prohibit certain exponential-time classical simulations.
I also show the stabilizer rank conjecture under fine-grained complexity conjectures.