Quantum Lower Bounds for Approximate Counting via Laurent Polynomials

This paper proves new limitations on the power of quantum computers to solve approximate counting -- that is, multiplicatively estimating the size of a nonempty set $S\subseteq [N]$. Given only a membership oracle for $S$, it is well known that approximate counting takes $\Theta(\sqrt{N/|S|})$ quantum queries. But what if a quantum algo...More