Approximate Counting refers to the problem where we are given query access to a function f : [N] → {0,1}, and we wish to estimate K = #{x : f(x) = 1} to within a factor of 1+ε (with high probability), while minimizing the number of queries. In the quantum setting, Approximate Counting can be done with O(min (√{N/ε}, √{N/K} / ε) queries. It has recently been shown that this can be achieved by a simple algorithm that only uses "Grover iterations"; however the algorithm performs these iterations

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... aptively. Motivated by concerns of computational simplicity, we consider algorithms that use Grover iterations with limited adaptivity. We show that algorithms using only nonadaptive Grover iterations can achieve O(√{N/ε}) query complexity, which is tight.