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TR19-015 | 7th February 2019 10:06
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#### QMA Lower Bounds for Approximate Counting

**Abstract:**
We prove a query complexity lower bound for $QMA$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $SBP^A \not\subset QMA^A$, resolving an open problem of Aaronson [2]. Our proof uses the polynomial method to derive a lower bound for the $SBQP$ query complexity of the $AND$ of two approximate counting instances. We use Laurent polynomials as a tool in our proof, showing that the "Laurent polynomial method" can be useful even for problems involving ordinary polynomials.