QMA Lower Bounds for Approximate Counting
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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 ⊂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.
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