
Quantum Lower Bounds for Approximate Counting via Laurent Polynomials
This paper proves new limitations on the power of quantum computers to s...
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Lower Bounding the ANDOR Tree via Symmetrization
We prove a nearly tight lower bound on the approximate degree of the two...
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The gradient complexity of linear regression
We investigate the computational complexity of several basic linear alge...
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On the complexity of the (approximate) nearest colored node problem
Given a graph G=(V,E) where each vertex is assigned a color from the set...
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Resolution with Counting: Lower Bounds over Different Moduli
Resolution over linear equations (introduced in [RT08]) emerged recently...
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A Quadratic Lower Bound for Algebraic Branching Programs
We show that any Algebraic Branching Program (ABP) computing the polynom...
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Lower Bounds for Parallel Quantum Counting
We prove a generalization of the parallel adversary method to multivalu...
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QMA Lower Bounds for Approximate Counting
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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