A Super-Grover Separation Between Randomized and Quantum Query Complexities release_vhyaeypfkfgrzicgnhwenzjw6q

by Shalev Ben-David

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2015  

Abstract

We construct a total Boolean function f satisfying R(f)=Ω̃(Q(f)^5/2), refuting the long-standing conjecture that R(f)=O(Q(f)^2) for all total Boolean functions. Assuming a conjecture of Aaronson and Ambainis about optimal quantum speedups for partial functions, we improve this to R(f)=Ω̃(Q(f)^3). Our construction is motivated by the Göös-Pitassi-Watson function but does not use it.
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Date   2015-06-26
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arXiv  1506.08106v1
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