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A Super-Grover Separation Between Randomized and Quantum Query
Complexities
release_vhyaeypfkfgrzicgnhwenzjw6q
by
Shalev Ben-David
Released
as a article
.
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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