A Super-Grover Separation Between Randomized and Quantum Query Complexities [article]

Shalev Ben-David
2015 arXiv   pre-print
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.
arXiv:1506.08106v1 fatcat:vhyaeypfkfgrzicgnhwenzjw6q