Colloquium: Shalev Ben-David
Separations in query complexity using cheat sheets
Shalev Ben-David, Massachusetts Institute of Technology (MIT)
We show a power 2.5 separation between bounded-error randomized and quantum query complexity for a total Boolean function, refuting the widely believed conjecture that the best such separation could only be quadratic (from Grover's algorithm). We also present a total function with a power 4 separation between quantum query complexity and approximate polynomial degree, showing severe limitations on the power of the polynomial method.