A quantum algorithm is exact if, on any input data, it outputs the correct
answer with certainty (probability 1). A key question is: how big is the
advantage of exact quantum algorithms over their classical counterparts:
deterministic algorithms. For total Boolean functions in the query model, the
biggest known gap was just a factor of 2: PARITY of N inputs bits requires N
queries classically but can be computed with N/2 queries by an exact quantum
algorithm.
We present the first example of a Boolean function f(x_1, ..., x_N) for which
exact quantum algorithms have superlinear advantage over the deterministic
algorithms. Any deterministic algorithm that computes our function must use N
queries but an exact quantum algorithm can compute it with O(N^{0.8675...})
queries.Comment: 20 pages, v6: small number of small correction
