  We show that almost all n-bit Boolean functions have bounded-error quantum
query complexity at least n/2, up to lower-order terms. This improves over an
earlier n/4 lower bound of Ambainis, and shows that van Dam's oracle
interrogation is essentially optimal for almost all functions. Our proof uses
the fact that the acceptance probability of a T-query algorithm can be written
as the sum of squares of degree-T polynomials.
