  We show that quantum query complexity satisfies a strong direct product
theorem. This means that computing $k$ copies of a function with less than $k$
times the quantum queries needed to compute one copy of the function implies
that the overall success probability will be exponentially small in $k$. For a
boolean function $f$ we also show an XOR lemma---computing the parity of $k$
copies of $f$ with less than $k$ times the queries needed for one copy implies
that the advantage over random guessing will be exponentially small.
  We do this by showing that the multiplicative adversary method, which
inherently satisfies a strong direct product theorem, is always at least as
large as the additive adversary method, which is known to characterize quantum
query complexity.
