  We show that Nechiporuk's method for proving lower bounds for Boolean
formulas can be extended to the quantum case. This leads to an $\Omega(n^2 /
\log^2 n)$ lower bound for quantum formulas computing an explicit function. The
only known previous explicit lower bound for quantum formulas states that the
majority function does not have a linear-size quantum formula. We also show
that quantum formulas can be simulated by Boolean circuits of almost the same
size.
