  Shannon proved that almost all Boolean functions require a circuit of size
$\Theta(2^n/n)$. We prove a quantum analog of this classical result. Unlike in
the classical case the number of quantum circuits of any fixed size that we
allow is uncountably infinite. Our main tool is a classical result in real
algebraic geometry bounding the number of realizable sign conditions of any
finite set of real polynomials in many variables.
