  We find that generic entanglement is physical, in the sense that it can be
generated in polynomial time from two-qubit gates picked at random. We prove as
the main result that such a process generates the average entanglement of the
uniform (Haar) measure in at most $O(N^3)$ steps for $N$ qubits. This is
despite an exponentially growing number of such gates being necessary for
generating that measure fully on the state space. Numerics furthermore show a
variation cut-off allowing one to associate a specific time with the
achievement of the uniform measure entanglement distribution. Various
extensions of this work are discussed. The results are relevant to entanglement
theory and to protocols that assume generic entanglement can be achieved
efficiently.
