  We construct a quantum algorithm that creates the Laughlin state for an
arbitrary number of particles $n$ in the case of filling fraction one. This
quantum circuit is efficient since it only uses $n(n-1)/2$ local qudit gates
and its depth scales as $2n-3$. We further prove the optimality of the circuit
using permutation theory arguments and we compute exactly how entanglement
develops along the action of each gate. Finally, we discuss its experimental
feasibility decomposing the qudits and the gates in terms of qubits and two
qubit-gates as well as the generalization to arbitrary filling fraction.
