Latorre, J I

Quantum algorithm for the Laughlin wave function

We construct a quantum algorithm that creates the Laughlin state for an arbitrary number n of particles for a filling fraction of one. This quantum circuit is efficient since it only uses n(n-1)/2 local qudit gates and its depth scales as 2n-3. Furthermore, we 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 by decomposing the qudits and the gates in terms of qubits and two qubit-gates, as well as its generalization to arbitrary filling fraction.