Quantum algorithm for the Laughlin wave function

TL;DR

This paper presents an efficient quantum algorithm for generating the Laughlin wave function at filling fraction one, with optimized circuit depth and proven optimality, and discusses its experimental implementation and generalization.

Contribution

It introduces a quantum circuit that efficiently constructs the Laughlin state with optimality proof and analyzes entanglement development during the process.

Findings

Circuit uses n(n-1)/2 local qudit gates

Circuit depth scales as 2n-3

Exact entanglement development computed

Abstract

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.