Realization of fermionic Laughlin state on a quantum processor.

Strongly correlated topological phases of matter are central to modern condensed matter physics and quantum information technology but often challenging to probe and control in material systems. The experimental difficulty of accessing these phases has motivated the use of engineered quantum platforms for simulation and manipulation of exotic topological states. Among these, the Laughlin state stands as a cornerstone for topological matter, embodying fractionalization, anyonic excitations, and incompressibility. Although its bosonic analogs have been realized on programmable quantum simulators, a genuine fermionic Laughlin state has yet to be demonstrated on a quantum processor. Here, we realize the ν = 1/3 fermionic Laughlin state on IonQ's trapped-ion quantum computer using an efficient and scalable Hamiltonian variational ansatz with 369 two-qubit gates on a 16-qubit circuit. Employing symmetry-verification error mitigation, we extract key observables that characterize the Laughlin state, including correlation hole, bulk-edge correspondence, and topological entanglement entropy, with strong agreement to exact diagonalization benchmarks. This work demonstrates an end-to-end workflow to simulate material-intrinsic topological orders and provides a starting point to explore its dynamics and excitations on digital quantum processors.