Preparation of a Laughlin-like fractional Chern insulator on a superconducting quantum processor

Abstract

Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states, hosting topological order and fractionalized anyonic excitations. Their realization poses a demanding target for quantum simulation. Here, we realize a bosonic FCI on an IBM Nighthawk superconducting quantum processor using classically optimized variational circuits. We target a Laughlin-like state that is an exact zero-energy ground state of a long-range parent Hamiltonian on a torus, eliminating physical edges and providing a favorable geometry for accessing fractional quantum Hall physics in a small system. On a $4\times4$ qubit lattice, we prepare both the four-boson FCI ground state and a three-boson state hosting two quasiholes. Measurements of particle densities and correlations reproduce the characteristic structure of the target states, while reconstructed chiral magnetization currents resolve the circulating current pattern associated with the quasiholes. The preparation of these strongly correlated topological states with shallow circuits establishes a route toward the digital simulation and manipulation of fractionalized excitations, including measurements of topological invariants and anyonic braiding.

The paper addresses digital preparation and detection of bosonic Laughlin-like fractional Chern insulator states on a small superconducting processor. It targets the hard-core Kapit–Mueller model on a $4\times4$ torus at flux density $\phi=1/2$: a four-boson, $\nu=1/2$ ground state and a three-boson state with two pinned quasiholes. Exact diagonalization supplies the two-dimensional target manifolds. Particle-number-conserving circuits built from nearest-neighbor hopping, interactions and on-site rotations are optimized classically against manifold fidelity, without implementing the parent Hamiltonian’s long-range hopping. Both circuits reach $0.95$ noiseless manifold fidelity. The three- and four-boson preparations use respectively 168 and 264 CZ gates, with two-qubit depths 28 and 44, on 16 IBM Nighthawk qubits. After particle-number post-selection, retaining approximately one-third of shots, measured densities, conditional correlations and symmetry-grouped configuration probabilities reproduce the target distributions with attenuation. Distribution-fit slopes relative to a maximally mixed baseline are $0.813$ and $0.742$. For the quasihole state, two-qubit Pauli measurements reconstruct coherences and associated Kapit–Mueller bond currents, giving total loop circulation $-0.19\pm0.06$, versus $-0.319$ for the target state. The reported $0.95$ fidelities are simulation results, not experimental fidelity measurements. Noise-model-dependent estimates put post-selected error-free fractions at $60(2)\%$ and $46(5)\%$. Stated scaling limitations include reliance on classically accessible targets, increasing circuit depth for long-range entanglement, hardware noise and connectivity. Topological invariants, topological entanglement entropy and fractional braiding are proposed future measurements rather than demonstrated diagnostics.