Curator's Take
This article demonstrates that near‑term variational quantum algorithms can actually prepare and diagnose fractional quantum Hall states, a class of strongly correlated topological phases long considered out of reach for noisy hardware. By tackling both the Haldane sphere and torus geometries—especially the threefold degenerate ground manifold on the torus—the work bridges the gap between toy one‑dimensional models and genuine two‑dimensional topological matter, showing that hybrid VQE/VQD workflows can capture low‑energy spectra with error mitigation. If these techniques scale, they could give quantum processors a practical foothold in simulating exotic condensed‑matter systems that are otherwise intractable for classical computers, though current results remain limited to very small particle numbers.
— Mark Eatherly
Summary
We investigate the use of variational quantum algorithms to prepare and characterize fractional quantum Hall states on near-term quantum processors. Focusing on the $ν=1/3$ Laughlin phase described by the $V_1$ Haldane pseudopotential, we formulate the lowest-Landau-level problem in second quantization, and implement particle-number-preserving variational circuits combined with the variational quantum eigensolver (VQE) and variational quantum deflation (VQD). We benchmark the approach in two complementary geometries: Haldane sphere and torus shape. On the Haldane sphere, the target state is a unique zero-energy Laughlin ground state, providing a controlled test of the variational workflow and of excited-state reconstruction. On the torus, the problem retains the genuinely two-dimensional periodic character of the quantum Hall liquid and exhibits the threefold topological ground-state degeneracy expected for the $ν=1/3$ fractional filling factor. This feature makes the torus a more demanding benchmark than the quasi-one-dimensional cylinder or thin-torus limits commonly exploited in state-preparation quantum protocols. We benchmark the hardware-optimized variational states against exact diagonalization using energy estimates, error-mitigated observables, and subspace-containment diagnostics. Our results show that hybrid quantum algorithms can approximately reconstruct the low-energy structure of small fractional quantum Hall systems, including the topological ground-state manifold on the torus. Beyond serving as a benchmark for quantum hardware, this geometry-resolved approach provides a route toward quantum simulations of fractional Chern insulators and strongly correlated topological phases in realistic two-dimensional materials.