Toward Quantum Utility in Correlated Topological Matter: Variational Preparation of Fractional Quantum Hall Manifolds
Abstract
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 V1 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.
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BibTeX
@misc{exposito2026toward,
title = {{Toward Quantum Utility in Correlated Topological Matter: Variational Preparation of Fractional Quantum Hall Manifolds}},
author = {Sergio F. Expósito and Unai Aseginolaza and Raúl Guerrero-Avilés and Joaquim Jornet-Somoza and Francisco Guinea and Juan Borge},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.11380},
eprint = {2607.11380},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.11380},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Toward Quantum Utility in Correlated Topological Matter: Variational Preparation of Fractional Quantum Hall Manifolds
AU - Sergio F. Expósito
AU - Unai Aseginolaza
AU - Raúl Guerrero-Avilés
AU - Joaquim Jornet-Somoza
AU - Francisco Guinea
AU - Juan Borge
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2607.11380
UR - https://arxiv.org/abs/2607.11380
AB - 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.
ER -