Mamba Quantum Eigensolver (MQE): A Selective State Space Model for Scalable Ground State Simulations in Quantum Chemistry
Abstract
Predicting molecular electronic structure using Quantum Computing approaches is a challenge in Computational Chemistry. Traditional Variational Quantum Eigensolvers (VQEs) are typically hindered by optimization challenges. The alternative Generative Quantum Eigensolver (GQE) mitigates this by reformulating ground-state search as discrete sequence generation, but its Transformer backbone suffers from quadratic computational complexity, bottlenecking scalability for larger molecules. To address this, we introduce the Mamba Quantum Eigensolver (Mamba-QE), which replaces the Transformer with a Selective State Space Model (SSM) to process operator sequences with linear 𝒪(L) complexity. Additionally, we integrate a distance-conditioned mechanism enabling the direct prediction of complete potential energy surfaces (PES). Evaluated on the H2 molecule, Mamba-QE reproduces Full Configuration Interaction (FCI) reference energies well within chemical accuracy, achieving an energy error below 3×10−6 Ha across 16 geometries with zero variational violations. Mamba-QE maintains high expressive power while establishing a robust, scalable foundation for quantum simulations of complex molecular systems.
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BibTeX
@misc{petronilo2026mamba,
title = {{Mamba Quantum Eigensolver (MQE): A Selective State Space Model for Scalable Ground State Simulations in Quantum Chemistry}},
author = {G. X. A. Petronilo and M. R. Araújo and Erico S. Teixeira and Clebson Cruz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29779},
eprint = {2610.29779},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29779},
}
RIS
TY - UNPB
TI - Mamba Quantum Eigensolver (MQE): A Selective State Space Model for Scalable Ground State Simulations in Quantum Chemistry
AU - G. X. A. Petronilo
AU - M. R. Araújo
AU - Erico S. Teixeira
AU - Clebson Cruz
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29779
UR - https://arxiv.org/abs/2610.29779
AB - Predicting molecular electronic structure using Quantum Computing approaches is a challenge in Computational Chemistry. Traditional Variational Quantum Eigensolvers (VQEs) are typically hindered by optimization challenges. The alternative Generative Quantum Eigensolver (GQE) mitigates this by reformulating ground-state search as discrete sequence generation, but its Transformer backbone suffers from quadratic computational complexity, bottlenecking scalability for larger molecules. To address this, we introduce the Mamba Quantum Eigensolver (Mamba-QE), which replaces the Transformer with a Selective State Space Model (SSM) to process operator sequences with linear 𝒪(L) complexity. Additionally, we integrate a distance-conditioned mechanism enabling the direct prediction of complete potential energy surfaces (PES). Evaluated on the H_2 molecule, Mamba-QE reproduces Full Configuration Interaction (FCI) reference energies well within chemical accuracy, achieving an energy error below 3×10^−6 Ha across 16 geometries with zero variational violations. Mamba-QE maintains high expressive power while establishing a robust, scalable foundation for quantum simulations of complex molecular systems.
ER -