Grow, Compress, and Perturb: A Hybrid Quantum-Classical Pathway to Scalable Quantum Chemistry on Quantum Computers
Abstract
While Variational Quantum Eigensolver (VQE) variants are among leading candidates for electronic structure calculations on quantum computers, gradient-based operator selection limits their scalability. To solve this, we introduce the Hamiltonian-gradient-free VULCAN (Variational Upbuilding, Layered Compression, Adaptive N-body perturbation) layered VQE framework. Our method dynamically generates ansatz operators using Variational Double Bracket Flow (VDBF) equations. Combined with a linearly scaling minimal complete pool, it creates a pool 4-12 times smaller than QEB (Qubit-Excitation-Based) pools. By appending entire layers simultaneously, Hamiltonian gradient measurements are completely eliminated. Circuit depth is managed via a grow-then-compress scheme using efficient state-overlap measurements, and qubit requirements are reduced by projecting the Hamiltonian onto a dominant-determinant subspace. Using high-performance emulation up to 32 logical qubits, we achieve chemical accuracy at just 5-20% of the measurement cost of batched ADAPT-VQE for hydrogen chains, BeH2 and H2O. For the 32-qubit C3H6, where batched ADAPT-VQE does not reach chemical accuracy, a single VULCAN layer combined with a GPU-accelerated stochastic Epstein-Nesbet (ENPT2) correction does. This stochastic ENPT2 post-processing step enables early termination at chemical accuracy.
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BibTeX
@misc{nogueira2026grow,
title = {{Grow, Compress, and Perturb: A Hybrid Quantum-Classical Pathway to Scalable Quantum Chemistry on Quantum Computers}},
author = {Hugo D. Nogueira and Siwar Badreddine and Olivier Adjoua and Diata Traore and Guillaume Michel and Jean-Philip Piquemal},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40561},
eprint = {2610.40561},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05844789v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Grow, Compress, and Perturb: A Hybrid Quantum-Classical Pathway to Scalable Quantum Chemistry on Quantum Computers
AU - Hugo D. Nogueira
AU - Siwar Badreddine
AU - Olivier Adjoua
AU - Diata Traore
AU - Guillaume Michel
AU - Jean-Philip Piquemal
PY - 2026
DA - 2026/10/29
PB - HAL
DO - 10.48550/arxiv.2610.40561
UR - https://hal.science/hal-05844789v1
AB - While Variational Quantum Eigensolver (VQE) variants are among leading candidates for electronic structure calculations on quantum computers, gradient-based operator selection limits their scalability. To solve this, we introduce the Hamiltonian-gradient-free VULCAN (Variational Upbuilding, Layered Compression, Adaptive N-body perturbation) layered VQE framework. Our method dynamically generates ansatz operators using Variational Double Bracket Flow (VDBF) equations. Combined with a linearly scaling minimal complete pool, it creates a pool 4-12 times smaller than QEB (Qubit-Excitation-Based) pools. By appending entire layers simultaneously, Hamiltonian gradient measurements are completely eliminated. Circuit depth is managed via a grow-then-compress scheme using efficient state-overlap measurements, and qubit requirements are reduced by projecting the Hamiltonian onto a dominant-determinant subspace. Using high-performance emulation up to 32 logical qubits, we achieve chemical accuracy at just 5-20% of the measurement cost of batched ADAPT-VQE for hydrogen chains, BeH2 and H2O. For the 32-qubit C3H6, where batched ADAPT-VQE does not reach chemical accuracy, a single VULCAN layer combined with a GPU-accelerated stochastic Epstein-Nesbet (ENPT2) correction does. This stochastic ENPT2 post-processing step enables early termination at chemical accuracy.
ER -