Sequential optimization for orbital-optimized variational quantum eigensolvers
Abstract
Orbital optimization within the variational quantum eigensolver (VQE) framework is useful for improving active-space quality and accurately capturing electron correlation with shallow quantum circuits. The orbital-optimized unitary coupled cluster (OO-UCC) method [W. Mizukami et al., Phys. Rev. Res. 2, 033421 (2020)], in its original formulation, employs the orbital gradient and Hessian in a Newton--Laphson procedure. In this study, we propose sequential orbital-optimized unitary coupled cluster doubles (SOO-UCCD), extending the gradient-free sequential minimal optimization approach [K. M. Nakanishi et al., Phys. Rev. Res. 2, 043158 (2020)] to orbital rotation parameters. Based on the frequency structure implied by the algebraic properties of the orbital rotation generators, our method determines each orbital rotation angle from a nine-point energy profile. The energy landscape is evaluated by classically transforming the Hamiltonian integrals and contracting them with the reduced density matrices already measured for the VQE energy evaluation. This allows for orbital optimization without evaluating the orbital gradient or Hessian. By building on the core benefits of the OO-UCC framework, our method provides a gradient-free and hyperparameter-free orbital-optimization procedure. State-vector simulations for LiH in the STO-3G basis show that SOO-UCCD reproduces UCCSD-level accuracy along the bond-stretching curve and exhibits macro-iteration convergence comparable to that of L-BFGS-based orbital optimization.
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BibTeX
@misc{hayashi2026sequential,
title = {{Sequential optimization for orbital-optimized variational quantum eigensolvers}},
author = {Hiromichi Hayashi and Takeshi Sato},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16032},
eprint = {2610.16032},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16032},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sequential optimization for orbital-optimized variational quantum eigensolvers
AU - Hiromichi Hayashi
AU - Takeshi Sato
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16032
UR - https://arxiv.org/abs/2610.16032
AB - Orbital optimization within the variational quantum eigensolver (VQE) framework is useful for improving active-space quality and accurately capturing electron correlation with shallow quantum circuits. The orbital-optimized unitary coupled cluster (OO-UCC) method [W. Mizukami et al., Phys. Rev. Res. 2, 033421 (2020)], in its original formulation, employs the orbital gradient and Hessian in a Newton--Laphson procedure. In this study, we propose sequential orbital-optimized unitary coupled cluster doubles (SOO-UCCD), extending the gradient-free sequential minimal optimization approach [K. M. Nakanishi et al., Phys. Rev. Res. 2, 043158 (2020)] to orbital rotation parameters. Based on the frequency structure implied by the algebraic properties of the orbital rotation generators, our method determines each orbital rotation angle from a nine-point energy profile. The energy landscape is evaluated by classically transforming the Hamiltonian integrals and contracting them with the reduced density matrices already measured for the VQE energy evaluation. This allows for orbital optimization without evaluating the orbital gradient or Hessian. By building on the core benefits of the OO-UCC framework, our method provides a gradient-free and hyperparameter-free orbital-optimization procedure. State-vector simulations for LiH in the STO-3G basis show that SOO-UCCD reproduces UCCSD-level accuracy along the bond-stretching curve and exhibits macro-iteration convergence comparable to that of L-BFGS-based orbital optimization.
ER -