Pauli-Sparse regularised Counterdiabatic Shortcuts for Linear-Ramp QAOA
Abstract
Combinatorial optimization is a leading target for quantum algorithms, but finite-depth QAOA can suffer from strong diabatic errors when the interpolation Hamiltonian has small, or exponentially small, spectral gaps. We propose a Pauli-sparse counterdiabatic extension of linear-ramp QAOA based on the regularised adiabatic gauge potential (ℒH2+ηI)Aλ(η) = −iℒH(∂λH), ℒH(X)=[H,X]. Instead of computing a dense AGP, we solve this equation approximately by an inexact conjugate-gradient method in Pauli coordinates, truncating the Pauli expansion during the iteration to obtain a gate-budget-aware set of implementable rotations. The selected support is then improved by a Galerkin refit and certified by an a posteriori residual bound. The regularization parameter η acts as an energy-resolution scale: it suppresses transitions below √η while retaining larger-gap transitions. Thus, the method can avoid resolving exponentially small splittings inside a low-energy solution manifold while reducing leakage away from it. Numerical experiments on Ferromagnetic Chain (FC) and perturbed FC--MaxCut/MarketSplit instances show that the resulting LR-CD-QAOA ansatz improves approximation ratios over the uncorrected linear ramp, especially in regimes where LR-QAOA remains far from the optimum. Overall, the proposed regularized LR-CD-QAOA framework substantially broadens the practical applicability of QAOA to QUBO optimization by improving its robustness across heterogeneous problem landscapes, including instances with near-degenerate low-energy structures and small spectral gaps.
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BibTeX
@misc{cipolla2026paulisparse,
title = {{Pauli-Sparse regularised Counterdiabatic Shortcuts for Linear-Ramp QAOA}},
author = {Stefano Cipolla and Fabio Durastante},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.28536},
eprint = {2606.28536},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.28536},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pauli-Sparse regularised Counterdiabatic Shortcuts for Linear-Ramp QAOA
AU - Stefano Cipolla
AU - Fabio Durastante
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2606.28536
UR - https://arxiv.org/abs/2606.28536
AB - Combinatorial optimization is a leading target for quantum algorithms, but finite-depth QAOA can suffer from strong diabatic errors when the interpolation Hamiltonian has small, or exponentially small, spectral gaps. We propose a Pauli-sparse counterdiabatic extension of linear-ramp QAOA based on the regularised adiabatic gauge potential (ℒ_H^2+ηI)A_λ^(η) = −iℒ_H(∂_λH), ℒ_H(X)=[H,X]. Instead of computing a dense AGP, we solve this equation approximately by an inexact conjugate-gradient method in Pauli coordinates, truncating the Pauli expansion during the iteration to obtain a gate-budget-aware set of implementable rotations. The selected support is then improved by a Galerkin refit and certified by an a posteriori residual bound. The regularization parameter η acts as an energy-resolution scale: it suppresses transitions below √η while retaining larger-gap transitions. Thus, the method can avoid resolving exponentially small splittings inside a low-energy solution manifold while reducing leakage away from it. Numerical experiments on Ferromagnetic Chain (FC) and perturbed FC--MaxCut/MarketSplit instances show that the resulting LR-CD-QAOA ansatz improves approximation ratios over the uncorrected linear ramp, especially in regimes where LR-QAOA remains far from the optimum. Overall, the proposed regularized LR-CD-QAOA framework substantially broadens the practical applicability of QAOA to QUBO optimization by improving its robustness across heterogeneous problem landscapes, including instances with near-degenerate low-energy structures and small spectral gaps.
ER -