Pauli-Sparse regularised Counterdiabatic Shortcuts for Linear-Ramp QAOA

• URL: http://arxiv.org/abs/2606.28536v1
• Date: Fri, 26 Jun 2026 18:41:15 GMT
• Title: Pauli-Sparse regularised Counterdiabatic Shortcuts for Linear-Ramp QAOA
• Abstract summary: Combinatorial optimization is a leading target for quantum algorithms.<n> finite-depth QAOA can suffer from strong diabatic errors when the Hamiltonian has small, or exponentially small, spectral gaps.<n>We propose a Pauli-sparse counterdiabatic extension of linear-ramp QAOA based on the regularised adiabatic gauge potential.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 \[ \bigl(\mathcal L_H^2+ηI\bigr)A_λ^{(η)} = -\mathrm{i}\mathcal L_H(\partial_λH), \qquad \mathcal L_H(X)=[H,X]. \] 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 \(\sqrtη\) 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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