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arXiv · 2611.09229

Exploring Variational Regularization of Krylov Subspaces

Alexandre Perrin·Jérémie Messud·Sébastien Burdin·Matthieu Saubanère
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Abstract

Krylov subspace methods efficiently approximate extremal eigenstates and eigenvalues of many-body Hamiltonians, but non-orthogonal bases can suffer from ill-conditioning. This challenge is amplified in quantum computing, where direct state access and thus straightforward orthogonalization are unavailable. We investigate a variational Krylov-like framework that iteratively optimizes a parametrized sequence of states to mimic Lanczos-like couplings while penalizing linear dependencies. Analyzed against exact Krylov and Lanczos on a finite Anderson impurity model, ansatz expressivity strongly influences the performance: Hamiltonian-inspired ansätze preserve Krylov-like convergence while improving the conditioning, whereas shallow ansätze remain stable but miss low-energy directions.

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Alexandre Perrin, Jérémie Messud, Sébastien Burdin, Matthieu Saubanère. 2026-11-06. Exploring Variational Regularization of Krylov Subspaces. https://arxiv.org/abs/2611.09229

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