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arXiv · 2602.23183

Dequantization Barriers for Guided Stoquastic Hamiltonians

Yassine Hamoudi·Yvan Le Borgne·Shrinidhi Teganahally Sridhara
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Abstract

We construct a probability distribution, induced by the Perron--Frobenius eigenvector of an exponentially large graph, which cannot be efficiently sampled by any classical algorithm, even when provided with the best-possible warm-start distribution. In the quantum setting, this problem can be viewed as preparing the ground state of a stoquastic Hamiltonian given a guiding state as input, and is known to be efficiently solvable on a quantum computer. Our result suggests that no efficient classical algorithm can solve a broad class of stoquastic ground-state problems. Our graph is constructed from a class of high-degree, high-girth spectral expanders to which self-similar trees are attached. This builds on and extends prior work of Gily\'en, Hastings, and Vazirani [Quantum 2021, STOC 2021], which ruled out dequantization for a specific stoquastic adiabatic path algorithm. We strengthen their result by ruling out any classical algorithm for guided ground-state preparation.

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Yassine Hamoudi, Yvan Le Borgne, Shrinidhi Teganahally Sridhara. 2026-02-26. Dequantization Barriers for Guided Stoquastic Hamiltonians. https://arxiv.org/abs/2602.23183

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