Dequantization Barriers for Guided Stoquastic Hamiltonians

2026-02-26

AI Summary

This study investigates whether efficient classical algorithms can simulate the preparation of the ground state of a stoquastic Hamiltonian given a guiding state. By constructing exponentially large graphs composed of high-degree, high-girth spectral expanders combined with self-similar trees, the authors analyze the sampling complexity of the probability distribution induced by the Perron–Frobenius eigenvector of these graphs. They prove that no classical algorithm can efficiently sample from this distribution, even when equipped with the optimal warm-start distribution. This work extends the previously known “dequantization barrier”—which applied only to specific adiabatic quantum algorithms—to all classical algorithms, thereby establishing for the first time the classical intractability of stoquastic ground-state preparation with a guiding state and strengthening the theoretical foundation for quantum advantage.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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 Gilyén, 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.

Problem

• stoquastic Hamiltonians
• dequantization
• ground-state preparation
• classical sampling
• guided quantum computation

Innovation

• stoquastic Hamiltonians
• dequantization barriers
• guided ground-state preparation
• Perron–Frobenius eigenvector
• spectral expanders