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.

翻译：我们构建了一个由指数大规模图的Perron-Frobenius特征向量导出的概率分布，该分布无法被任何经典算法高效采样，即使提供最优预热初始分布。在量子背景下，该问题可视为在给定引导态作为输入的情况下制备随机哈密顿量的基态，且已知可在量子计算机上高效求解。我们的结果表明，不存在能解决广泛类别随机基态问题的高效经典算法。我们的图由一类高度数、高围长的谱扩展图构造而成，其上附着自相似树结构。此工作基于并拓展了Gilyén、Hastings和Vazirani [Quantum 2021, STOC 2021] 的前期研究——该研究排除了特定随机绝热路径算法的去量化可能性。我们通过排除任意用于有向导基态制备的经典算法，强化了他们的结论。