发表机构
Paderborn University; Nagoya University; University of Hyogo（帕德博恩大学; 名古屋大学; 兵库大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对$k$-局域哈密顿量的低能估计与态制备，提出由二进制熵函数控制的更快量子算法，并给出近最优的低能子空间维数下界，改进现有Grover界。
AI 中文摘要
一般$k$-局域哈密顿量的低能估计和态制备是量子复杂性理论中的基本挑战。Buhrman等人[BGLGST, PRL 2025]最近打破了这两个问题的自然Grover界$O^\ast(2^{n/2})$，其改进取决于相对精度$\varepsilon$和局域性$k$。在本工作中，我们为这些问题提出了更快的指数级量子算法，其中二进制熵函数控制运行时间指数。对于足够小的$\varepsilon/k$，我们的算法将指数相对于[BGLGST, PRL 2025]改进了一个因子$\log(k/\varepsilon)$。我们的主要技术结果是一个由熵控制的哈密顿量低能子空间维数下界，通过对其基态进行去极化获得。对于固定的$k$，该下界在指数上达到常数因子内的最优。同一框架为任意相互作用图上的Heisenberg、$XY$和Ising模型提供了更紧的界。
英文摘要
Low-energy estimation and state preparation for general $k$-local Hamiltonians are fundamental challenges in quantum complexity theory. Buhrman et al.~ [BGLGST, PRL 2025] recently broke the natural Grover bound $O^\ast(2^{n/2})$ for both problems, with the improvement depending on the relative accuracy $\varepsilon$ and the locality $k$. In this work, we present faster exponential quantum algorithms for these problems, where the binary entropy function governs the runtime exponent. For sufficiently small $\varepsilon/k$, our algorithms improve the exponent by a factor of $\log(k/\varepsilon)$ over [BGLGST, PRL 2025]. Our main technical result is an entropy-governed lower bound on the dimension of the Hamiltonian's low-energy subspace, obtained by depolarizing its ground state. For fixed $k$, this bound is optimal up to constant factors in the exponent. The same framework yields tighter bounds for Heisenberg, $XY$, and Ising models on arbitrary interaction graphs.
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