发表机构
Virginia Tech; Phasecraft; University of Edinburgh（弗吉尼亚理工大学; Phasecraft; 爱丁堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出两种仅通过非受控哈密顿量演化查询即可实现近最优基态制备的算法，基于谱下降原理，并证明额外受控演化无法超越对数因子改进复杂度。
AI 中文摘要
基态制备、能量估计和性质估计是量子模拟中的基本任务。现有的基态制备算法通过块编码或受控哈密顿量演化实现了近最优复杂度，这引发了一个自然问题：受控哈密顿量演化是否是必要的，或者能否在仅提供非受控哈密顿量演化的较弱访问模型中获得相同的缩放？我们通过给出两种仅通过查询$U_H$及其逆$U_H^\dagger$来访问输入哈密顿量$H$的算法解决了这个问题，其中$\\|H\\|\le\alpha_H$且$\tau=\Theta(1/\alpha_H)$。给定一个基态权重至少为$\eta$且$H$的谱隙至少为$\gamma$的输入态，我们的第一种算法使用输入态的新副本，需要对$U_H$和$U_H^\dagger$进行$\widetilde O(\alpha_H/(\gamma\eta))$次查询，而我们的第二种算法使用输入态制备酉算子及其逆的相干访问，将该复杂度改进为$\widetilde O(\alpha_H/(\gamma\sqrt{\eta}))$。后一个界限在对数因子内匹配已知下界，表明额外访问受控哈密顿量演化的算法不能将基态制备的查询复杂度改进到对数因子之外。两种算法都基于一个我们称之为谱下降原理的简单机制，其中算法从输入态$|\psi\rangle$开始，逐步下降穿过能量谱，向基态靠近，直到达到期望的保真度。我们还将此框架扩展到基态性质估计和能量估计，并为这两项任务给出了明确的复杂度保证。
英文摘要
Ground-state preparation, energy estimation, and property estimation are fundamental tasks in quantum simulation. Existing ground-state preparation algorithms achieve near-optimal complexity using block encodings or controlled Hamiltonian evolution, raising a natural question: is controlled Hamiltonian evolution necessary, or can the same scaling be attained in the weaker access model that provides access to only uncontrolled Hamiltonian evolution? We resolve this question by giving two algorithms that access the input Hamiltonian $H$ only through queries to $U_H$ and its inverse $U_H^\dagger$, where $\|H\|\leα_H$ and $τ=Θ(1/α_H)$. Given an input state with ground-state weight at least $η$ and a spectral gap of $H$ of at least $γ$, our first algorithm uses fresh copies of the input state and requires $\widetilde O(α_H/(γη))$ queries to $U_H$ and $U_H^\dagger$, while our second algorithm uses coherent access to the input-state preparation unitary and its inverse to improve this complexity to $\widetilde O(α_H/(γ\sqrtη))$. The latter bound matches the known lower bound up to logarithmic factors, showing that algorithms with additional access to controlled Hamiltonian evolution cannot improve the query complexity for ground-state preparation beyond logarithmic factors. Both algorithms are based on a simple mechanism that we call the spectral descent principle, in which the algorithm starts from the input state $|ψ\rangle$ and progressively descends through the energy spectrum, moving closer to the ground state until the desired fidelity is reached. We also extend this framework to ground-state property and energy estimation and give explicit complexity guarantees for both tasks.
CommentsThe authors acknowledge the use of ChatGPT 5.6 and 6 for help with writing and reviewing the manuscript, including identifying technical errors and inconsistencies in earlier versions
