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arXiv 2108.03249quant-phcond-mat.str-el
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近无阻挫基态制备

Nearly-frustration-free ground state preparation

Matthew Thibodeau, Bryan K. Clark

备注：
13 pages, 1 figure
发表信息：
Quantum 7, 1084 (2023)
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AI总结：

针对近无阻挫哈密顿量的基态制备问题，提出了能隙依赖标度更优的最优算法，给出物理实例并拓展至激发态制备。

摘要：

求解量子基态对于理解量子多体系统的性质至关重要，而量子计算机在求解量子基态方面具备潜在优势。近期研究提出了一种近乎最优的方案，可在量子计算机上为完全通用的哈密顿量制备基态，其查询复杂度的标度为$δ^{-1}$，即与归一化能隙成反比。本文转而研究限定于一类特殊哈密顿量子集的基态制备问题，其中包含我们称之为“近无阻挫”的哈密顿量：这类哈密顿量的块编码形式（即其归一化哈密顿量$α^{-1}H$）的基态能量与-1的差值在$δ^y$范围内，其中$δ$为$α^{-1}H$的谱隙，且$0 ≤ y ≤ 1$。针对该子类，我们提出了一种算法，其对能隙的依赖关系在渐近意义上更优，标度为$δ^{y/2-1}$，并证明这种新的依赖关系在相差$\text{log }δ$因子的意义下是最优的。此外，我们给出了属于该子类的、具有物理动机的哈密顿量实例。最后，我们拓展了该方法，使其既可以为通用哈密顿量制备激发态，也能以与基态情形相近的加速比为近无阻挫哈密顿量制备激发态。

英文摘要：

Solving for quantum ground states is important for understanding the properties of quantum many-body systems, and quantum computers are potentially well-suited for solving for quantum ground states. Recent work has presented a nearly optimal scheme that prepares ground states on a quantum computer for completely generic Hamiltonians, whose query complexity scales as $δ^{-1}$, i.e. inversely with their normalized gap. Here we consider instead the ground state preparation problem restricted to a special subset of Hamiltonians, which includes those which we term "nearly-frustration-free": the class of Hamiltonians for which the ground state energy of their block-encoded and hence normalized Hamiltonian $α^{-1}H$ is within $δ^y$ of -1, where $δ$ is the spectral gap of $α^{-1}H$ and $0 \leq y \leq 1$. For this subclass, we describe an algorithm whose dependence on the gap is asymptotically better, scaling as $δ^{y/2-1}$, and show that this new dependence is optimal up to factors of $\log δ$. In addition, we give examples of physically motivated Hamiltonians which live in this subclass. Finally, we describe an extension of this method which allows the preparation of excited states both for generic Hamiltonians as well as, at a similar speedup as the ground state case, for those which are nearly frustration-free.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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