最优基态制备：基于引导态的方法
Optimal Ground-State Preparation with a Guiding State
浏览论文内容
中文总结 AI 辅助
本文提出两种算法，利用引导态和哈密顿量演化，在 $O(\log(1/\varepsilon)/\gamma\delta)$ 复杂度内实现最优基态制备，为量子模拟提供了高效方法。
中文摘要 AI 辅助
假设哈密顿量 $H$ 具有唯一的基态 $|\psi_0\rangle$，其本征值为 $E_0$，并且我们有一个估计值 $\tilde{E}_0$ 满足 $|\tilde{E}_0-E_0|\leq\delta$，且 $E_0$ 与所有其他本征值之间存在至少 $3\delta$ 的能隙。假设我们有一个可用的酉算子 $A$，能够产生一个与 $|\psi_0\rangle$ 重叠至少为 $\gamma$ 的“引导态” $A|0\rangle$。我们展示了如何利用 $O(\log(1/\varepsilon)/\gamma\delta)$ 次 $U=e^{iH}$ 和 $A$ 及其逆的应用，获得 $|\psi_0\rangle$ 的 $\varepsilon$-近似。我们给出了两种不同的算法：一种基于 [HMdW03] 风格的振幅放大与误差抑制的交错，另一种使用换能器的组合。本文是我们最近两篇基态能量估计论文 [JW26, SdW26] 的态制备后续工作。综合来看，我们的结果展示了基态制备的最优 $O(\log(1/\varepsilon)/\gamma\delta)$ 上界。
英文摘要
Suppose a Hamiltonian $H$ has a unique ground state $|ψ_0\rangle$ with an eigenvalue $E_0$, and we have an estimate $\tilde{E}_0$ such that $|\tilde{E}_0-E_0|\leqδ$, and there is a gap of at least $3δ$ between $E_0$ and all other eigenvalues. Suppose we have a unitary $A$ available that can produce a "guiding state'" $A|0\rangle$ that has overlap at least $γ$ with $|ψ_0\rangle$. We show how to obtain an $η$-approximation of $|ψ_0\rangle$ with probability at least $1-\varepsilon$ using $O(\log(1/\varepsilon)/γδ+ \log(1/η)/δ)$ applications of $U=e^{iH}$ its inverse, and $O(\log(1/\varepsilon)/γ)$ applications of $A$ and its inverse. We give two different algorithms, one based on interleaving amplitude amplification and error-reduction in the style of [HMdW03], and one using the composition of transducers. This paper is the state-preparation follow-up to our two recent ground-state-energy estimation papers [JW26,SdW26]. Combined with the optimal energy-estimation of [JW26], our results show the claimed upper bound for ground-state preparation. The bound is optimal up to a constant factor in terms of the number of applications of $U$ and $U^\dagger$ if $\varepsilon=η$, as follows from [SdW26]. In one of our approaches to ground state preparation, we construct transducers for amplitude amplification and LCU that might be of independent interest.
发表机构
- CWI and University of Amsterdam, the Netherlands（荷兰国家数学与计算机科学研究中心与阿姆斯特丹大学）
- Google Quantum AI, Venice, CA 90291, United States（谷歌量子人工智能部）
- QuSoft and CWI, Amsterdam, the Netherlands（QuSoft与荷兰国家数学与计算机科学研究中心）
机构由 AI 辅助整理，请以论文原文为准。
