基于引导态的基态能量估计的最优量子算法
Optimal Quantum Algorithm for Ground-State Energy Estimation with a Guiding State
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中文总结 AI 辅助
该研究提出一种基于换能器的量子算法，可在引导态设定下以更少查询次数估计酉算子最大本征相位，解答了开放问题且匹配下界。
中文摘要 AI 辅助
在基态能量估计问题中，目标是估计哈密顿量的最小特征值，通常给定一个与基态空间具有承诺重叠度γ的引导态。该问题的主要方法是模拟其演化并估计所得酉算子U的最小（或等价的最大）本征相位。我们提出一种量子算法，在该引导态设定下估计酉算子U的最大本征相位，相比此前最优方法，对U的查询次数减少了log(1/γ)倍。该结果与现有下界匹配，解答了Mande和de Wolf提出的开放问题。该算法基于换能器（transducers），这类换能器常可实现量子算法的组合且无误差降低带来的开销。
英文摘要
In the problem of ground-state energy estimation, one aims to estimate the smallest eigenvalue of a Hamiltonian, often given a guiding state, with some promised overlap $γ$ with the ground space. The main approach to this problem is to simulate its evolution, and estimate the smallest (or equivalently, largest) eigenphase of the resulting unitary $U$. We give a quantum algorithm that estimates the largest eigenphase of a unitary $U$ in this guided setting using a factor of $\log\frac{1}γ$ fewer queries to $U$ than the previous best approach. The result matches an existing lower bound, and answers an open question from Mande and de Wolf. The algorithm is based on transducers, which often allow composition of quantum algorithms without overhead from error reduction.
