基于多个初始态的量子谱估计：改进的误差与代价缩放
Quantum Spectral Estimation with Multiple Initial States: Improved Error and Cost Scaling
AI总结：
该研究基于QFAMES框架提出多初始态量子谱估计新方法，可降低哈密顿量模拟代价与重数恢复代价，保留海森堡极限缩放，数值实验验证了误差缩放关系。
摘要：
我们研究利用多个初始态和广义哈达玛检验的量子谱与本征态性质估计。在QFAMES（量子滤波与本征谱重数分析）框架基础上，我们提出一种对每对初始态独立采样演化时间的新方法。在给定假设下，当统计误差决定采样代价时，固定精度的本征值与可观测量估计所需的总哈密顿量模拟代价与初始态数量无关，仅差对数因子。这在需要大量初始态探索目标本征空间时提升了可扩展性。该方法还降低了重数恢复的代价，并保留了本征值估计的海森堡极限缩放。数值实验验证了预测的统计误差缩放关系。
英文摘要：
We study quantum spectrum and eigenstate property estimation using multiple initial states and generalized Hadamard tests. Building on the QFAMES (quantum filtering and analysis of multiplicities in eigenvalue spectra) framework, we introduce a new method that samples evolution times independently for each initial-state pair. Under the stated assumptions, when statistical error determines the sampling cost, the total Hamiltonian simulation cost required for fixed-accuracy eigenvalue and observable estimation is independent of the number of initial states, up to logarithmic factors. This improves scalability when many initial states are needed to explore the target eigenspaces. The method also reduces the cost of multiplicity recovery and retains Heisenberg-limited scaling for eigenvalue estimation. Numerical experiments support the predicted statistical error scalings.
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