AI 中文总结
研究针对希尔伯特空间过大难以对角化时态密度重构难的问题，利用Rodeo算法，通过对Haar随机输入态上的响应平均来估计态密度，推导了估计器及不确定性并验证方法，建立了相关字典。
AI 中文摘要
态密度（DoS）编码了量子多体系统的热力学和光谱特性，然而对于过大而难以对角化的希尔伯特空间，其重构变得难以处理。经典地，核多项式方法（KPM）通过将随机迹估计与平滑核相结合来解决此问题。本文表明，Rodeo算法——一种用于近期量子硬件的最简单的特征值定位协议之一——提供了这种方法的直接量子类似物。对Haar随机输入态上的Rodeo响应进行平均，得到与完全由演化时间分布确定的光谱核卷积的DoS：随机态起到随机迹估计的作用，时间采样分布起到阻尼核的作用。该构造仅需要标准的单辅助量子电路，并且随着希尔伯特空间维度的增加，量子典型性抑制了统计误差。我们推导了估计器及其不确定性，建立了信号处理窗口函数与量子重构核之间的显式字典，并在一维横向场伊辛模型和自旋-1模型上验证了该方法。
英文摘要
The density of states (DoS) encodes the thermodynamic and spectral properties of quantum many-body systems, yet its reconstruction becomes intractable for Hilbert spaces too large to diagonalize. Classically, the kernel polynomial method (KPM) addresses this by combining stochastic trace estimation with a smoothing kernel. Here we show that the Rodeo algorithm---one of the simplest eigenvalue-location protocols for near-term quantum hardware---provides a direct quantum analogue of this approach. Averaging the Rodeo response over Haar-random input states yields the DoS convolved with a spectral kernel fixed entirely by the distribution of evolution times: the random states play the role of stochastic trace estimation, and the temporal sampling distribution that of the damping kernel. The construction requires only the standard single-ancilla circuit, and quantum typicality suppresses the statistical error as the Hilbert-space dimension grows. We derive the estimator and its uncertainties, establish an explicit dictionary between signal-processing window functions and quantum reconstruction kernels, and validate the method on the one-dimensional transverse-field Ising and spin-1 models.
Comments13 pages, 5 figures, and 3 tables
