论文标题
光谱密度估计与高斯积分变换
Spectral density estimation with the Gaussian Integral Transform
论文作者
论文摘要
频谱密度运算符$ \hatρ（ω）=δ（ω-\ hat {h}）$在线性响应理论中起着核心作用，因为其期望值，即动态响应函数，可用于计算散射横截面。在这项工作中，我们描述了一种接近最佳的量子算法，该算法可通过能量分辨率$δ$和错误$ε$使用光谱密度近似$ \ MATHCAL {o} \ left（\ sqrt {\ log \ left（1/ε\ right）\ left（\ log \ left（1/δ\ right）+\ log \ log \ log \ left（1/ε\ \ right）\ right）\ right）}/Δ\ \ \ \ \右）$ right）$ right）$ right）$ right）。这是可以实现的，而无需对时间进化运算符使用昂贵的近似值，而是利用Qubitized来实现光谱密度的近似高斯积分变换（GIT）。我们还描述了适当的误差指标，以更广泛地评估光谱函数近似值的质量。
The spectral density operator $\hatρ(ω)=δ(ω-\hat{H})$ plays a central role in linear response theory as its expectation value, the dynamical response function, can be used to compute scattering cross-sections. In this work, we describe a near optimal quantum algorithm providing an approximation to the spectral density with energy resolution $Δ$ and error $ε$ using $\mathcal{O}\left(\sqrt{\log\left(1/ε\right)\left(\log\left(1/Δ\right)+\log\left(1/ε\right)\right)}/Δ\right)$ operations. This is achieved without using expensive approximations to the time-evolution operator but exploiting instead qubitization to implement an approximate Gaussian Integral Transform (GIT) of the spectral density. We also describe appropriate error metrics to assess the quality of spectral function approximations more generally.
