Energy Optimal Interpolation in Quantum Evolution

Optimal Quantum Algorithm for Vector Interpolation

In this paper we study the functions that can be learned through the polynomial interpolation quantum algorithm designed by Childs et al. This algorithm was initially intended to find the coefficients of a multivariate polynomial function defined on finite fields $\mathbb{F}_q$. We extend its scope to vector inner product functions of the form $\mathcal{O}_{\mathbf{s}}(\mathbf{v}) = \mathbf{s}\cdot\mathbf{v}$ where the goal is to find the vector $\mathbf{s} \in \mathbb{F}_q^n$. We examine the necessary conditions on the domain $\mathcal{V}$ of $\mathcal{O}_{\mathbf{s}}$ and prove that the algo…

通过概率角度插值实现连续时间演进及其应用

Continuous-time evolution via probabilistic angle interpolation and its applications

本文提出基于概率角度插值的随机时间演进算法，通过连续时间极限消除Trotter误差，应用于氢分子基态能估计和稀疏Sachdev-Ye-Kitaev模型的非时间有序关联子计算。

使用最优控制引导连续参数化量子门的神经网络插值

Using optimal control to guide neural-network interpolation of continuously-parameterized gates

本文提出将量子最优控制与物理信息神经网络结合，通过主动学习预训练和迁移学习快速综合连续参数化量子门控制曲面，超越线性插值并提升变分量子算法的噪声鲁棒性与运行速度。

Schroedinger's interpolation problem through Feynman-Kac kernels

We discuss the so-called Schr{ö}dinger problem of deducing the microscopic (basically stochastic) evolution that is consistent with given positive boundary probability densities for a process covering a finite fixed time interval. The sought for dynamics may preserve the probability measure or induce its evolution, and is known to be uniquely reproducible, if the Markov property is required. Feynman-Kac type kernels are the principal ingredients of the solution and determine the transition probability density of the corresponding stochastic process. The result applies to a large variety of non…

基于李代数的量子最优控制插值

Lie Algebra-Based Quantum Optimal Controls Interpolation

提出结合李群理论与前馈神经网络的方法，无需推理时优化即可高效生成超导量子比特系统中任意酉操作的量子最优控制脉冲，解决了Trotterized量子模拟中大量传播子处理的瓶颈。

Optimal quantum algorithm for polynomial interpolation

We consider the number of quantum queries required to determine the coefficients of a degree-d polynomial over GF(q). A lower bound shown independently by Kane and Kutin and by Meyer and Pommersheim shows that d/2+1/2 quantum queries are needed to solve this problem with bounded error, whereas an algorithm of Boneh and Zhandry shows that d quantum queries are sufficient. We show that the lower bound is achievable: d/2+1/2 quantum queries suffice to determine the polynomial with bounded error. Furthermore, we show that d/2+1 queries suffice to achieve probability approaching 1 for large q. Thes…