论文标题
使用近期量子算法的密度功能理论及其量子内核的征费嵌入：哈伯德二聚体的插图
The Levy-Lieb embedding of density functional theory and its Quantum Kernel: Illustration for the Hubbard Dimer using near-term quantum algorithms
论文作者
论文摘要
LIEB和LIEB的限制搜索配方提供了从N-代表性密度到N颗粒波函数空间的具体映射，并明确定义了密度功能理论的通用功能。我们使用修改后的变分量子eigensolver方法，为范式晶格系统（Hubbard Dimer）实施了数值的LIEB程序。我们使用所得的杂种量子经典方案来证明密度变化最小化，该方案具有沿搜索轨迹的Levy-LieB功能的实时计算。我们进一步说明了基于忠诚度的量子内核与Levy-Lieb程序所隐含的纯状嵌入密度相关，并使用内核来学习密度可观察的功能。我们研究内核通过在哈伯德二聚体上的数值实验以高精度概括的能力。
The constrained-search formulation of Levy and Lieb provides a concrete mapping from N-representable densities to the space of N-particle wavefunctions and explicitly defines the universal functional of density functional theory. We numerically implement the Levy-Lieb procedure for a paradigmatic lattice system, the Hubbard dimer, using a modified variational quantum eigensolver approach. We demonstrate density variational minimization using the resulting hybrid quantum-classical scheme featuring real-time computation of the Levy-Lieb functional along the search trajectory. We further illustrate a fidelity based quantum kernel associated with the density to pure-state embedding implied by the Levy-Lieb procedure and employ the kernel for learning observable functionals of the density. We study the kernel's ability to generalize with high accuracy through numerical experiments on the Hubbard dimer.
