Materia Davide, Ratini Leonardo, Angeli Celestino, Guidoni Leonardo
Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell'Aquila, Coppito, L'Aquila 67100, Italy.
Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università degli Studi dell'Aquila, Coppito, L'Aquila 67100, Italy.
J Phys Chem A. 2024 Oct 3;128(39):8533-8543. doi: 10.1021/acs.jpca.4c03756. Epub 2024 Sep 23.
Hardware-efficient empirical variational ansätze for Variational Quantum Eigensolver (VQE) simulations of quantum chemistry often lack a direct connection to classical quantum chemistry methods. In this work, we propose a method to bridge this gap by introducing a novel approach to constructing a starting point for variational quantum circuits, leveraging quantum mutual information from classical quantum chemistry states to design simple yet effective heuristic ansätze with a topology reflecting the molecular system's correlations. As a first step, we make use of quantum chemistry calculations, such as Mo̷ller-Plesset (MP2) perturbation theory, to initially provide approximate Natural Orbitals, which have been shown to be the best candidate one-electron basis for developing compact empirical wave functions. Second, we evaluate the quantum mutual information matrix, which provides insights about the main correlations between qubits of the quantum circuit, and enables a direct design of entangling blocks for the circuit. The resulting ansatz is then used with a VQE to obtain a short-depth variational ground state of the electronic Hamiltonian. To validate our approach, we perform a comprehensive statistical analysis through simulations of various molecular systems (, , ) and apply it to the more complex molecule. The reported results demonstrate that the proposed methodology gives rise to highly effective ansätze, outperforming the standard empirical ladder-entangler ansatz. Overall, our approach can be used as an effective state preparation, providing a promising route for designing efficient variational quantum circuits for large molecular systems.
用于量子化学变分量子本征求解器（VQE）模拟的硬件高效经验变分方法通常与经典量子化学方法缺乏直接联系。在这项工作中，我们提出了一种方法来弥合这一差距，即引入一种新颖的方法来构建变分量子电路的起点，利用经典量子化学态的量子互信息来设计简单而有效的启发式方法，其拓扑结构反映分子系统的相关性。作为第一步，我们利用量子化学计算，如莫勒-普列斯特定理（MP2）微扰理论，初步提供近似自然轨道，这些自然轨道已被证明是开发紧凑经验波函数的最佳单电子基候选。其次，我们评估量子互信息矩阵，它提供了关于量子电路量子比特之间主要相关性的见解，并能够直接设计电路的纠缠块。然后将得到的方法与VQE一起使用，以获得电子哈密顿量的短深度变分基态。为了验证我们的方法，我们通过对各种分子系统（，，）的模拟进行了全面的统计分析，并将其应用于更复杂的分子。报告的结果表明，所提出的方法产生了高效的方法，优于标准的经验阶梯纠缠器方法。总体而言，我们的方法可以用作有效的态制备，为设计大分子系统的高效变分量子电路提供了一条有前途的途径。
