Majland Marco, Ettenhuber Patrick, Zinner Nikolaj Thomas, Christiansen Ove
Kvantify Aps, DK-2300 Copenhagen S, Denmark.
Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark.
J Chem Phys. 2024 Apr 21;160(15). doi: 10.1063/5.0191074.
Quantum chemistry is one of the most promising applications for which quantum computing is expected to have a significant impact. Despite considerable research in the field of electronic structure, calculating the vibrational properties of molecules on quantum computers remains a relatively unexplored field. In this work, we develop a vibrational Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (vADAPT-VQE) formalism based on an infinite product representation (IPR) of anti-Hermitian excitation operators of the Full Vibrational Configuration Interaction (FVCI) wavefunction, which allows for preparing eigenstates of vibrational Hamiltonians on quantum computers. In order to establish the vADAPT-VQE algorithm using the IPR, we study the exactness of disentangled Unitary Vibrational Coupled Cluster (dUVCC) theory and show that dUVCC can formally represent the FVCI wavefunction in an infinite expansion. To investigate the performance of the vADAPT-VQE algorithm, we numerically study whether the vADAPT-VQE algorithm generates a sequence of operators that may represent the FVCI wavefunction. Our numerical results indicate frequent appearance of critical points in the wavefunction preparation using vADAPT-VQE. These results imply that one may encounter diminishing usefulness when preparing vibrational wavefunctions on quantum computers using vADAPT-VQE and that additional studies are required to find methods that can circumvent this behavior.
量子化学是量子计算有望产生重大影响的最具前景的应用领域之一。尽管在电子结构领域已有大量研究，但在量子计算机上计算分子的振动特性仍是一个相对未被探索的领域。在这项工作中，我们基于全振动组态相互作用（FVCI）波函数的反厄米激发算符的无限乘积表示（IPR），开发了一种振动自适应导数组装伪 Trotter 变分量子本征求解器（vADAPT-VQE）形式，它能够在量子计算机上制备振动哈密顿量的本征态。为了使用 IPR 建立 vADAPT-VQE 算法，我们研究了解缠酉振动耦合簇（dUVCC）理论的精确性，并表明 dUVCC 可以在无限展开中形式地表示 FVCI 波函数。为了研究 vADAPT-VQE 算法的性能，我们通过数值研究 vADAPT-VQE 算法是否生成了一个可能表示 FVCI 波函数的算符序列。我们的数值结果表明，在使用 vADAPT-VQE 制备波函数时频繁出现临界点。这些结果意味着，在量子计算机上使用 vADAPT-VQE 制备振动波函数时，可能会遇到效用递减的情况，并且需要进一步研究以找到能够规避这种行为的方法。
