Sajjan Manas, Sureshbabu Shree Hari, Kais Sabre
Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States.
Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States.
J Am Chem Soc. 2021 Nov 10;143(44):18426-18445. doi: 10.1021/jacs.1c06246. Epub 2021 Oct 27.
Quantum machine-learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure calculations of molecular systems and spin models in magnetic systems. However, the discussion in all these recipes focuses specifically on targeting the ground state. Herein we demonstrate a quantum algorithm that can filter any energy eigenstate of the system based on either symmetry properties or a predefined choice of the user. The workhorse of our technique is a shallow neural network encoding the desired state of the system with the amplitude computed by sampling the Gibbs-Boltzmann distribution using a quantum circuit and the phase information obtained classically from the nonlinear activation of a separate set of neurons. We show that the resource requirements of our algorithm are strictly quadratic. To demonstrate its efficacy, we use state filtration in monolayer transition metal dichalcogenides which are hitherto unexplored in any flavor of quantum simulations. We implement our algorithm not only on quantum simulators but also on actual IBM-Q quantum devices and show good agreement with the results procured from conventional electronic structure calculations. We thus expect our protocol to provide a new alternative in exploring the band structures of exquisite materials to usual electronic structure methods or machine-learning techniques that are implementable solely on a classical computer.
量子机器学习算法已成为其经典对应算法的一种有前途的替代方案，因为它们利用了量子计算机的强大功能。此类算法已被开发用于解决诸如分子系统的电子结构计算和磁性系统中的自旋模型等问题。然而，所有这些方法的讨论都特别侧重于针对基态。在此，我们展示了一种量子算法，它可以根据对称性或用户预先定义的选择来筛选系统的任何能量本征态。我们技术的核心是一个浅层神经网络，它通过使用量子电路对吉布斯 - 玻尔兹曼分布进行采样计算的幅度以及从另一组神经元的非线性激活中经典获得的相位信息来编码系统的期望状态。我们表明我们算法的资源需求严格为二次方。为了证明其有效性，我们在单层过渡金属二卤化物中使用态过滤，这在任何类型的量子模拟中都是前所未有的。我们不仅在量子模拟器上实现了我们的算法，还在实际的IBM - Q量子设备上实现，并与从传统电子结构计算获得的结果显示出良好的一致性。因此，我们期望我们的协议为探索精细材料的能带结构提供一种新的替代方法，以替代通常仅可在经典计算机上实现的电子结构方法或机器学习技术。
