VQE method: a short survey and recent developments

Dmitry A. Fedorov, Bo Peng, Niranjan Govind, Yuri Alexeev
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引用次数: 96

Abstract

The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation (QPE) because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schrödinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by the choice of the variational ansatz used to represent the trial wave function. Hence, the construction of an efficient ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatzes for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing efficient ansatzes that fall into two categories—chemistry–inspired and hardware–efficient—that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.

VQE方法:简要综述及近期发展
变分量子特征求解器(VQE)是一种利用量子-经典混合计算方法求解哈密顿算子特征值的方法。VQE已被提议作为全量子算法(如量子相位估计(QPE))的替代方案,因为全量子算法需要量子硬件,而这在不久的将来是无法实现的。VQE已成功地应用于求解各种小分子的电子Schrödinger方程。然而,该方法的可扩展性受到两个因素的限制:量子电路的复杂性和经典优化问题的复杂性。这两个因素都受到用来表示试波函数的变分方差的选择的影响。因此,构建高效的ansatz是一个活跃的研究领域。换句话说,现代量子计算机无法执行深度量子电路,这些电路是通过使用当前可用的分析来生成的,这些分析可以映射到多个量子比特上。在这篇综述中,我们介绍了设计高效分析领域的最新进展,这些分析分为两类——化学启发型和硬件高效型——它们生产的量子电路更容易在现代硬件上运行。我们讨论了最初为VQE模拟制定的分析的不足之处,如何在更复杂的方法中解决这些问题,以及进一步改进的潜在方法。
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期刊介绍: Journal of Materials Science: Materials Theory publishes all areas of theoretical materials science and related computational methods. The scope covers mechanical, physical and chemical problems in metals and alloys, ceramics, polymers, functional and biological materials at all scales and addresses the structure, synthesis and properties of materials. Proposing novel theoretical concepts, models, and/or mathematical and computational formalisms to advance state-of-the-art technology is critical for submission to the Journal of Materials Science: Materials Theory. The journal highly encourages contributions focusing on data-driven research, materials informatics, and the integration of theory and data analysis as new ways to predict, design, and conceptualize materials behavior.
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