Dmitry A. Fedorov, Bo Peng, Niranjan Govind, Yuri Alexeev
{"title":"VQE method: a short survey and recent developments","authors":"Dmitry A. Fedorov, Bo Peng, Niranjan Govind, Yuri Alexeev","doi":"10.1186/s41313-021-00032-6","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":693,"journal":{"name":"Materials Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://materialstheory.springeropen.com/counter/pdf/10.1186/s41313-021-00032-6","citationCount":"96","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Materials Theory","FirstCategoryId":"1","ListUrlMain":"https://link.springer.com/article/10.1186/s41313-021-00032-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.
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.