{"title":"Pure quantum gradient descent algorithm and full quantum variational eigensolver","authors":"Ronghang Chen, Zhou Guang, Cong Guo, Guanru Feng, Shi-Yao Hou","doi":"10.1007/s11467-023-1346-7","DOIUrl":null,"url":null,"abstract":"<div><p>Optimization problems are prevalent in various fields, and the gradient-based gradient descent algorithm is a widely adopted optimization method. However, in classical computing, computing the numerical gradient for a function with <i>d</i> variables necessitates at least <i>d</i> + 1 function evaluations, resulting in a computational complexity of <i>O</i>(<i>d</i>). As the number of variables increases, the classical gradient estimation methods require substantial resources, ultimately surpassing the capabilities of classical computers. Fortunately, leveraging the principles of superposition and entanglement in quantum mechanics, quantum computers can achieve genuine parallel computing, leading to exponential acceleration over classical algorithms in some cases. In this paper, we propose a novel quantum-based gradient calculation method that requires only a single oracle calculation to obtain the numerical gradient result for a multivariate function. The complexity of this algorithm is just <i>O</i>(1). Building upon this approach, we successfully implemented the quantum gradient descent algorithm and applied it to the variational quantum eigensolver (VQE), creating a pure quantum variational optimization algorithm. Compared with classical gradient-based optimization algorithm, this quantum optimization algorithm has remarkable complexity advantages, providing an efficient solution to optimization problems. The proposed quantum-based method shows promise in enhancing the performance of optimization algorithms, highlighting the potential of quantum computing in this field.</p><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":573,"journal":{"name":"Frontiers of Physics","volume":null,"pages":null},"PeriodicalIF":6.5000,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Frontiers of Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11467-023-1346-7","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 1
Abstract
Optimization problems are prevalent in various fields, and the gradient-based gradient descent algorithm is a widely adopted optimization method. However, in classical computing, computing the numerical gradient for a function with d variables necessitates at least d + 1 function evaluations, resulting in a computational complexity of O(d). As the number of variables increases, the classical gradient estimation methods require substantial resources, ultimately surpassing the capabilities of classical computers. Fortunately, leveraging the principles of superposition and entanglement in quantum mechanics, quantum computers can achieve genuine parallel computing, leading to exponential acceleration over classical algorithms in some cases. In this paper, we propose a novel quantum-based gradient calculation method that requires only a single oracle calculation to obtain the numerical gradient result for a multivariate function. The complexity of this algorithm is just O(1). Building upon this approach, we successfully implemented the quantum gradient descent algorithm and applied it to the variational quantum eigensolver (VQE), creating a pure quantum variational optimization algorithm. Compared with classical gradient-based optimization algorithm, this quantum optimization algorithm has remarkable complexity advantages, providing an efficient solution to optimization problems. The proposed quantum-based method shows promise in enhancing the performance of optimization algorithms, highlighting the potential of quantum computing in this field.
期刊介绍:
Frontiers of Physics is an international peer-reviewed journal dedicated to showcasing the latest advancements and significant progress in various research areas within the field of physics. The journal's scope is broad, covering a range of topics that include:
Quantum computation and quantum information
Atomic, molecular, and optical physics
Condensed matter physics, material sciences, and interdisciplinary research
Particle, nuclear physics, astrophysics, and cosmology
The journal's mission is to highlight frontier achievements, hot topics, and cross-disciplinary points in physics, facilitating communication and idea exchange among physicists both in China and internationally. It serves as a platform for researchers to share their findings and insights, fostering collaboration and innovation across different areas of physics.