{"title":"Kernel Descent -- a Novel Optimizer for Variational Quantum Algorithms","authors":"Lars Simon, Holger Eble, Manuel Radons","doi":"arxiv-2409.10257","DOIUrl":null,"url":null,"abstract":"In recent years, variational quantum algorithms have garnered significant\nattention as a candidate approach for near-term quantum advantage using noisy\nintermediate-scale quantum (NISQ) devices. In this article we introduce kernel\ndescent, a novel algorithm for minimizing the functions underlying variational\nquantum algorithms. We compare kernel descent to existing methods and carry out\nextensive experiments to demonstrate its effectiveness. In particular, we\nshowcase scenarios in which kernel descent outperforms gradient descent and\nquantum analytic descent. The algorithm follows the well-established scheme of\niteratively computing classical local approximations to the objective function\nand subsequently executing several classical optimization steps with respect to\nthe former. Kernel descent sets itself apart with its employment of reproducing\nkernel Hilbert space techniques in the construction of the local approximations\n-- which leads to the observed advantages.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"40 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10257","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In recent years, variational quantum algorithms have garnered significant
attention as a candidate approach for near-term quantum advantage using noisy
intermediate-scale quantum (NISQ) devices. In this article we introduce kernel
descent, a novel algorithm for minimizing the functions underlying variational
quantum algorithms. We compare kernel descent to existing methods and carry out
extensive experiments to demonstrate its effectiveness. In particular, we
showcase scenarios in which kernel descent outperforms gradient descent and
quantum analytic descent. The algorithm follows the well-established scheme of
iteratively computing classical local approximations to the objective function
and subsequently executing several classical optimization steps with respect to
the former. Kernel descent sets itself apart with its employment of reproducing
kernel Hilbert space techniques in the construction of the local approximations
-- which leads to the observed advantages.