Normalized Gradient Descent for Variational Quantum Algorithms

Yudai Suzuki, Hiroshi Yano, Rudy Raymond, Naoki Yamamoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Variational quantum algorithms (VQAs) are promising methods that leverage noisy quantum computers and classical computing techniques for practical applications. In VQAs, the classical optimizers such as gradient-based optimizers are utilized to adjust the parameters of the quantum circuit so that the objective function is minimized. However, they often suffer from the so-called vanishing gradient or barren plateau issue. On the other hand, the normalized gradient descent (NGD) method, which employs the normalized gradient vector to update the parameters, has been successfully utilized in several optimization problems. Here, we study the performance of the NGD methods in the optimization of VQAs for the first time. Our goal is two-fold. The first is to examine the effectiveness of NGD and its variants for overcoming the vanishing gradient problems. The second is to propose a new NGD that can attain the faster convergence than the ordinary NGD. We performed numerical simulations of these gradient-based optimizers in the context of quantum chemistry where VQAs are used to find the ground state of a given Hamiltonian. The results show the effective convergence property of the NGD methods in VQAs, compared to the relevant optimizers without normalization. Moreover, we make use of some normalized gradient vectors at the past iteration steps to propose the novel historical NGD that has a theoretical guarantee to accelerate the convergence speed, which is observed in the numerical experiments as well.

Original languageEnglish
Title of host publicationProceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021
EditorsHausi A. Muller, Greg Byrd, Candace Culhane, Travis Humble
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1-9
Number of pages9
ISBN (Electronic)9781665416917
DOIs
Publication statusPublished - 2021
Event2nd IEEE International Conference on Quantum Computing and Engineering, QCE 2021 - Virtual, Online, United States
Duration: 2021 Oct 172021 Oct 22

Publication series

NameProceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021

Conference

Conference2nd IEEE International Conference on Quantum Computing and Engineering, QCE 2021
Country/TerritoryUnited States
CityVirtual, Online
Period21/10/1721/10/22

Keywords

  • Normalized Gradient Descent
  • Optimization
  • Variational Quantum Algorithms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Science Applications
  • Computational Mathematics
  • Control and Optimization
  • Modelling and Simulation

Fingerprint

Dive into the research topics of 'Normalized Gradient Descent for Variational Quantum Algorithms'. Together they form a unique fingerprint.

Cite this