Normalized Gradient Descent for Variational Quantum Algorithms

Yudai Suzuki, Hiroshi Yano, Rudy Raymond, Naoki Yamamoto

研究成果: Conference contribution

抄録

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.

本文言語English
ホスト出版物のタイトルProceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021
編集者Hausi A. Muller, Greg Byrd, Candace Culhane, Travis Humble
出版社Institute of Electrical and Electronics Engineers Inc.
ページ1-9
ページ数9
ISBN(電子版)9781665416917
DOI
出版ステータスPublished - 2021
イベント2nd IEEE International Conference on Quantum Computing and Engineering, QCE 2021 - Virtual, Online, United States
継続期間: 2021 10月 172021 10月 22

出版物シリーズ

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

Conference

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

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 計算理論と計算数学
  • コンピュータ サイエンスの応用
  • 計算数学
  • 制御と最適化
  • モデリングとシミュレーション

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