TY - GEN
T1 - Normalized Gradient Descent for Variational Quantum Algorithms
AU - Suzuki, Yudai
AU - Yano, Hiroshi
AU - Raymond, Rudy
AU - Yamamoto, Naoki
N1 - Funding Information:
This work was supported by MEXT Quantum Leap Flag-ship Program Grant Number JPMXS0118067285 and JP-MXS0120319794. RR would like to thank Daisuke Okanohara for introducing [27] that inspired him to conceive the idea of historical NGD.
Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Normalized Gradient Descent
KW - Optimization
KW - Variational Quantum Algorithms
UR - http://www.scopus.com/inward/record.url?scp=85123217981&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85123217981&partnerID=8YFLogxK
U2 - 10.1109/QCE52317.2021.00015
DO - 10.1109/QCE52317.2021.00015
M3 - Conference contribution
AN - SCOPUS:85123217981
T3 - Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021
SP - 1
EP - 9
BT - Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021
A2 - Muller, Hausi A.
A2 - Byrd, Greg
A2 - Culhane, Candace
A2 - Humble, Travis
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2nd IEEE International Conference on Quantum Computing and Engineering, QCE 2021
Y2 - 17 October 2021 through 22 October 2021
ER -