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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2026. Vol 57

Gradient Projection Method and Stochastic Search for Some Optimal Control Models with Spin Chains. I

Author(s)

Oleg V. Morzhin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russian Federation

Abstract
This article (I) considers optimal control models for both transferring an excitation from the first spin to the last spin in a chain of 𝑁 spins and keeping an excitation initially given at the last spin. Each model employs an external controlled parabolic magnetic field represented by two control functions. For these models, the corresponding infinite-dimensional gradients and the projection-type linearized Pontryagin maximum principle are given along with their finite-dimensional analogues. The finite-dimensional gradient projection method in its one-, two-, and three-step forms is represented. A special class of controls for the transfer model is introduced for a genetic algorithm, and the corresponding transfer example for the case of 𝑁 = 30 spins is given.
About the Authors
Oleg V. Morzhin, Cand. Sci. (Phys.-Math.), Senior Scientific Researcher, Steklov Mathematical Institute of RAS, Member of the Editorial Board of the Journal “Automation and Remote Control
For citation
Morzhin O. V. Gradient Projection Method and Stochastic Search for Some Optimal Control Models with Spin Chains. I. The Bulletin of Irkutsk State University. Series Mathematics, 2026, vol. 57, pp. 19–34. https://doi.org/10.26516/1997-7670.2026.57.19
Keywords
quantum optimal control, gradient projection method, genetic algorithm, spin chains
UDC
517.97, 530.145, 517.98
MSC
81Q93, 34H05
DOI
https://doi.org/10.26516/1997-7670.2026.57.19
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