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This research examines optimization techniques applied to quantum systems, focusing on Riemannian methods and their applications.

March 26, 2026

Some Optimization Methods for Quantum Systems: Gradient Projection Method on Stiefel Manifolds and Beyond

Key Points

This research examines optimization techniques applied to quantum systems, focusing on Riemannian methods and their applications.
Outline Riemannian optimization techniques in quantum systems
Introduce gradient projection method on complex Stiefel manifolds
Describe incoherent GRAPE modifications of existing algorithms
Investigate optimization efficiency in constrained and unconstrained landscapes
Demonstrated operation of GRAPE and GPM on a quantum $9$-system
Showed improved optimization efficiency using these methods
Highlighted the effectiveness of GPM on complex landscapes

Abstract

Methods of optimization and control of quantum systems are widely used for various applications in quantum technologies including laser control of chemical reactions, nuclear magnetic resonance, gate generation for quantum computing, describing quantum transport in photosynthesis, etc. Among many topics in quantum control, we briefly outline Riemannian optimization and gradient projection method (GPM) on complex Stiefel manifolds and their relation to quantum control, as well as various related optimization tools such as incoherent GRAPE (InGRAPE) modification of the gradient ascent pulse engineering (GRAPE) algorithm, GPM in the dynamic picture for constrained optimization, and demonstrate operation of GRAPE and GPM for an investigation of the optimization efficiency over unconstrained and constrained quantum control landscapes for an example of a three-level -system having a seventh-order trap. 1

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