Dynamical Decomposition of Bilinear Control Systems subject to Symmetries

Abstract

We describe a method to analyze and decompose the dynamics of a control system on a Lie group subject to symmetries. The method is based on the concept of generalized Young symmetrizers of representation theory. It naturally applies to the situation where the system evolves on a tensor product space and there exists a finite group of symmetries for the dynamics which interchanges the various factors. This is the case for quantum mechanical multipartite systems, such as spin networks, where each factor of the tensor product represents the state of one of the component systems. We present several examples of applications and indicate directions for future research.

24 pages

References in corpus (3)

• Preparing Greenberger-Horne-Zeilinger and $W$ states on a long-range Ising spin model by global controls
• Controllability of Symmetric Spin Networks
• Compact Hermitian Young Projection Operators

Cited by in corpus (8)

• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• Remotely Controlled Entanglement Generation
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Optimally generating $\mathfrak{su}(2^N)$ using Pauli strings
• Subspace controllability of bipartite symmetric spin networks under global control
• Quantum Advantage in Identifying the Parity of Permutations with Certainty