Time-optimal Control of Spin Systems

2006/01/19 by Jan Swoboda, Swoboda, Jan · 10 citations
Physics and Astronomy · Chemistry · Mathematics · #Quantum chaos and dynamical systems #Advanced NMR Techniques and Applications #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.quant-ph/0601131

Abstract

The paper discusses various aspects of time-optimal control of quantum spin systems, modelled as right-invariant systems on a compact Lie group G. The main results are the reduction of such a system to an equivalent system on a homogeneous space G/H, and the explicit determination of optimal trajectories on G/H in the case where G/H is a Riemannian symmetric space. These results are mainly obtained by using methods from Lie theory and geometric control.

Cited by

• Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition
• Trade-off relations and enhancement protocol of quantum battery capacities in multipartite systems
• Introduction to quantum control: From basic concepts to applications in quantum technologies
• Generation of spin-squeezed states using dipole-coupled spins
• Engineering multi-mode bosonic squeezed states using Monte-Carlo optimization
• Small-time approximate controllability of the logarithmic Schr''dinger equation
• Spectral gaps of ironed two-qubit gadgets matching the iSWAP gap
• Time optimal control in coupled spin systems: a second order analysis
• Free Cumulants and Full Eigenstate Thermalization from Boundary Scrambling
• Time-Optimal Control of Finite Dimensional Open Quantum Systems via a Model Predictive Strategy

Related

• Time optimal simultaneous control of two level quantum systems
• Time optimal control in coupled spin systems: a second order analysis
• Minimum Time Optimal Synthesis for a Control System on SU(2)
• Left-invariant optimal control problems on Lie groups
• Time Optimal Quantum Control of Spinor States