Time-optimal control of a two-level dissipative quantum system

2007/08/21 by Dominique Sugny, D. Sugny, C. Kontz +2 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Computer science #Construct (python library) #Control (management) #Control theory (sociology) #Dissipation #Dissipative system #Geometry #Laser-Matter Interactions and Applications #Master equation #Mathematical optimization #Mathematics #Optimal control #Physics #Point (geometry) #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum system #Set (abstract data type) #Simple (philosophy) #State (computer science) #quant-ph

paper · pdf · doi:10.1103/physreva.76.023419

published as Physical review A 76, 023419 (2007) · 25 pages, 10 figures

openalex publication_date 2007/08/21 · arxiv created 2007/08/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We propose an analysis of the time-optimal control of a dissipative two-level quantum system whose dynamics is governed by the Lindblad equation. This simple system allows one to use tools of geometric control theory and to construct its optimal synthesis, i.e., to determine the set of all the optimal trajectories starting from a given initial point. We study different processes such as conversion of a pure state into a mixed state and purification of a mixed state. In particular cases, we show that dissipation is not undesirable and can help accelerating the control.

Citations

• Complete controllability of finite-level quantum systems
• Efficient and Long-Lived Field-Free Orientation of Molecules by a Single Hybrid Short Pulse
• Controllability properties for finite dimensional quantum Markovian master equations
• Decoherence assisting a measurement-driven quantum evolution process
• Completely positive dynamical semigroups of N-level systems
• Orbits of quantum states and geometry of Bloch vectors forN-level systems
• Laser control in a bifurcating region
• Universal simulation of Markovian quantum dynamics
• Cooperating or fighting with decoherence in the optimal control of quantum dynamics
• Sub-Riemannian geometry and time optimal control of three spin systems: Quantum gates and coherence transfer
• Quantum control and the Strocchi map

Cited by

• Effect of feedback on the control of a two-level dissipative quantum system
• Saturation of a spin-1/2 particle by generalized local control
• Connection between optimal control theory and adiabatic-passage techniques in quantum systems