Reachability, Coolability, and Stabilizability of Open Markovian Quantum Systems with Fast Unitary Control

Abstract

Open Markovian quantum systems with fast and full Hamiltonian control can be reduced to an equivalent control system on the standard simplex modelling the dynamics of the eigenvalues of the density matrix describing the quantum state. We explore this reduced control system for answering questions on reachability and stabilizability with immediate applications to the cooling of Markovian quantum systems. We show that for certain tasks of interest, the control Hamiltonian can be chosen time-independent. -- The reduction picture is an example of dissipative interconversion between equivalence classes of states, where the classes are induced by fast controls.

arXiv comment38 pages, one figure

References in corpus (19)

• The Physical Implementation of Quantum Computation
• Decoherence Free Subspaces for Quantum Computation
• Preparation of Entangled States by Quantum Markov Processes
• Time Optimal Control in Spin Systems
• The European Quantum Technologies Roadmap
• Qubit architecture with high coherence and fast tunable coupling
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Symmetries and conserved quantities in Lindblad master equations
• Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer
• Stabilizing Open Quantum Systems by Markovian Reservoir Engineering
• Controllability of the discrete-spectrum Schrodinger equation driven by an external field
• Optimal Control of Quantum Dissipative Dynamics: Analytic solution for cooling the three level $\Lambda$ system
• Lie-Semigroup Structures for Reachability and Control of Open Quantum Systems: Viewing Markovian Quantum Channels as Lie Semigroups and GKS-Lindblad Generators as Lie Wedge
• Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed
• Time-optimal synthesis of unitary transformations in coupled fast and slow qubit system
• A tunable quantum dissipator for active resonator reset in circuit QED
• Exploring the Limits of Controlled Markovian Quantum Dynamics with Thermal Resources
• Reachability in Infinite Dimensional Unital Open Quantum Systems with Switchable GKS-Lindblad Generators
• Mixing of quantum states under Markovian dissipation and coherent control

Cited by in corpus (1)

• Bringing Quantum Systems under Control: A Tutorial Invitation to Quantum Computing and Its Relation to Bilinear Control Systems