Related papers: Total Variation of the Control and Energy of Bilin…
This paper presents an energy estimate in terms of the total variation of the control for bilinear infinite dimensional quantum systems with unbounded potentials. These estimates allow a rigorous construction of propagators associated with…
In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…
This note presents a sufficient condition for partial approximate ensemble controllability of a set of bilinear conservative quantum systems in an infinite dimensional Hilbert space. The proof relies on classical geometric and averaging…
Quantum control is traditionally expressed through bilinear models and their associated Lie algebra controllability criteria. But, the first order approximation are not always sufficient and higher order developpements are used in recent…
Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin…
In this article, we give a complete characterization of all the unitary transformations that can be synthesized in a given time for a system of coupled spin-1/2 in presence of general time varying coupling tensor. Our treatment is quite…
We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal…
We consider the problem of steering control for the systems of one spin 1/2 particle and two interacting homonuclear spin 1/2 particles in an electro-magnetic field. The describing models are bilinear systems whose state varies on the Lie…
We present a scheme for controlling the state of a quantum system by modifying the boundary conditions. This constitutes an infinite-dimensional control problem. We provide conditions for the existence of solutions of the dynamics and prove…
Sufficient conditions for complete controllability of $N$-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and…
We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for…
We consider a bilinear control problem for the wave equation on a torus of arbitrary dimension. We show that the system is globally approximately controllable in arbitrarily small times from a dense family of initial states. The control…
Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are…
Optimal quantum control of continuous variable systems poses a formidable computational challenge because of the high-dimensional character of the system dynamics. The framework of quantum invariants can significantly reduce the complexity…
In this manuscript, we investigate optimal control problems which arise in connection with manipulation of dissipative quantum dynamics. These problems motivate the study of a class of dissipative bilinear control systems. For these systems…
We provide bounds on the error between dynamics of an infinite dimensional bilinear Schr\"odinger equation and of its finite dimensional Galerkin approximations. Standard averaging methods are used on the finite dimensional approximations…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
In this paper, we study the control of a class of time-invariant linear ensemble systems whose natural dynamics are linear in the system parameter. This class of ensemble control systems arises from practical engineering and physical…
Complete controllability is a fundamental issue in the field of control of quantum systems, not least because of its implications for dynamical realizability of the kinematical bounds on the optimization of observables. In this paper we…
We show that if an efficient classical representation of the dynamics exists, optimal control problems on many-body quantum systems can be solved efficiently with finite precision. We show that the size of the space of parameters necessary…