Related papers: Role of control constraints in quantum optimal con…
Recently, there has been a surge of research on a class of methods called feedback optimization. These are methods to steer the state of a control system to an equilibrium that arises as the solution of an optimization problem. Despite the…
The optimal control problem for open quantum systems can be formulated as a time-dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the…
Mathematical theory of the quantum systems control is based on some ideas of the optimal control theory. These ideas are developed here as applied to these systems. The results obtained meet the deficiencies in the basis and algorithms of…
We study the interplay between rotating wave approximation and optimal control. In particular, we show that for a wide class of optimal control problems one can choose the control field such that the Hamiltonian becomes time-independent…
The quantum speed limit sets the minimum time required to transfer a quantum system completely into a given target state. At shorter times the higher operation speed has to be paid with a loss of fidelity. Here we quantify the trade-off…
It has recently been shown that the minimum energy solution of the control problem for a linear system produces a control trajectory that is nonlocal. An issue then arises when the dynamics represents a linearization of the underlying…
In this paper we present a reformulation--framed as a constrained optimization problem--of multi-robot tasks which are encoded through a cost function that is to be minimized. The advantages of this approach are multiple. The…
Quadratic programming (QP) is a common and important constrained optimization problem. Here, we derive a surprising duality between constrained optimization with inequality constraints -- of which QP is a special case -- and consumer…
We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…
A common goal of quantum control is to maximize a physical observable through the application of a tailored field. The observable value as a function of the field constitutes a quantum control landscape. Previous works have shown, under…
In this note, we consider the existence and uniqueness of the solution of a time-dependent optimal control problem constrained by a partial differential equation with uncertain inputs. Relying on the Lions' Lemma for deterministic problems,…
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…
A class of time-optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints and final point constraints is considered. By introducing the so-called locally optimal solution to time-optimal control…
Coherent carrier control in quantum nanostructures is studied within the framework of Optimal Control. We develop a general solution scheme for the optimization of an external control (e.g., lasers pulses), which allows to channel the…
For a class of quasi-variational inequalities (QVIs) of obstacle-type the stability of its solution set and associated optimal control problems are considered. These optimal control problems are non-standard in the sense that they involve…
We investigate the control landscapes of closed, finite level quantum systems beyond the dipole approximation by including a polarizability term in the Hamiltonian. Theoretical analysis is presented for the $n$ level case and formulas for…
The possibility of control of phenomena at microscopic level compatible with quantum mechanics and quantum field theory is outlined. The theory could be used in nanotechnology.
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…
We study the correction of errors intervening in two-qubit dissipating into their own environments. This is done by resorting to local feedback actions with the aim of preserving as much as possible the initial amount of entanglement.…
We introduce a novel algorithm for the task of coherently controlling a quantum mechanical system to implement any chosen unitary dynamics. It performs faster than existing state of the art methods by one to three orders of magnitude…