Related papers: Introduction to the Pontryagin Maximum Principle f…
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…
Optimization of constrained quantum control problems powers quantum technologies. This task becomes very difficult when these control problems are nonconvex and plagued with dense local extrema. For such problems current optimization…
Quantum optimal control theory is a powerful tool for engineering quantum systems subject to external fields such as the ones created by intense lasers. The formulation relies on a suitable definition for a target functional, that…
The key element of the approach to the theory of necessary conditions in optimal control discussed in the paper is reduction of the original constrained problem to unconstrained minimization with subsequent application of a suitable…
In this work, we address the problem of maximizing fidelity in a quantum state transformation process controlled in such a way as to keep decoherence within given bounds. We consider a three-level $\Lambda$-type atom subjected to Markovian…
An optimal control problem associated with the dynamics of the orientation of a bipolar molecule in the plane can be understood by means of tools in differential geometry. For first time in the literature $k$-symplectic formalism is used to…
This paper is a survey on some recent aspects and developments in stochastic control. We discuss the two main historical approaches, Bellman's optimality principle and Pontryagin's maximum principle, and their modern exposition with…
Quantum control is a ubiquitous research field that has enabled physicists to delve into the dynamics and features of quantum systems, delivering powerful applications for various atomic, optical, mechanical, and solid-state systems. In…
We present a Pontryagin maximum principle for discrete time optimal control problems with (a) pointwise constraints on the control actions and the states, (b) frequency constraints on the control and the state trajectories, and (c)…
We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether theorem are…
We derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ODEs and a PDE of Vlasov-type. Such problems arise naturally as ${\Gamma}$-limits of optimal control problems subject to ODE…
The ability to characterise a Hamiltonian with high precision is crucial for the implementation of quantum technologies. In addition to the well-developed approaches utilising optimal probe states and optimal measurements, the method of…
A New theoretical formalism for the optimal quantum control has been presented. The approach stems from the consideration of describing the time-dependent quantum system in terms of the real physical observables, viz., the probability…
A dynamical system entrains to a periodic input if its state converges globally to an attractor with the same period. In particular, for a constant input the state converges to a unique equilibrium point for any initial condition. We…
Optimizing quantum circuits is critical for enhancing computational speed and mitigating errors caused by quantum noise. Effective optimization must be achieved without compromising the correctness of the computations. This survey explores…
We investigate the optimal control problem for non-Markovian open, dissipative quantum system. Optimal control using Pontryagin maximum principle is specifically derived. The influences of Ohmic reservoir with Lorentz-Drude regularization…
This paper proposes an integrated quantum-classical approach that merges quantum computational dynamics with classical computing methodologies tailored to address control problems based on Pontryagin's minimum principle within a…
Pontryagin type maximum principle and Bellman's dynamic programming principle serve as two of the most important tools in solving optimal control problems. There is a huge literature on the study of relationship between them. The main…
This tutorial introduces a systematic approach for addressing the key question of quantum metrology: For a generic task of sensing an unknown parameter, what is the ultimate precision given a constrained set of admissible strategies. The…
This article (I) considers the known optimal control model of a quantum information transfer along a spin chain with controlled external parabolic magnetic field, with an arbitrary length. The article adds certain lower and upper pointwise…