4 research outputs found
Quantum State Transfer Optimization: Balancing Fidelity and Energy Consumption using Pontryagin Maximum Principle
In this study, we address a control-constrained optimal control problem
pertaining to the transformation of quantum states. Our objective is to
navigate a quantum system from an initial state to a desired target state while
adhering to the principles of the Liouville-von Neumann equation. To achieve
this, we introduce a cost functional that balances the dual goals of fidelity
maximization and energy consumption minimization. We derive optimality
conditions in the form of the Pontryagin Maximum Principle (PMP) for the
matrix-valued dynamics associated with this problem. Subsequently, we present a
time-discretized computational scheme designed to solve the optimal control
problem. This computational scheme is rooted in an indirect method grounded in
the PMP, showcasing its versatility and efficacy. To illustrate the
practicality and applicability of our methodology, we employ it to address the
case of a spin particle subjected to interaction with a magnetic
field. Our findings shed light on the potential of this approach to tackle
complex quantum control scenarios and contribute to the broader field of
quantum state transformations
Quantum Pontryagin Neural Networks in Gamkarlidze form subjected to the purity of quantum channels
We investigate a time and energy minimization optimal control problem for
open quantum systems, whose dynamics is governed through the Lindblad (or
Gorini-Kossakowski-Sudarshan-Lindblad) master equation. The dissipation is
Markovian time-independent, and the control is governed by the Hamiltonian of a
quantum-mechanical system. We are specifically interested to study the purity
in a dissipative system constrained by state and control inputs. The idea for
solving this problem is by the combination of two following techniques. We deal
with the state constraints through Gamkarlidze revisited method, while handling
control constraints through the idea of saturation functions and system
extensions. This is the first time that quantum purity conservation is
formulated in such framework. We obtain the necessary conditions of optimality
through the Pontryagin Minimum Principle. Finally, the resulted boundary value
problem is solved by a Physics-Informed Neural Network (PINN) approach. The
exploited Pontryagin PINN technique is also new in quantum control context. We
show that these PINNs play an effective role in learning optimal control
actions.Comment: 6 pages, 2 figure
Quantum Control Modelling, Methods, and Applications
This review concerns quantum control results and methods that, over the years, have been used in the various operations involving quantum systems. Most of these methods have been originally developed outside the context of quantum physics, and, then, adapted to take into account the specificities of the various quantum physical platforms. Quantum control consists in designing adequate control signals required to efficiently manipulate systems conforming the laws of quantum mechanics in order to ensure the associated desired behaviours and performances. This work attempts to provide a thorough and self-contained introduction and review of the various quantum control theories and their applications. It encompasses issues spanning quantum control modelling, problem formulation, concepts of controllability, as well as a selection of the main control theories. Given the vastness of the field, we tried our best to be as concise as possible, and, for the details, the reader is pointed out to a profusion of references. The contents of the review are organized in the three major classes of control problems - open-loop control, closed-loop learning control, and feedback control - and, for each one of them, we present the main developments in quantum control theory. Finally, concerning the importance of attaining robustness and reliability due to inherent fragility of quantum systems, methods for quantum robust control are also surveyed