Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

Re-exploring Control Strategies in a Non-Markovian Open Quantum System by Reinforcement Learning

In this study, we reexamine a recent optimal control simulation targeting the preparation of a superposition of two excited electronic states in the UV range in a complex molecular system. We revisit this control from the perspective of reinforcement learning, offering an efficient alternative to conventional quantum control methods. The two excited states are addressable by orthogonal polarizations and their superposition corresponds to a right or left localization of the electronic density. The pulse duration spans tens of femtoseconds to prevent excitation of higher excited bright states what leads to a strong perturbation by the nuclear motions. We modify an open source software by L. Giannelli et al., Phys. Lett. A, 434, 128054 (2022) that implements reinforcement learning with Lindblad dynamics, to introduce non-Markovianity of the surrounding either by timedependent rates or more exactly by using the hierarchical equations of motion with the QuTiP-BoFiN package. This extension opens the way to wider applications for non-Markovian environments, in particular when the active system interacts with a highly structured noise.Comment: 18 pages, 11 figure

Characterizing non-Markovian Quantum Processes by Fast Bayesian Tomography

To push gate performance to levels beyond the thresholds for quantum error correction, it is important to characterize the error sources occurring on quantum gates. However, the characterization of non-Markovian error poses a challenge to current quantum process tomography techniques. Fast Bayesian Tomography (FBT) is a self-consistent gate set tomography protocol that can be bootstrapped from earlier characterization knowledge and be updated in real-time with arbitrary gate sequences. Here we demonstrate how FBT allows for the characterization of key non-Markovian error processes. We introduce two experimental protocols for FBT to diagnose the non-Markovian behavior of two-qubit systems on silicon quantum dots. To increase the efficiency and scalability of the experiment-analysis loop, we develop an online FBT software stack. To reduce experiment cost and analysis time, we also introduce a native readout method and warm boot strategy. Our results demonstrate that FBT is a useful tool for probing non-Markovian errors that can be detrimental to the ultimate realization of fault-tolerant operation on quantum computing