Mesoscopic ensembles of polar bosons in triple-well potentials

Mesoscopic dipolar Bose gases in triple-well potentials offer a minimal system for the analysis of the long-range character of the dipole-dipole interactions. We show that this long-range character may be clearly revealed by a variety of possible ground-state phases. In addition, an appropriate control of short-range and dipolar interactions may lead to novel scenarios for the dynamics of atoms and polar molecules in lattices, including the dynamical creation of mesoscopic Schr\"odinger cats, which may be employed as a source of highly-nonclassical states for Heisenberg-limited interferometry.Comment: 4 pages, 3 figures. Identical to the published version, including supplemental material (4 pages, 6 figures)

Electromechanical Quantum Simulators

Digital quantum simulators are among the most appealing applications of a quantum computer. Here we propose a universal, scalable, and integrated quantum computing platform based on tunable nonlinear electromechanical nano-oscillators. It is shown that very high operational fidelities for single and two qubits gates can be achieved in a minimal architecture, where qubits are encoded in the anharmonic vibrational modes of mechanical nanoresonators, whose effective coupling is mediated by virtual fluctuations of an intermediate superconducting artificial atom. An effective scheme to induce large single-phonon nonlinearities in nano-electromechanical devices is explicitly discussed, thus opening the route to experimental investigation in this direction. Finally, we explicitly show the very high fidelities that can be reached for the digital quantum simulation of model Hamiltonians, by using realistic experimental parameters in state-of-the art devices, and considering the transverse field Ising model as a paradigmatic example.Comment: 14 pages, 8 figure

On Steady State of Continuous Min-Plus Systems

We study the steady state of a class of continuous min-plus linear systems by using the notion of system type. The aim is to control systems in order that outputs asymptotically track certain polynomial reference inputs in relation with the just-in-time criterion. As in conventional system theory, the use of system type property gives very simple expression for the resulting controllers. Disturbances acting on the system output are also considered

Supervisory Control of (max,+) Automata: A Behavioral Approach

A behavioral framework for control of (max,+) automata is proposed. It is based on behaviors (formal power series) and a generalized version of the Hadamard product, which is the behavior of a generalized tensor product of the plant and controller (max,+) automata in their linear representations. In the tensor product and the Hadamard product, the uncontrollable events that can neither be disabled nor delayed are distinguished. Supervisory control of (max,+) automata is then studied using residuation theory applied to our generalization of the Hadamard product of formal power series. This yields a notion of controllability of formal power series as well as (max,+)-counterparts of supremal controllable languages. Finally, rationality as an equivalent condition to realizability of the resulting controller series is discussed together with hints on future use of this approach

Modeling of timed Petri nets using deterministic (max,+) automata

International audienc

Modeling of Time-Varying (max,+) Systems by means of Weighted Timed Event Graphs

International audienceThe (max,+) theory allows to describe the behavior of Timed Event Graphs (TEG) with constant holding times. For time-varying systems, a class of First-In First-Out TEGs with periodic holding times has already been studied in the literature. We show here that such time-varying TEGs can be modeled by equivalent Weighted TEGs for which an input-output model exists. In summary, we can describe FIFO TEGs with periodic holding times by means of ultimately periodic formal series in a dioid denoted E * per δ

Le produit synchrone des automates (max,+)

Une extension des automates (max,+) est étudiée dans le but de modéliser le parrallélisme (occurrence simultanée d\u27évements). Pour cela, on introduit une composition synchrone des automates (max, +) vus comme des automates temporisés. Ceci nous amène à introduire des automates (max, +) avec multi-événements qui correspondent à une classe des automates temporisés avec plusieurs horloges. Nous obtenons la formule pour le comportement de produit synchrone d\u27automates (max,+) et montrons que dans le cas général il n\u27est pas possible de définir le produit synchrone des comportement (séries formelles) sans prendre en compte leurs représentations par automates (max,+)

Application of product dioids for dead token detection in interval P-time event graphs

Linear description of interval P-time event graphs using a product idempotent semiring is proposed and applied to dead token detection. The dependence of dead token on initial condition is studied using residuation theory. Finally, the relationship with the spectral theory of matrices over product semirings is discusse