Related papers: Ultimate Limits to Computation: Anharmonic Oscilla…
The large-N expansion technique is tested via an anomalous, soft-core potential which admits the tunneling through its central barrier. The precision of the approximation is found sensitive to the asymptotic component of the interaction.…
Optimal Control Problems consist on the optimisation of an objective functional subjected to a set of Ordinary Differential Equations. In this work, we consider the effects on the stability of the numerical solution when this optimisation…
We discuss the problem of counting the maximum number of distinct states that an isolated physical system can pass through in a given period of time---its maximum speed of dynamical evolution. Previous analyses have given bounds in terms of…
In the absence of external forcing, all trajectories on the phase plane of the van der Pol oscillator tend to a closed, periodic, trajectory -- the limit cycle -- after infinite time. Here, we drive the van der Pol oscillator with an…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
Solving for the minimum time bounded acceleration trajectory with prescribed position and velocity at endpoints is a highly nonlinear problem. The methods and bounds developed in this paper distinguish when there is a continuous…
Starting from a solution of the problem of a mechanical oscillator coupled to a scalar field inside a reflecting sphere of radius $R$, we study the behaviour of the system in free space as the limit of an arbitrarily large radius in the…
quest for processing speed potential. In fact, we always get a fraction of the technically available computing power (so-called {\em theoretical peak}), and the gap is likely to go hand-to-hand with the hardware complexity of the target…
We present an efficient transcription method for highly oscillatory optimal control problems. For these problems, the optimal state trajectory consists of fast oscillations that change slowly over the time horizon. Out of a large number of…
The ever increasing demands placed upon machine performance have resulted in the need for more comprehensive particle accelerator modeling. Computer simulations are key to the success of particle accelerators. Many aspects of particle…
Combinatorial optimization problems are computationally hard in general, but they are ubiquitous in our modern life. A coherent Ising machine (CIM) based on a multiple-pulse degenerate optical parametric oscillator (DOPO) is an alternative…
We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the…
It is proposed that measurement devices can be modelled to have an open decoherence dynamics that is faster than any other relevant timescale, which is referred to as the ultradecoherence limit. In this limit, the measurement device always…
A very simple procedure to calculate eigenenergies of quantum anharmonic oscillators is presented. The method, exact but for numerical computations, consists merely in requiring the vanishing of the Wronskian of two solutions which are…
A common aspect of today's cyber-physical systems is that multiple optimization-based control tasks may execute in a shared processor. Such control tasks make use of online optimization and thus have large execution times; hence, their…
Optical oscillators present a powerful optimization mechanism. The inherent competition for the gain resources between possible modes of oscillation entails the prevalence of the most efficient single mode. We harness this 'ultrafast'…
We investigate the capabilities of a quantum computer based on cold trapped ions in presence of non-dissipative decoherence. The latter is accounted by using the evolution time as a random variable and then averaging on a properly defined…
We analyze the proposal of achieving a Mott state of Laughlin wave functions in an optical lattice [M. Popp {\it et al.}, Phys. Rev. A 70, 053612 (2004)] and study the consequences of considering the anharmonic corrections to each single…
In this paper we use optimal control to design minimum-time adiabatic-like paths for the expansion of a quantum piston. Under realistic experimental constraints, we calculate the minimum expansion time and compare it with that obtained from…
Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…