Related papers: Limitations of the classical phase-locked loop ana…
We identify a broad class of physical processes in an optical quantum circuit that can be efficiently simulated on a classical computer: this class includes unitary transformations, amplification, noise, and measurements. This…
The terms hold-in, pull-in (capture), and lock-in ranges are widely used by engineers for the concepts of frequency deviation ranges within which PLL-based circuits can achieve lock under various additional conditions. Usually only…
We develop a general theoretical framework of semiclassical phase reduction for analyzing synchronization of quantum limit-cycle oscillators. The dynamics of quantum dissipative systems exhibiting limit-cycle oscillations are reduced to a…
Linear and nonlinear resonant states can be restrictive: they exist at particular discrete states in frequency and/or elasticity, under particular (e.g., simple-harmonic) waveforms. In forced oscillators, this restrictiveness is an obstacle…
In a phase-locked loop (PLL) synchronized inverter, due to the strong nonlinear coupling between the PLL's parame-ters and the operation power angle, the equivalent damping coefficient will quickly deteriorate while the power angle is close…
We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for…
A number of popular measures of dependence between pairs of band-limited signals rely on analytic phase. A common misconception is that the dependence revealed by these measures must be specific to the spectral range of the filtered input…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
Modern communication and computer systems require rapid (Gbps), efficient and large bandwidth data transfers. Agressive scaling of digital integrated systems allow buses and communication controller circuits to be integrated with the…
Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…
Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the…
The ambition constrained validity and the model witness problems in the logic UCL, for reasoning about circuits with unreliable gates, are analyzed. Moreover, two additional problems, motivated by the applications, are studied. One consists…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
It is well known from classical physics that weakly coupled self-sustained oscillators may spontaneously lock their phases. Just like classical synchronization is known to break down due to noise induced phase slips, we show here how the…
The dynamics of a quantum nonlinear oscillator is studied in terms of its quasi-flow, a dynamical mapping of the classical phase plane that represents the time-evolution of the quantum observables. Explicit expressions are derived for the…
We propose a method for setting limits that avoids excluding parameter values for which the sensitivity falls below a specified threshold. These "power-constrained" limits (PCL) address the issue that motivated the widely used CLs…
Nowadays, formal methods are used in various areas for the verification of programs or for code generation from models in order to increase the quality of software and to reduce costs. However, there are still fields in which formal methods…
We investigate the limitations of quantum computers for solving nonlinear dynamical systems. In particular, we tighten the worst-case bounds of the quantum Carleman linearisation (QCL) algorithm [Liu et al., PNAS 118, 2021] answering one of…
In recent years, strong expectations have been raised for the possible power of quantum computing for solving difficult optimization problems, based on theoretical, asymptotic worst-case bounds. Can we expect this to have consequences for…
Cyclic boundaries are used in many branches of physics and mathematics, typically to assist the approximation of a large space. We show that when determining the performance of planar, fault-tolerant, topological quantum error correction,…