Related papers: Constrained Mechanics and Noiseless Subsystems
Quantum machine learning is a discipline that holds the promise of revolutionizing data processing and problem-solving. However, dissipation and noise arising from the coupling with the environment are commonly perceived as major obstacles…
We consider qualitative simulation involving a finite set of qualitative relations in presence of complete knowledge about their interrelationship. We show how it can be naturally captured by means of constraints expressed in temporal logic…
Component systems - ensembles of realizations built from a shared repertoire of modular parts - are ubiquitous in biological, ecological, technological, and socio-cultural domains. From genomes to texts, cities, and software, these systems…
The Nelson stochastic mechanics is derived as a consequence of the basic physical principles such as the principle of relativity of observations and the invariance of the action quantum. The unitary group of quantum mechanics is represented…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
The abstract notion of a Universal Turing machine cannot exist as a physical subsystem without the introduction of noise from an external energy source. Like all other physical systems, physical Turing machines must convert energy sourced…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
In a recent article [A. Kurcz et al., Phys. Rev. A 81, 063821 (2010)] we predicted an energy concentrating mechanism in composite quantum systems. Its result is a non-zero stationary state photon emission rate even in the absence of…
The operator and the functional formulations of the dynamics of constrained systems are explored for determining unambiguously the quantum Hamiltonian of a nonrelativistic particle in a curved space.
This paper addresses the qualitative theory of mixed-order positive linear coupled systems with bounded or unbounded delays. First, we introduce a general result on the existence and uniqueness of solutions to mixed-order linear coupled…
For an arbitrary preparation, quantum mechanical descriptions refer to the complementary contexts set by incompatible measurements. We argue that an arbitrary preparation, therefore, should be described with respect to such a context by its…
Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which…
The identification of the constrained dynamics of mechanical systems is often challenging. Learning methods promise to ease an analytical analysis, but require considerable amounts of data for training. We propose to combine insights from…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
Quantum theory allows the traversing of multiple channels in a superposition of different orders. When the order in which the channels are traversed is controlled by an auxiliary quantum system, various unknown parameters of the channels…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…