Related papers: Algorithmic Complexity in Noise Induced Transport …

The complexity of the quantum state of a multiparticle system and the maximum possible accuracy of its quantum description are connected by a relation similar to the coordinate-momentum uncertainty relation. The coefficient in this relation…

This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied…

Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…

Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There…

Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…

The dynamics of a weakly dissipative Hamiltonian system submitted to stochastic perturbations has been investigated by means of asymptotic methods. The probability of noise-induced separatrix crossing, which drastically changes the fate of…

Complexity of two-level systems, e.g. spins, qubits, magnetic moments etc, are analysed based on the so-called correlational entropy in the case of pure quantum systems and the thermal entropy in case of thermal equilibrium that are…

We introduce a definition of algorithmic symmetry able to capture essential aspects of geometric symmetry. We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov-Chaitin complexity) of…

In this paper machine learning and artificial neural network models are proposed for the classification of external noise sources affecting a given quantum dynamics. For this purpose, we train and then validate support vector machine,…

Every quantum system is coupled to an environment. Such system-environment interaction leads to temporal correlation between quantum operations at different times, resulting in non-Markovian noise. In principle, a full characterisation of…

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…

Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. In this review we study the…

Quantum graphs with leads to infinity serve as convenient models for studying various aspects of systems which are usually attributed to chaotic scattering. They are also studied in several experimental systems and practical applications.…

In spite of the fact that the Newtonian dynsmics of the underlying molecules do not seem to favor one direction of time over its opposite, the non-decreasing entropy of macroscopic physical systems provides a unique direction to 'the arrow…

The complexity of round robin method of intraprocedural data flow analysis is measured in number of iterations over the control flow graph. Existing complexity bounds realistically explain the complexity of only Bit-vector frameworks which…

Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…

The problem of characterizing complexity of quantum dynamics - in particular of locally interacting chains of quantum particles - will be reviewed and discussed from several different perspectives: (i) stability of motion against external…

Disorder, noise and interaction play a crucial role in the transport properties of real systems, but they are typically hard to control and study both theoretically and experimentally, especially in the quantum case. Here we explore a…

The ability to precisely quantify similarity between various entities has been a fundamental complication in various problem spaces specifically in the classification of cellular images. Contemporary similarity measures applied in the…

Many learning algorithms can be represented as Markov processes, and understanding their generalization error is a central topic in learning theory. For specific continuous-time noisy algorithms, a prominent analysis technique relies on…