Related papers: From Classical to quantum stochastic process

Various physical effects resulting from decoherence are discussed in the algebraic framework. In particular, it is shown that the environment may induce not only classical properties like superselection rules, pointer states or even…

We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum dynamics emerges and…

Classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin. The constrained quantum evolution corresponds to an appropriate coarse-graining of the quantum…

Current technologies in quantum-based communications bring a new integration of quantum data with classical data for hybrid processing. However, the frameworks of these technologies are restricted to a single classical or quantum task,…

The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…

We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding…

The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those which have, as their classical limit, a non-integrable classical system. In order to obtain this limit, the self-induced…

The quantum to classical transition of fluctuations in the early universe is still not completely understood. Some headway has been made incorporating the effects of decoherence and the squeezing of states, though the methods and procedures…

We define a map which relates four dimensional classical stochastic matrices to qubit quantum channels. The map preserves the spectrum and the composition of processes. To do this we introduce the concept of Bloch tetrahedron which plays…

To make sense of the world around us, we develop models, constructed to enable us to replicate, describe, and explain the behaviours we see. Focusing on the broad case of sequences of correlated random variables, i.e., classical stochastic…

The paper develops the idea that the dynamics of both classical and quantum processes is time reversible. It is shown how this classical analogy allows one to define the measure for the path integral in quantum mechanics.

A homogeneous and isotropic cosmological model with a positive cosmological constant is considered. The matter sector is given by a massless scalar field, which can be used as an internal time to deparametrize the theory. The idea is to…

Machine Learning algorithms are extensively used in an increasing number of systems, applications, technologies, and products, both in industry and in society as a whole. They enable computing devices to learn from previous experience and…

The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, stochastic dynamics is ubiquitous because of thermal fluctuations. The Fokker-Plank-Smoluchowski equation models the time evolution of the…

We investigate the correspondence between classical noise and quantum environments. Although it has been known that the classical noise can be mapped to the quantum environments only for pure dephasing and infinite-temperature dissipation…

This paper argues that every quantum system can be understood as a sufficiently general kind of stochastic process unfolding in an old-fashioned configuration space according to ordinary notions of probability. This argument is based on an…

The initial time-dependence of a state in circumstances where it makes transitions to, or decay to, a second state has been investigated. In classical stochastic processes, the observed time dependence of transition or decay proportional to…

Hybrid quantum-classical optimization algorithms represent one of the most promising application for near-term quantum computers. In these algorithms the goal is to optimize an observable quantity with respect to some classical parameters,…

Instead of producing quantum languages that are fit for current quantum computers, we build a language from standard classical assembler and augment it with quantum capabilities so that quantum algorithms become a subset of it. This paves…

We study a quantum oscillator interacting and back-reacting on a classical oscillator. This can be done consistently provided the quantum system decoheres, while the backreaction has a stochastic component which causes the classical system…