Related papers: Quantum stochastic processes and quantum non-Marko…

Simulations of stochastic processes play an important role in the quantitative sciences, enabling the characterisation of complex systems. Recent work has established a quantum advantage in stochastic simulation, leading to quantum devices…

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…

Recent advancements in quantum computing have positioned it as a prospective solution for tackling intricate computational challenges, with supervised learning emerging as a promising domain for its application. Despite this potential, the…

Quantum process tomography --- a primitive in many quantum information processing tasks --- can be cast within the framework of the theory of design of experiment (DoE), a branch of classical statistics that deals with the relationship…

Stochastic processes are shown to emerge from the time evolution of complex quantum systems. Using parametric, banded random matrix ensembles to describe a quantum chaotic environment, we show that the dynamical evolution of a particle…

Quantum thermodynamics studies how quantum systems and operations may be exploited as sources of work to perform useful thermodynamic tasks. In real-world conditions, the evolution of open quantum systems typically displays memory effects,…

Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue…

Physical processes in the quantum regime possess non-classical properties of quantum mechanics. However, methods for quantitatively identifying such processes are still lacking. Accordingly, in this study, we develop a framework for…

A study of the non-dissipative Brownian motion in vacuum is presented. The noise source associated to the stochastic process assumed in this work is vacuum fluctuations of some quantum field capable of interact with a massive particle. For…

Memory is the fundamental form of temporal complexity: when present but uncontrollable, it manifests as non-Markovian noise; conversely, if controllable, memory can be a powerful resource for information processing. Memory effects arise…

This course of lectures has been taught for several years at the Lomonosov Moscow State University; its modified version in 2021 is read in the Zhejiang University (Hangzhou), in the framework of summer school on quantum computing. The…

Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…

Molecular science is governed by the dynamics of electrons, atomic nuclei, and their interaction with electromagnetic fields. A reliable physicochemical understanding of these processes is crucial for the design and synthesis of chemicals…

Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic…

Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…

These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…

I propose to treat quantum evolution as a stochastic process consisting from a sequence of doubly stochastic matrices, which naturally arise in the generalized quantum evolution. Then it is proved that the law of non-decreasing entropy is…

Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…

We present a detailed account of the technical aspects of stochastic quantum molecular dynamics, an approach introduced recently by the authors [H. Appel and M. Di Ventra, Phys. Rev. B 80 212303 (2009)] to describe coupled electron-ion…

How much information do we need about a process' past to faithfully simulate its future? The statistical complexity is a prominent quantifier of structure for stochastic processes. Quantum machines, however, can simulate classical…