Related papers: Quantum theory in finite dimension cannot explain …
The goal of generative machine learning is to model the probability distribution underlying a given data set. This probability distribution helps to characterize the generation process of the data samples. While classical generative machine…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously…
We classify the rare events of structured, memoryful stochastic processes and use this to analyze sequential and parallel generators for these events. Given a stochastic process, we introduce a method to construct a new process whose…
Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm. This discrepancy is usually addressed by subjectively making the…
We consider Markov processes of cubic stochastic (in a fixed sense) matrices which are also called quadratic stochastic process (QSPs). A QSP is a particular case of a continuous-time dynamical system whose states are stochastic cubic…
Generalized probabilistic theories (GPTs) provide a framework in which a range of possible theories can be examined, including classical theory, quantum theory and those beyond. In general, enlarging the state space of a GPT leads to fewer…
The field of classical stochastic processes forms a major branch of mathematics. They are, of course, also very well studied in biology, chemistry, ecology, geology, finance, physics, and many more fields of natural and social sciences.…
In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states…
Stochastic processes described by evolution equations in the universality class of the FKPP equation may be approximately factorized into a linear stochastic part and a nonlinear deterministic part. We prove this factorization on a model…
A growing body of work has established the modelling of stochastic processes as a promising area of application for quantum techologies; it has been shown that quantum models are able to replicate the future statistics of a stochastic…
We consider quantum formalism limited by the classical simulating computer with the fixed memory. The memory is redistributed in the course of modeling by the variation of the set of classical states and the accuracy of the representation…
We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories,…
The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…
Stochastic models are highly relevant tools in science, engineering, and society. Recent work suggests emerging quantum computing technologies can substantially decrease the memory requirements for simulating stochastic models. Here we show…
Quantum technologies offer a promising route to the efficient sampling and analysis of stochastic processes, with potential applications across the sciences. Such quantum advantages rely on the preparation of a quantum sample state of the…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two…
We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of…
A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level…
We investigate the problem of simulating classical stochastic processes through quantum dynamics, and present three scenarios where memory or time quantum advantages arise. First, by introducing and analysing a quantum version of the…