Related papers: Virtual Quantum Markov Chains
The non-Markovianity of the stochastic process called the quantum semi-Markov (QSM) process is studied using a recently proposed quantification of memory based on the deviation from semigroup evolution, that provides a unified description…
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
It is well-known that the conditional mutual information of a quantum state is zero if, and only if, the quantum state is a quantum Markov chain. Replacing the Umegaki relative entropy in the definition of the conditional mutual information…
Neural quantum states (NQS) provide a flexible and highly expressive parameterization of wave functions for strongly correlated problems in quantum chemistry. Despite rapid advances in network architectures, the evaluation of electronic…
This paper studies three kinds of long-term behaviours, namely reachability, repeated reachability and persistence, of quantum Markov chains (qMCs). As a stepping-stone, we introduce the notion of bottom strongly connected component (BSCC)…
The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex…
The quantum channels with memory, known as non-Markovian channels, are of crucial importance for a realistic description of a variety of physical systems, and pave ways for new methods of decoherence control by manipulating the properties…
Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…
This thesis deals with the study of quantum communication protocols with Continuous Variable (CV) systems. Continuous Variable systems are those described by canonical conjugated coordinates x and p endowed with infinite dimensional Hilbert…
Stationary quantum information sources emit sequences of correlated qudits -- that is, structured quantum stochastic processes. If an observer performs identical measurements on a qudit sequence, the outcomes are a realization of a…
Quantum non-Markovianity of a quantum noisy channel manifests typically as information backflow, characterized by the departure of the intermediate map from complete positivity, though we indicate certain noisy channels that don't exhibit…
Hidden Markov Models are widely used in classical computer science to model stochastic processes with a wide range of applications. This paper concerns the quantum analogues of these machines --- so-called Hidden Quantum Markov Models…
This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties and the problem of quantum measurement. A considerable progress has…
Quantum state tomography is a key process in most quantum experiments. In this work, we employ quantum machine learning for state tomography. Given an unknown quantum state, it can be learned by maximizing the fidelity between the output of…
Quantum computing offers an alternative paradigm for addressing combinatorial optimization problems compared to classical computing. Despite recent hardware improvements, the execution of empirical quantum optimization experiments at scales…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
Recently, the idea of classical Metropolis sampling through Markov chains has been generalized for quantum Hamiltonians. However, the underlying Markov chain of this algorithm is still classical in nature. Due to Szegedy's method, the…
We study a class of Markov chains that model the evolution of a quantum system subject to repeated measurements. Each Markov chain in this class is defined by a measure on the space of matrices. It is then given by a random product of…
Markov states have been defined for tripartite quantum systems. In this paper, we generalize the definition of the Markov states to arbitrary multipartite case and find the general structure of an important subset of them, which we will…