Related papers: Quantum Markov Networks and Commuting Hamiltonians
Graphical Models have various applications in science and engineering which include physics, bioinformatics, telecommunication and etc. Usage of graphical models needs complex computations in order to evaluation of marginal functions,so…
We prove that any one-dimensional (1D) quantum state with small quantum conditional mutual information in all certain tripartite splits of the system, which we call a quantum approximate Markov chain, can be well-approximated by a Gibbs…
A quantum network is an open system consisting of several component Markovian input-output subsystems interconnected by boson field channels carrying quantum stochastic signals. Generalizing the work of Chebotarev and Gregoratti, we…
We demonstrate that any Euclidean-time quantum mechanical theory may be represented as a neural network, ensured by the Kosambi-Karhunen-Lo\`eve theorem, mean-square path continuity, and finite two-point functions. The additional constraint…
The Markov property entails the conditional independence structure inherent in Gibbs distributions for general classical Hamiltonians, a feature that plays a crucial role in inference, mixing time analysis, and algorithm design. However,…
The aim of this paper is to derive the global Hamiltonian form for a quantum system and bath, or more generally a quantum network with multiple quantum input field connections, based on the local descriptions. We give a new simple argument…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
Statistical mechanics assumes that a quantum many-body system at low temperature can be effectively described by its Gibbs state. However, many complex quantum systems exist only as metastable states of dissipative open system dynamics,…
A quantum system coupled to a bath at some fixed, finite temperature converges to its Gibbs state. This thermalization process defines a natural, physically-motivated model of quantum computation. However, whether quantum computational…
Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is…
We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes.…
We introduce a class of so called Markovian marginals, which gives a natural framework for constructing solutions to the quantum marginal problem. We consider a set of marginals that possess a certain internal quantum Markov chain…
In the present paper we study a unified approach for Quantum Markov Chains. A new quantum Markov property that generalizes the old one, is discussed. We introduce Markov states and chains on general local algebras, possessing a generic…
We prove that the quantum Gibbs states of spin systems above a certain threshold temperature are approximate quantum Markov networks, meaning that the conditional mutual information decays rapidly with distance. We demonstrate the…
Quantum Markov chains (QMCs) are positive maps on a trace-class space describing open quantum dynamics on graphs. Such objects have a statistical resemblance with classical random walks, while at the same time it allows for internal…
Quantum Markov chains generalize classical Markov chains for random variables to the quantum realm and exhibit unique inherent properties, making them an important feature in quantum information theory. In this work, we propose the concept…
It has been proposed that random wide neural networks near Gaussian process are quantum field theories around Gaussian fixed points. In this paper, we provide a novel map with which a wide class of quantum mechanical systems can be cast…
We introduce generalized quantum Markov states and generalized d-Markov chains which extend the notion quantum Markov chains on spin systems to that on $C^*$-algebras defined by general graphs. As examples of generalized d-Markov chains, we…
We study a class of commuting Markov kernels whose simplest element describes the movement of $k$ particles on a discrete circle of size $n$ conditioned to not intersect each other. Such Markov kernels are related to the quantum cohomology…
Cubelike graphs are the Cayley graphs of the elementary abelian group (Z_2)^n (e.g., the hypercube is a cubelike graph). We give conditions for perfect state transfer between two particles in quantum networks modeled by a large class of…