Related papers: Superposed Random Spin Tensor Networks and their H…
The AdS/CFT correspondence conjectures a holographic duality between gravity in a bulk space and a critical quantum field theory on its boundary. Tensor networks have come to provide toy models to understand such bulk-boundary…
The relation between Loop Quantum Gravity (LQG) and tensor network is explored from the perspectives of bulk-boundary duality and holographic entanglement entropy. We find that the LQG spin-network states in a space $\Sigma$ with boundary…
We study the realization of anyon-permuting symmetries of topological phases on the lattice using tensor networks. Working on the virtual level of a projected entangled pair state, we find matrix product operators (MPOs) that realize all…
In this paper, we introduce a novel model for random hypergraphs based on weighted random connection models. In accordance with the standard theory for hypergraphs, this model is constructed from a bipartite graph. In our stochastic model,…
In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, where we focus on…
In this paper, we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process, which may serve as a mobile wireless network model. The transition probability matrix…
We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the…
We present a scheme to perform an iterative variational optimization with infinite projected entangled-pair states (iPEPS), a tensor network ansatz for a two-dimensional wave function in the thermodynamic limit, to compute the ground state…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
There exists a remarkable four-qutrit state that carries absolute maximal entanglement in all its partitions. Employing this state, we construct a tensor network that delivers a holographic many body state, the H-code, where the physical…
Tensor networks provide a powerful tool for studying many-body quantum systems, particularly making quantum simulations more efficient. In this article, we construct a tensor network representation of the spin network states, which…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
Tensor networks implementing quantum error correcting codes have recently been used to construct toy models of holographic duality explicitly realizing some of the more puzzling features of the AdS/CFT correspondence. These models reproduce…
We propose a vertex representation of the tensor network (TN) for classical spin systems on hyperbolic lattices. The tensors form a network of regular $p$-sided polygons ($p>4$) with the coordination number four. The response to multi-state…
We analyze few-body quantum states with particular correlation properties imposed by the requirement of maximal bipartite entanglement for selected partitions of the system into two complementary parts. A novel framework to treat this…
We provide a description of virtual non-local matrix product operator (MPO) symmetries in projected entangled pair state (PEPS) representations of string-net models. Given such a PEPS representation, we show that the consistency conditions…
We examine in details the connections between topological and entanglement properties of short-range resonating valence bond (RVB) wave functions using Projected Entangled Pair States (PEPS) on kagome and square lattices on (quasi-)infinite…
Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…
We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…
In this paper, we study the structure of a family of superposition states on tensor algebras. The correlation functions of the considered states are described through a new kind of positive definite kernels valued in the dual of…