Related papers: SpinGlassPEPS.jl: Tensor-network package for Ising…
The study of strongly frustrated magnetic systems has drawn great attentions from both theoretical and experimental physics. Efficient simulations of these models are essential for understanding their exotic properties. Here we present…
Belief Propagation is a well-studied message-passing algorithm that runs over graphical models and can be used for approximate inference and approximation of local marginals. The resulting approximations are equivalent to the Bethe-Peierls…
We present a methodology for generating Ising Hamiltonians of tunable complexity and with a priori known ground states based on a decomposition of the model graph into edge-disjoint subgraphs. The idea is illustrated with a spin-glass model…
We introduce TensorMixedStates, a Julia library built on top of ITensor which allows the simulation of quantum systems in the presence of dissipation using matrix product states (MPS). It offers three key features: i) it implements the MPS…
PowerDynamics.jl is an Open-Source library for dynamic power grid modeling built in the latest scientific programming language, Julia. It provides all the tools necessary to analyze the dynamical stability of power grids with high share of…
We investigate the disordered spin-$\frac12$Heisenberg model in two dimensions and employ tree tensor networks (TTNs) with a physics-informed structural optimization of the tree layout, to simulate dynamics in the many-body localization…
Graphical models for finite-dimensional spin glasses and real-world combinatorial optimization and satisfaction problems usually have an abundant number of short loops. The cluster variation method and its extension, the region graph…
The norms or expectation values of infinite projected entangled-pair states (PEPS) cannot be computed exactly, and approximation algorithms have to be applied. In the last years, many efficient algorithms have been devised -- the corner…
The projected entangled pair state (PEPS) representation of quantum states on two-dimensional lattices induces an entanglement based hierarchy in state space. We show that the lowest levels of this hierarchy exhibit an enormously rich…
Recent work has shown that for one-dimensional quantum states that can be effectively approximated by matrix product operators (MPOs), a polynomial number of copies of the state suffices for reconstruction. Compared to MPOs in one…
In this paper we present BilevelJuMP, a new Julia package to support bilevel optimization within the JuMP framework. The package is a Julia library that enables the user to describe both upper and lower-level optimization problems using the…
Time evolution of an infinite 2D many body quantum lattice system can be described by the Suzuki-Trotter decomposition applied to the infinite projected entangled pair state (iPEPS). Each Trotter gate increases the bond dimension of the…
Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
Two dimensional tensor networks such as projected entangled pairs states (PEPS) are generally hard to contract. This is arguably the main reason why variational tensor network methods in 2D are still not as successful as in 1D. However,…
Using mappings to computer-science problems and by applying sophisticated algorithms, one can study numerically many problems much better compared to applying standard approaches like Monte Carlo simulations. Here, using calculations of…
We study the low temperature properties of p-spin glass models with finite connectivity and of some optimization problems. Using a one-step functional replica symmetry breaking Ansatz we can solve exactly the saddle-point equations for…
We have developed TTNOpt, a software package that utilizes tree tensor networks (TTNs) for quantum spin systems and high-dimensional data analysis. TTNOpt provides efficient and powerful TTN computations by locally optimizing the network…
Real-world complex networks are usually being modeled as graphs. The concept of graphs assumes that the relations within the network are binary (for instance, between pairs of nodes); however, this is not always true for many real-life…
Optimization problems pose challenges across various fields. In recent years, quantum annealers have emerged as a promising platform for tackling such challenges. To provide a new perspective, we develop a heuristic tensor network (TN)…