Related papers: Belief propagation for general graphical models wi…
Tensor network contraction on arbitrary graphs is a fundamental computational challenge with applications ranging from quantum simulation to error correction. While belief propagation (BP) provides a powerful approximation algorithm for…
Recent years have seen a growing interest in the use of belief propagation - an algorithm originally introduced for performing statistical inference on graphical models - for approximate, but highly efficient, tensor network contraction.…
Belief Propagation (BP) is an efficient message-passing algorithm widely used for inference in graphical models and for solving various problems in statistical physics. However, BP often yields inaccurate estimates of order parameters and…
Belief propagation (BP) can be a useful tool to approximately contract a tensor network, provided that the contributions from any closed loops in the network are sufficiently weak. In this manuscript we describe how a loop series expansion…
Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces…
Belief propagation (BP) provides a scalable heuristic for contracting tensor networks on loopy graphs, but its success in quantum many-body settings has largely rested on empirical evidence. Developing upon a recently introduced…
Belief propagation is a well-studied algorithm for approximating local marginals of multivariate probability distribution over complex networks, while tensor network states are powerful tools for quantum and classical many-body problems.…
The belief propagation (BP) based algorithm is investigated as a potential decoder for both of error correcting codes and lossy compression, which are based on non-monotonic tree-like multilayer perceptron encoders. We discuss that whether…
Belief propagation has recently emerged as a powerful framework for evaluating tensor networks in higher dimensions, combining computational efficiency with provable analytical guarantees. In this work, we develop the first end-to-end…
Simulating many-body quantum systems on a classical computer is difficult due to the large number of degrees of freedom, causing the computational complexity to grow exponentially with system size. Tensor Networks (TN) is a framework that…
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…
Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief…
Belief propagation is a widely used message passing method for the solution of probabilistic models on networks such as epidemic models, spin models, and Bayesian graphical models, but it suffers from the serious shortcoming that it works…
Belief propagation (BP) algorithm is a widely used message-passing method for inference in graphical models. BP on loop-free graphs converges in linear time. But for graphs with loops, BP's performance is uncertain, and the understanding of…
We consider belief propagation (BP) as an efficient and scalable tool for state estimation and optimization problems in supply networks such as power grids. BP algorithms make use of factor graph representations, whose assignment to the…
Belief propagation (BP) is well-known as a low complexity decoding algorithm with a strong performance for important classes of quantum error correcting codes, e.g. notably for the quantum low-density parity check (LDPC) code class of…
Belief propagation (BP) is a message-passing method for solving probabilistic graphical models. It is very successful in treating disordered models (such as spin glasses) on random graphs. On the other hand, finite-dimensional lattice…
Belief propagation is a powerful tool in statistical physics, machine learning, and modern coding theory. As a decoding method, it is ubiquitous in classical error correction and has also been applied to stabilizer-based quantum error…
Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors.…
Belief propagation (BP) is a classical algorithm that approximates the marginal distribution associated with a factor graph by passing messages between adjacent nodes in the graph. It gained popularity in the 1990's as a powerful decoding…