Related papers: Partitioned Expansions for Approximate Tensor Netw…
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 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…
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…
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…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
Tensor network contraction is a fundamental mathematical operation that generalizes the dot product and matrix multiplication. It finds applications in numerous domains, such as database systems, graph theory, machine learning, probability…
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…
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…
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.…
Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…
The approximate contraction of a Projected Entangled Pair States (PEPS) tensor network is a fundamental ingredient of any PEPS algorithm, required for the optimization of the tensors in ground state search or time evolution, as well as for…
Tensor networks have proven to be a valuable tool, for instance, in the classical simulation of (strongly correlated) quantum systems. As the size of the systems increases, contracting larger tensor networks becomes computationally…
We investigate a novel approach to approximate tensor-network contraction via the exact, matrix-free decomposition of full tensor-networks. We study this method as a means to eliminate the propagation of error in the approximation of…
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.…
Tensor network contraction is a powerful computational tool in quantum many-body physics, quantum information and quantum chemistry. The complexity of contracting a tensor network is thought to mainly depend on its entanglement properties,…
The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such…
We propose a novel technique for faster deep neural network training which systematically applies sample-based approximation to the constituent tensor operations, i.e., matrix multiplications and convolutions. We introduce new sampling…
In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of…
Tensor network algorithms have proven to be very powerful tools for studying one- and two-dimensional quantum many-body systems. However, their application to three-dimensional (3D) quantum systems has so far been limited, mostly because…
There is an increasing interest in scaling tensor network methods through belief propagation (BP), as well as increasing the accuracy of BP through tensor network methods. We develop a unification framework that takes an arbitrary graphical…