Related papers: Sampling two-dimensional isometric tensor network …
Network sampling is a crucial technique for analyzing large or partially observable networks. However, the effectiveness of different sampling methods can vary significantly depending on the context. In this study, we empirically compare…
Tensor networks are factorisations of high rank tensors into networks of lower rank tensors and have primarily been used to analyse quantum many-body problems. Tensor networks have seen a recent surge of interest in relation to supervised…
We provide dual algorithms for sampling the space of abstract simplicial complexes on a fixed number of vertices. We develop a generative and descriptive sampler designed with heuristics to help balance the combinatorial multiplicities of…
A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…
This paper presents a novel algorithm solving the classic problem of generating a random sample of size s from population of size n with non-uniform probabilities. The sampling is done with replacement. The algorithm requires constant…
In this paper, we build and explore supervised learning models of ferromagnetic system behavior, using Monte-Carlo sampling of the spin configuration space generated by the 2D Ising model. Given the enormous size of the space of all…
In the context of quantum information, highly nonlinear regimes, such as those supporting solitons, are marginally investigated. We miss general methods for quantum solitons, although they can act as entanglement generators or as…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…
We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to…
Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement…
We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is based on inverse transform sampling with a…
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…
We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we…
We show how to develop sampling-based alternating least squares (ALS) algorithms for decomposition of tensors into any tensor network (TN) format. Provided the TN format satisfies certain mild assumptions, resulting algorithms will have…
Optimized sensing is important for computational imaging in low-resource environments, when images must be recovered from severely limited measurements. In this paper, we propose a physics-constrained, fully differentiable, autoencoder that…
Tensor networks are efficient factorisations of high-dimensional tensors into a network of lower-order tensors. They have been most commonly used to model entanglement in quantum many-body systems and more recently are witnessing increased…
Novel randomness-induced disordered ground states in two-dimensional (2D) quantum spin systems have been attracting much interest. For quantitative analysis of such random quantum spin systems, one of the most promising numerical approaches…
Tensor network methods are powerful tools for studying quantum many-body systems. In this paper, we investigate the emergent statistical properties of random high-dimensional tensor-network states and the trainability of variational tensor…
Tensor networks are a powerful modeling framework developed for computational many-body physics, which have only recently been applied within machine learning. In this work we utilize a uniform matrix product state (u-MPS) model for…