Related papers: Efficient Tensor Network Algorithms for Spin Foam …
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…
Tensor network methods are powerful and efficient tools to study the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods were applied to lattice gauge theories,…
Numerical methods are a powerful tool for doing calculations in spinfoam theory. We review the major frameworks available, their definition, and various applications. We start from $\texttt{sl2cfoam-next}$, the state-of-the-art library to…
The intricated combinatorial structure and the non-compactness of the Lorentz group have always made the computation of $SL(2,\mathbb{C})$ EPRL spin foam transition amplitudes a very hard and resource demanding task. With \texttt{sl2cfoam}…
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…
Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…
Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete…
We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the…
A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…
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…
Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…
The efficient optimization of actuated soft structures, particularly under complex nonlinear forces, remains a critical challenge in advancing robotics. Simulations of nonlinear structures, such as soft-bodied robots modeled using the…
Binary Neural Networks (BNNs) enable efficient deep learning by saving on storage and computational costs. However, as the size of neural networks continues to grow, meeting computational requirements remains a challenge. In this work, we…
Monte Carlo algorithms are barely considered in spin foam quantum gravity. Due to the quantum nature of spin foam amplitudes one cannot readily apply them, and the present sign problem is a threat to convergence and thus efficiency. Yet,…
We present the first numerical calculation of the 4D Euclidean spin foam vertex amplitude for vertices with hypercubic combinatorics. Concretely, we compute the amplitude for coherent boundary data peaked on cuboid and frustum shapes. We…
We introduce a tensor network algorithm for the solution of $p$-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system…
We use TensorNetwork [C. Roberts et al., arXiv: 1905.01330], a recently developed API for performing tensor network contractions using accelerated backends such as TensorFlow, to implement an optimization algorithm for the Multi-scale…
Despite the potential of neural scene representations to effectively compress 3D scalar fields at high reconstruction quality, the computational complexity of the training and data reconstruction step using scene representation networks…
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to…
Neural networks have been able to achieve groundbreaking accuracy at tasks conventionally considered only doable by humans. Using stochastic gradient descent, optimization in many dimensions is made possible, albeit at a relatively high…