Related papers: Improving accuracy of tree-tensor network approach…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…
Quantum Key Distribution (QKD) networks require routing methodologies capable of jointly optimizing latency, secret key generation rate, congestion, finite capacity and operational security constraints under dynamically evolving traffic…
Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…
We present how to compute vibrational eigenstates with tree tensor network states (TTNSs), the underlying ansatz behind the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. The eigenstates are computed with an…
The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially…
Multi-task and multi-domain learning methods seek to learn multiple tasks/domains, jointly or one after another, using a single unified network. The primary challenge and opportunity lie in leveraging shared information across these tasks…
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…
Tree tensor networks, or tree-based tensor formats, are prominent model classes for the approximation of high-dimensional functions in computational and data science. They correspond to sum-product neural networks with a sparse connectivity…
With the increasing adoption of machine learning tools like neural networks across several domains, interesting connections and comparisons to concepts from other domains are coming to light. In this work, we focus on the class of Tensor…
Tree tensor networks (TTNs) offer powerful models for image classification. While these TTN image classifiers already show excellent performance on classical hardware, embedding them into quantum neural networks (QNNs) may further improve…
We adopt a two-dimensional tensor-network (TN) ansatz to simulate variational quantum algorithms on two-dimensional qubit architectures, demonstrating its capability to accurately simulate deep circuits through the Quantum Approximate…
We apply a series of projection techniques on top of tensor networks to compute energies of ground state wave functions with higher accuracy than tensor networks alone with minimal additional cost. We consider both matrix product states as…
Deep neural networks (DNNs) have delivered a remarkable performance in many tasks of computer vision. However, over-parameterized representations of popular architectures dramatically increase their computational complexity and storage…
The restricted Boltzmann machine (RBM) is one of the fundamental building blocks of deep learning. RBM finds wide applications in dimensional reduction, feature extraction, and recommender systems via modeling the probability distributions…
Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…
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…
Exact many-body quantum problems are known to be computationally hard due to the exponential scaling of the numerical resources required. Since the advent of the Density Matrix Renormalization Group, it became clear that a successful…
This paper presents an adaptive convolutional neural network (CNN) architecture that can automate diverse topology optimization (TO) problems having different underlying physics. The architecture uses the encoder-decoder networks with dense…
We consider the minimum spanning tree problem with predictions, using the weight-arrival model, i.e., the graph is given, together with predictions for the weights of all edges. Then the actual weights arrive one at a time and an…
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…