Related papers: Contracting Arbitrary Tensor Networks: General App…

Graphical models use graphs to compactly capture stochastic dependencies amongst a collection of random variables. Inference over graphical models corresponds to finding marginal probability distributions given joint probability…

One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor…

Quantum mechanics is inherently probabilistic in light of Born's rule. Using quantum circuits as probabilistic generative models for classical data exploits their superior expressibility and efficient direct sampling ability. However,…

Inexpensive machine learning potentials are increasingly being used to speed up structural optimization and molecular dynamics simulations of materials by iteratively predicting and applying interatomic forces. In these settings, it is…

It is one of the most fundamental objectives in quantum information science to understand the boundary between the computational power of classical and quantum computers. One possible avenue to explore this boundary is to identify classes…

The process of translating a quantum algorithm into a form suitable for implementation on a quantum computing platform is crucial but yet challenging. This entails specifying quantum operations with precision, a typically intricate task. In…

The quantum circuit model is the most commonly used model for implementing quantum computers and quantum neural networks whose essential tasks are to realize certain unitary operations. Here we propose an alternative approach; we use a…

In this paper, we present a technically simple method to establish upper bounds on the expected injective norm of real and complex random tensors. Our approach is somewhat analogous to the moment method in random matrix theory, and is based…

Graph neural networks, trained on experimental or calculated data are becoming an increasingly important tool in computational materials science. Networks, once trained, are able to make highly accurate predictions at a fraction of the cost…

We characterize the computational power of neural networks that follow the graph neural network (GNN) architecture, not restricted to aggregate-combine GNNs or other particular types. We establish an exact correspondence between the…

In many applications, it is needed to change the topology of a tensor network directly and without approximation. This work will introduce a general scheme that satisfies these needs. We will describe the procedure by two examples and show…

In this paper, we extend the analysis of random Kronecker graphs to multi-dimensional networks represented as tensors, enabling a more detailed and nuanced understanding of complex network structures. We decompose the adjacency tensor of…

Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…

Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…

Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…

Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…

A modification of the Adaptive Biasing Force method is introduced, in which the free energy is approximated by a sum of tensor products of one-dimensional functions. This enables to handle a larger number of reaction coordinates than the…

Printed electronics offer a promising alternative for applications beyond silicon-based systems, requiring properties like flexibility, stretchability, conformality, and ultra-low fabrication costs. Despite the large feature sizes in…

Gaussian boson sampling is a promising candidate for showing experimental quantum advantage. While there is evidence that noiseless Gaussian boson sampling is hard to efficiently simulate using a classical computer, the current Gaussian…

In recent times, Variational Quantum Circuits (VQC) have been widely adopted to different tasks in machine learning such as Combinatorial Optimization and Supervised Learning. With the growing interest, it is pertinent to study the…