Related papers: Neural network representation of quantum systems

In this paper, we develop a Lie group theoretic approach for parametric representation of unitary matrices. This leads to develop a quantum neural network framework for quantum circuit approximation of multi-qubit unitary gates. Layers of…

We study the extent to which wide neural networks may be approximated by Gaussian processes when initialized with random weights. It is a well-established fact that as the width of a network goes to infinity, its law converges to that of a…

Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection…

Artificial neural networks have achieved great success in many fields ranging from image recognition to video understanding. However, its high requirements for computing and memory resources have limited further development on processing…

It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way…

Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to…

Neural networks are computing models that have been leading progress in Machine Learning (ML) and Artificial Intelligence (AI) applications. In parallel, the first small scale quantum computing devices have become available in recent years,…

We show that deep neural networks, including transformers and RNNs, pretrained as usual on next-token prediction, intrinsically discover and represent beliefs over 'quantum' and 'post-quantum' low-dimensional generative models of their…

This paper discusses various theorems on the approximation capabilities of neural networks (NNs), which are known as universal approximation theorems (UATs). The paper gives a systematic overview of UATs starting from the preliminary…

As a compact representation of joint probability distributions over a dependence graph of random variables, and a tool for modelling and reasoning in the presence of uncertainty, Bayesian networks are of great importance for artificial…

Recurrent neural networks play an important role in both research and industry. With the advent of quantum machine learning, the quantisation of recurrent neural networks has become recently relevant. We propose fully quantum recurrent…

In this paper we cast the well-known convolutional neural network in a Gaussian process perspective. In this way we hope to gain additional insights into the performance of convolutional networks, in particular understand under what…

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…

Quantum neural network architectures that have little-to-no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by…

In the wake of the growing popularity of machine learning in particle physics, this work finds a new application of geometric deep learning on Feynman diagrams to make accurate and fast matrix element predictions with the potential to be…

Machine learning techniques are employed to perform the full characterization of a quantum system. The particular artificial intelligence technique used to learn the Hamiltonian is called physics informed neural network (PINN). The idea…

This paper proposes a numerical method using neural networks to solve the path integral problem in quantum mechanics for arbitrary potentials. The method is based on a radial basis function expansion of the interaction term that appears in…

Spin networks, essentially labeled graphs, are ``good quantum numbers'' for the quantum theory of geometry. These structures encompass a diverse range of techniques which may be used in the quantum mechanics of finite dimensional systems,…

We define a neural network in infinite dimensional spaces for which we can show the universal approximation property. Indeed, we derive approximation results for continuous functions from a Fr\'echet space $\X$ into a Banach space $\Y$. The…

Deep neural networks have established themselves as one of the most promising machine learning techniques. Training such models at large scales is often parallelized, giving rise to the concept of distributed deep learning. Distributed…