Related papers: Gaussian continuous tensor network states: short-d…
We describe a method for simulating and characterizing realistic Gottesman-Kitaev-Preskill (GKP) cluster states, rooted in the representation of resource states in terms of sums of Gaussian distributions in phase space. We apply our method…
Boundary constraints in physical, environmental and engineering models restrict smooth states such as temperature to follow known physical laws at the edges of their spatio-temporal domain. Examples include fixed-state or fixed-derivative…
A promising application of neural-network quantum states is to describe the time dynamics of many-body quantum systems. To realize this idea, we employ neural-network quantum states to approximate the implicit midpoint rule method, which…
This paper is concerned with a translation invariant network of identical quantum stochastic systems subjected to external quantum noise. Each node of the network is directly coupled to a finite number of its neighbours. This network is…
(Quasi-)periodic solutions are constructed analytically for Galerkin-regularized or truncated nonlinear Schr\"odinger (GrNLS) systems preserving finite Fourier freedoms. GrNLS admits travelling-wave or multi-phase solutions, including…
Generating stable molecular conformations is crucial in several drug discovery applications, such as estimating the binding affinity of a molecule to a target. Recently, generative machine learning methods have emerged as a promising, more…
Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state…
Predicting future motion based on historical motion sequence is a fundamental problem in computer vision, and it has wide applications in autonomous driving and robotics. Some recent works have shown that Graph Convolutional Networks(GCN)…
We derive upper bounds on the Wasserstein distance ($W_1$), with respect to $\sup$-norm, between any continuous $\mathbb{R}^d$ valued random field indexed by the $n$-sphere and the Gaussian, based on Stein's method. We develop a novel…
We study some properties of a multi-species degenerate Ginzburg-Landau energy and its relation to a cross-diffusion Cahn-Hilliard system. The model is motivated by multicomponent mixtures where crossdiffusion effects between the different…
Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified…
We define generalised Gaussian states for quantum cosmological models based on the $\mathfrak{su(1,1)}$ algebra, with particular emphasis on its realisation in group field theory for a single field mode, and study their semiclassical…
We introduce Neural Tensor Network States ($\nu$TNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the $\nu$TNS framework, a neural network serves as a disentangler…
The Gaussian-radial-basis function neural network (GRBFNN) has been a popular choice for interpolation and classification. However, it is computationally intensive when the dimension of the input vector is high. To address this issue, we…
In this paper, we investigate the convergence performance of a cooperative diffusion Gauss-Newton (GN) method, which is widely used to solve the nonlinear least squares problems (NLLS) due to the low computation cost compared with Newton's…
The 2+1d continuum Lifshitz theory of a free compact scalar field plays a prominent role in a variety of quantum systems in condensed matter physics and high energy physics. It is known that in compact space, it has an infinite ground state…
In this paper, we provide the first precise distributional characterization of gradient descent iterates for general multi-layer neural networks under the canonical single-index regression model, in the `finite-width proportional regime'…
There is a recent and growing literature on large-width asymptotic and non-asymptotic properties of deep Gaussian neural networks (NNs), namely NNs with weights initialized as Gaussian distributions. For a Gaussian NN of depth $L\geq1$ and…
Even though Gaussian quantum states of multimode light are promising quantum resources due to their scalability, non-Gaussianity is indispensable for quantum technologies, in particular to reach quantum computational advantage. However,…
The intuitiveness of the tensor network graphical language is becoming well known through its use in numerical simulations using methods from tensor network algorithms. Recent times have also seen rapid progress in developing equations of…