Related papers: Quantum State Assignment Flows
We introduce a composition of quantum states of a bipartite system which is based on the reshuffling of density matrices. This non-Abelian product is associative and stems from the composition of quantum maps acting on a simple quantum…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
In this work, we establish non-asymptotic convergence bounds for the Gauss-Newton method in training neural networks with smooth activations. In the underparameterized regime, the Gauss-Newton gradient flow in parameter space induces a…
Quantum graph state is a special class of nonlocal state among multiple quantum particles, underpinning several nonclassical and promising applications such as quantum computing and quantum secret sharing. Recently, establishing quantum…
Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical…
In quantum physics, even simple data with a well-defined structure at the wave function level can be characterized by extremely complex correlations between its constituent elements. The inherent non-locality of the quantum correlations…
Deep generative models such as flow and diffusion models have proven to be effective in modeling high-dimensional and complex data types such as videos or proteins, and this has motivated their use in different data modalities, such as…
We study the inverse problem of model parameter learning for pixelwise image labeling, using the linear assignment flow and training data with ground truth. This is accomplished by a Riemannian gradient flow on the manifold of parameters…
Modeling distributions on Riemannian manifolds is a crucial component in understanding non-Euclidean data that arises, e.g., in physics and geology. The budding approaches in this space are limited by representational and computational…
The recent introduction of the gradient flow has provided a new tool to probe the dynamics of quantum field theories. The latest developments have shown how to use the gradient flow for the exploration of symmetries, and the definition of…
Constitutive laws relate fluid stress to deformation and underpin predictions of non-Newtonian behavior in industrial and biological fluids. Standard characterization relies on measurements in idealized flows that often miss physics…
In this article, we introduce a new approach towards the statistical learning problem $\operatorname{argmin}_{\rho(\theta) \in \mathcal P_{\theta}} W_{Q}^2 (\rho_{\star},\rho(\theta))$ to approximate a target quantum state $\rho_{\star}$ by…
This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the…
In this paper, we propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs). From a perspective of physical simulation, we redefine the problem of approximating the gradient flow utilizing…
In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a program by establishing a precise correspondence…
We show that a noncommutative dynamical system of the type that occurs in quantum theory can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. The nature of these…
In quantum information geometry, the curvature of von-Neumann entropy and relative entropy induce a natural metric on the space of mixed quantum states. Here we use this information metric to construct a random matrix ensemble for states…
We propose a scheme for data-driven parameterization of unresolved dimensions of dynamical systems based on the mathematical framework of quantum mechanics and Koopman operator theory. Given a system in which some components of the state…
Graph-theoretic structures play a central role in the description and analysis of quantum systems. In this work, we introduce a new class of quantum states, called $A_\alpha$-graph states, which are constructed from either unweighted or…
By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…