Related papers: Quantum State Assignment Flows
We consider network models of quantum localisation in which a particle with a two-component wave function propagates through the nodes and along the edges of an arbitrary directed graph, subject to a random SU(2) rotation on each edge it…
We discuss a model of spontaneous collapse of the quantum state that does not require adding any stochastic processes to the standard dynamics. The additional ingredient with respect to the wave function is a position in the configuration…
Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose,…
We provide a brief overview of approaches for calculating the density of states of quantum systems and random matrix Hamiltonians using the tools of free probability theory. For a given Hamiltonian of a quantum system or a generic random…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
We introduce and implement a method to compute stationary states of nonlinear Schr\''odinger equations on metric graphs. Stationary states are obtained as local minimizers of the nonlinear Schr\''odinger energy at fixed mass. Our method is…
A new quantum mechanical notion -- Conditional Density Matrix -- is discussed and is applied to describe some physical processes. This notion is a natural generalization of von Neumann density matrix for such processes as divisions of…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a…
We provide gradient flow interpretations for the continuous-time continuous-state Hopfield neural network (HNN). The ordinary and stochastic differential equations associated with the HNN were introduced in the literature as analog…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
Numerous applications of machine learning involve representing probability distributions over high-dimensional data. We propose autoregressive quantile flows, a flexible class of normalizing flow models trained using a novel objective based…
We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the…
Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…
This thesis seeks to develop a general method for solving so-called quantum realizability problems, which are questions of the following form: under which conditions does there exist a quantum state exhibiting a given collection of…
Weighted graph states are a natural generalization of graph states, which are generated by applying controlled-phase gates, instead of controlled-Z gates, to a separable state. In this paper, we show that uniformly weighted graph states on…
The accurate simulation of real--time quantum transport is notoriously difficult, requiring a consistent scheme to treat incoming and outgoing fluxes at the boundary of an open system. We demonstrate a method to converge non--equilibrium…
Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains, which is crucial for building graph foundation models. Despite initial success, existing solutions often fall short of…
We present a protocol that allows the estimation of any density matrix element for continuous-variable quantum states, without resorting to the complete reconstruction of the full density matrix. The algorithm adaptatively discretizes the…
The computation of electrical flows is a crucial primitive for many recently proposed optimization algorithms on weighted networks. While typically implemented as a centralized subroutine, the ability to perform this task in a fully…