Related papers: Quantum site percolation on amenable graphs
We introduce an elementary quantum system consisting of a set of spins on a graph and a particle hopping between its nodes. The quantum state is build sequentially, applying a unitary transformation that couples neighboring spins and, at a…
Consider a discrete locally finite subset $\Gamma$ of $R^d$ and the complete graph $(\Gamma,E)$, with vertices $\Gamma$ and edges $E$. We consider Gibbs measures on the set of sub-graphs with vertices $\Gamma$ and edges $E'\subset E$. The…
We study some spectral properties of random walks on infinite countable amenable groups with an emphasis on locally finite groups, e.g. the infinite symmetric group. On locally finite groups, the random walks under consideration are driven…
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…
Quantum graphity is a background independent model for emergent locality, spatial geometry and matter. The states of the system correspond to dynamical graphs on N vertices. At high energy, the graph describing the system is highly…
We discuss Hamiltonian learning in quantum field theories as a protocol for systematically extracting the operator content and coupling constants of effective field theory Hamiltonians from experimental data. Learning the Hamiltonian for…
Graphical Models have various applications in science and engineering which include physics, bioinformatics, telecommunication and etc. Usage of graphical models needs complex computations in order to evaluation of marginal functions,so…
Hypergraph states of many quantum bits share the rich interplay between simple combinatorial description and nontrivial entanglement properties enjoyed by the graph states that they generalize. In this paper, we consider hypergraph states…
Toy quantum Hamiltonians $H\neq H^\dagger$ with real spectra are considered as living on graphs $\mathbb{G}$ which only differ from the standard real line $\mathbb{R}$ locally, on a microscopic fundamental-length scale. In terms of a…
Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…
This paper presents an algebraic formulation of the renormalization group flow in quantum mechanics on flat target spaces. For any interacting quantum mechanical theory, the fixed point of this flow is a theory of classical probability, not…
We consider Schr\"odinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. Using the technique of self-adjoint extensions we obtain conditions for localization on…
The article surveys quantization schemes for metric graphs with spin. Typically quantum graphs are defined with the Laplace or Schrodinger operator which describe particles whose intrinsic angular momentum (spin) is zero. However, in many…
Quantum networks with bipartite resources and shared randomness present the simplest infrastructure for implementing a future quantum internet. Here, we shall investigate which kinds of entanglement can or cannot be generated from this kind…
We compute the spectrum for a class of quantum Markov semigroups describing systems of $N$ particle interacting through a binary collision mechanism. These quantum Markov semgroups are associated to a novel kind of quantum random walk on…
Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock…
In this work we show that the simple Hamiltonians used in Quantum Graphity models are highly degenerate, having multiple ground states that are not lattices. In order to assess the distance of the resulting graphs from a lattice graph, we…
In this paper we study the spectrum of long-range percolation graphs. The underlying geometry is given in terms of a finitely generated amenable group. We prove that the integrated density of states (IDS) or spectral distribution function…
This is the documentation for generating random samples from the quantum state space in accordance with a specified distribution, associated with this webpage: http://tinyurl.com/QSampling . Ready-made samples (each with at least a million…
In ${\cal PT}-$symmetric quantum mechanics one of the most characteristic mathematical features of the formalism is the explicit Hamiltonian-dependence of the physical Hilbert space of states ${\cal H}={\cal H}(H)$. Some of the most…