Related papers: Quantum Graphity: a model of emergent locality
We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime…
Quantum graph neural networks offer a powerful paradigm for learning on graph-structured data, yet their explainability is complicated by measurement-induced stochasticity and the combinatorial nature of graph structure. In this paper, we…
A quantum mechanical model of two interacting electrons in graphene is considered. We concentrate on the case of zero total momentum of the pair. We show that the dynamics of the system is very unusual. Both stationary and time-dependent…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
Strong nonlocality based on local distinguishability is a stronger form of quantum nonlocality recently introduced in multipartite quantum systems: an orthogonal set of multipartite quantum states is said to be of strong nonlocality if it…
The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…
In this paper, we develop the groundwork for a graph theoretic toy model of supersymmetric quantum mechanics. Using discrete Witten-Morse theory, we demonstrate that finite graphs have a natural supersymmetric structure and use this…
The implementation of the dynamics in Loop Quantum Gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We use the…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
Non-equilibrium steady states of quantum fields on star graphs are explicitly constructed. These states are parametrized by the temperature and the chemical potential, associated with each edge of the graph. Time reversal invariance is…
The quantum entanglement phenomenon was demonstrated to operate on a bipartite entangled system composed of two single layers of graphene embedded in an electrolytic medium (which did not permit the transport of electrons) and subjected to…
We study fermionic and bosonic systems coupled to a real or synthetic static gauge field that is quantized, so the field itself is a quantum degree of freedom and can exist in coherent superposition. A natural example is electrons on a…
Adapting a definition of Aaronson and Ambainis [Theory Comput. 1 (2005), 47--79], we call a quantum dynamics on a digraph "saturated Z-local" if the nonzero transition amplitudes specifying the unitary evolution are in exact correspondence…
We demonstrate a mechanism for the production of massive excitations in graphs. We treat the number of neighbors at each vertex in the graph (degree) as a scalar field. Then we introduce a mechanism inspired by the Higgs mechanism in…
Non-Abelian Gauss law is interpreted in terms of area bits described in a local frame which fit together into closed surfaces and the Non-Abelian Stokes law in terms of length bits described in a local frame which fit together into closed…
The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system, whose hamiltonian is identical to the adjacency matrix of a…
Connectivity is a fundamental property of quantum graphs, previously studied in the operator system model for matrix quantum graphs and via graph homomorphisms in the quantum adjacency matrix model. In this paper, we develop an algebraic…