Related papers: Quantum Graphs: Applications to Quantum Chaos and …
We present experimental and theoretical results for the fluctuation properties in the incomplete spectra of quantum systems with symplectic symmetry and a chaotic dynamics in the classical limit. To obtain theoretical predictions, we extend…
Based on earlier work on regular quantum graphs we show that a large class of scaling quantum graphs with arbitrary topology are explicitly analytically solvable. This is surprising since quantum graphs are excellent models of quantum chaos…
A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states),…
We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint realisations of the two-particle Laplacian. Showing…
We present a theory of quantum work statistics in generic chaotic, disordered Fermi liquid systems within a driven random matrix formalism. By extending P. W. Anderson's orthogonality determinant formula to compute quantum work…
This workshop brought together experts in classical graph theory and quantum information science to explore the intersection of these fields, with a focus on quantum graph states and their applications in computing, networking, and sensing.…
Matrix representations of quantum operators are computationally complete but often obscure the structural topology of information flow within a quantum circuit \cite{nielsen2000}. In this paper, we introduce a generalized graph-theoretic…
The statistical properties of quantum transport through a chaotic cavity are encoded in the traces $\T={\rm Tr}(tt^\dag)^n$, where $t$ is the transmission matrix. Within the Random Matrix Theory approach, these traces are random variables…
For a set of quantum states generated by the action of a group, we consider the graph obtained by considering two group elements adjacent whenever the corresponding states are non-orthogonal. We analyze the structure of the connected…
Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in…
We introduce quantum association schemes. This allows to define distance regular and strongly regular quantum graphs. We bring examples thereof. In addition, we formulate the duality for translation quantum association schemes corresponding…
Recently, the work on quantum automorphism groups of graphs has seen renewed progress, which we expand in this paper. Quantum symmetry is a richer notion of symmetry than the classical symmetries of a graph. In general, it is non-trivial to…
We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
The quantum ratchet effect in fully chaotic systems is approached by studying, for the first time, \emph{statistical} properties of the ratchet current over well-defined sets of initial states. Natural initial states in a semiclassical…
Quantum graphity is a background independent model for emergent geometry, in which space is represented as a complete graph. The high-energy pre-geometric starting point of the model is usually considered to be the complete graph, however…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
Quantum discord refers to an important aspect of quantum correlations for bipartite quantum systems. In our earlier works we have shown that corresponding to every graph (combinatorial) there are quantum states whose properties are…