Related papers: A universal graph description for one-dimensional …
We give a simple recipe for translating walks on Cayley graphs of a group G into a quantum operation on any irrep of G. Most properties of the classical walk carry over to the quantum operation: degree becomes the number of Kraus operators,…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
The study of perfect state transfer on graphs has attracted a great deal of attention during the past ten years because of its applications to quantum information processing and quantum computation. Perfect state transfer is understood to…
We investigate the bottom of the spectra of infinite quantum graphs, i.e., Laplace operators on metric graphs having infinitely many edges and vertices. We introduce a new definition of the isoperimetric constant for quantum graphs and then…
Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear…
A method for estimating the spectral gap along with higher eigenvalues of nonequilateral quantum graphs has been introduced by Amini and Cohen-Steiner recently: it is based on a new transference principle between discrete and continuous…
In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains.…
A family of oriented, normal, nonabelian Cayley graphs is presented, whose continuous-time quantum walks exhibit uniform mixing.
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
We consider quasirandom properties for Cayley graphs of finite abelian groups. We show that having uniform edge-distribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for such Cayley graphs, even if…
A wide variety of real-world data, such as sea measurements, e.g., temperatures collected by distributed sensors and multiple unmanned aerial vehicles (UAV) trajectories, can be naturally represented as graphs, often exhibiting…
We evaluate the variance of coefficients of the characteristic polynomial for binary quantum graphs using a dynamical approach. This is the first example where a spectral statistic can be evaluated in terms of periodic orbits for a system…
The finite dihedral group generated by one rotation and one flip is the simplest case of the non-abelian group. Cayley graphs are diagrammatic counterparts of groups. In this paper, much attention is given to the Cayley graph of the…
A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the…
Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix $U$. Observing that if $U$ has at most two eigenvalues, then the scattering matrix $\mathcal{S}(k)$ of the vertex is a linear combination of the…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
We characterize the spectrum of the transition matrix for simple random walk on graphs consisting of a finite graph with a finite number of infinite Cayley trees attached. We show that there is a continuous spectrum identical to that for a…
A causal model is an abstract representation of a physical system as a directed acyclic graph (DAG), where the statistical dependencies are encoded using a graphical criterion called `d-separation'. Recent work by Wood & Spekkens shows that…
We study a certain class of classical one dimensional piecewise linear maps. For these systems we introduce an infinite family of Markov partitions into equal cells. The symbolic dynamics generated by these systems is described by…
Owing to their interesting spectral properties, the synthetic crystals over lattices other than regular Euclidean lattices, such as hyperbolic and fractal ones, have attracted renewed attention, especially from materials and meta-materials…