Related papers: Quantum Graphs: A model for Quantum Chaos
This article presents a novel and succinct algorithmic framework via alternating quantum walks, unifying quantum spatial search, state transfer and uniform sampling on a large class of graphs. Using the framework, we can achieve exact…
We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…
We explore the generalization of scattering transforms from traditional (e.g., image or audio) signals to graph data, analogous to the generalization of ConvNets in geometric deep learning, and the utility of extracted graph features in…
A system of quantum computing structures is introduced and proven capable of making emerge, on average, the orbits of classical bounded nonlinear maps on \mathbb{C} through the iterative action of path-dependent quantum gates. The effects…
Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process.…
We consider the statistics of time delay in a chaotic cavity having $M$ open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay…
We present a novel approach to the regression of quantum mechanical energies based on a scattering transform of an intermediate electron density representation. A scattering transform is a deep convolution network computed with a cascade of…
Within the scattering matrix approach to electronic transport, the scattering and transport properties of tight-binding random graphs are analyzed. In particular, we compute the scattering matrix elements, the transmission, the…
Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…
In this article we give an in depth overview of the recent advances in the field of equilibrium networks. After outlining this topic, we provide a novel way of defining equilibrium graph (network) ensembles. We illustrate this concept on…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
We introduce structured random matrix ensembles, constructed to model many-body quantum systems with local interactions. These ensembles are employed to study equilibration of isolated many-body quantum systems, showing that rather complex…
Non-uniform hypergraphs appear in various domains of computer science as in the satisfiability problems and in data analysis. We analyse a general model where the probability for an edge of size $t$ to belong to the hypergraph depends of a…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
The spectral form factor (SFF) is a powerful diagnostic of random matrix behavior in quantum many-body systems. We introduce a family of random circuit ensembles whose SFFs can be computed \textit{exactly}. These ensembles describe the…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
We describe some basic tools in the spectral theory of Schr\"odinger operator on metric graphs (also known as "quantum graph") by studying in detail some basic examples. The exposition is kept as elementary and accessible as possible. In…
The classical dynamics and the construction of quantum states in a plane wave curved spacetime are examined, paying particular attention to the similarities with the case of an electromagnetic plane wave in flat spacetime. A natural map…
In an increasingly interconnected world, understanding and summarizing the structure of these networks becomes increasingly relevant. However, this task is nontrivial; proposed summary statistics are as diverse as the networks they…
We continue the analysis of the spectral curve of the normal random matrix ensemble, introduced in an earlier paper. Evolution of the full quantum curve is given in terms of compatibility equations of independent flows. The semiclassical…