Related papers: Random unitary matrices associated to a graph
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor and its moments in interacting chaotic few- and…
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…
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…
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…
We analyze properties of non-hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N>M, distributed according to the Haar measure. In this way we define ensembles of random matrices…
We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…
Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order models (ROMs) have a place to alleviate the computational…
We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…
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…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states…
We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in…
We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…
Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…
We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random--matrix theory. The stability of these correlations with regard to non--universal corrections is analyzed in…
Efficient methods for generating pseudo-randomly distributed unitary operators are needed for the practical application of Haar distributed random operators in quantum communication and noise estimation protocols. We develop a theoretical…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…