Related papers: Random unitary dynamics of quantum networks
While classical spin systems in random networks have been intensively studied, much less is known about quantum magnets in random graphs. Here, we investigate interacting quantum spins on small-world networks, building on mean-field theory…
One important question in neuroscience is how global behavior in a brain network emerges from the interplay between network connectivity and the neural dynamics of individual nodes. To better understand this theoretical relationship, we…
A given dynamics for a composite quantum system can exhibit several distinct properties for the asymptotic entanglement behavior, like entanglement sudden death, asymptotic death of entanglement, sudden birth of entanglement, etc. A…
The power and expressivity of deep classical neural networks can be attributed to non-linear input-output relations. Such non-linearities are at the heart of many computational tasks, such as data classification and pattern recognition.…
This study concerns with the dynamics of a quantum neural network unit in order to examine the suitability of simple neural computing tasks. More specifically, we examine the dynamics of an interacting spin model chosen as a candidate of a…
A quantum spin-$\frac{1}{2}$ chain with an axial symmetry is normally described by quasiparticles associated with the spins oriented along the axis of rotation. Kinetic constraints can enrich such a description by setting apart different…
We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions in order to have some form of almost sure asymptotic synchronization,…
Recently it has been shown that interparticle interactions\emph ongenerically\emph default destroy dynamical localization in periodically driven systems, resulting in diffusive transport and heating. In this work we rigorously construct a…
In this paper, we analyze the asymptotic behavior of a system of interacting reinforced stochastic processes $({\bf Z}_n, {\bf N}_n)_n$ on a directed network of $N$ agents. The system is defined by the coupled dynamics ${\bf…
We introduce two information-theoretical invariants for the projective unitary group acting on a finite-dimensional complex Hilbert space: PVM- and POVM-dynamical (quantum) entropies. They quantify the randomness of the successive quantum…
We have computed the low energy quantum states and low frequency dynamical susceptibility of complex quantum spin systems in the limit of strong interactions, obtaining exact results for system sizes enormously larger than accessible…
Neural networks are high-dimensional nonlinear dynamical systems that process information through the coordinated activity of many connected units. Understanding how biological and machine-learning networks function and learn requires…
It has been recently realized that dissipative processes can be harnessed and exploited to the end of coherent quantum control and information processing. In this spirit we consider strongly dissipative quantum systems admitting a…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
The promising performance increase offered by quantum computing has led to the idea of applying it to neural networks. Studies in this regard can be divided into two main categories: simulating quantum neural networks with the standard…
Many networks in nature and applications have an approximate low-rank structure in the sense that their connectivity structure is dominated by a few dimensions. It is natural to expect that dynamics on such networks would also be…
Quantum annealers play a major role in the ongoing development of quantum information processing and in the advent of quantum technologies. Their functioning is underpinned by the many-body adiabatic evolution connecting the ground state of…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…
Our ability to control network dynamical systems is often hindered by constraints on the number and nature of the available control actions, which make controlling the whole network unfeasible. In this manuscript, we focus on the case where…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…