Related papers: Quantum local random networks and the statistical …
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…
In this paper we investigate the asymptotic statistical theory of irreducible quantum Markov chains, focusing on identifiability properties and asymptotic convergence of associated quantum statistical models. We show that the space of…
The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding…
Quantum chaos plays a significant role in understanding several important questions of recent theoretical and experimental studies. Here, by focusing on the localization properties of eigenstates in phase space (by means of Husimi…
We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin…
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 revisit a quantum quench scenario in which either a scarring or thermalizing initial state evolves under the PXP Hamiltonian. Within this framework, we study the time evolution of spread complexity and related quantities in the Krylov…
The far-from-equilibrium dynamics of certain interacting quantum systems still defy precise understanding. One example is the so-called quantum many-body scars (QMBSs), where a set of energy eigenstates evade thermalization to give rise to…
Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase/decrease their…
The concept of local symmetry dynamics has recently been used to demonstrate the evolution of discrete symmetries in one-dimensional chains leading to emergent periodicity. Here we go one step further and show that the unboundedness of this…
One of the promising applications of digital quantum processors is the simulation of many-body quantum systems. They have been already used to investigate several ergodicity violating mechanisms, which were initially discovered in synthetic…
Quantum many-body scars are eigenstates in non-integrable isolated quantum systems that defy typical thermalization paradigms, violating the eigenstate thermalization hypothesis and quantum ergodicity. We identify exact analytic scar…
Understanding the emergence of chaos in many-body quantum systems away from semi-classical limits, particularly in spatially local interacting spin Hamiltonians, has been a long-standing problem. In these intrinsically quantum regimes,…
A fundamental problem in quantum physics is to establish whether a multiparticle quantum state can be uniquely determined from its local marginals. In theory, this problem has been addressed in the exact case where the marginals are…
Key quantum features like coherence are the fundamental resources enabling quantum advantages and ascertaining their presence in quantum systems is crucial for developing quantum technologies. This task, however, faces severe challenges in…
The theory of scarring of eigenfunctions of classically chaotic systems by short periodic orbits is extended in several ways. The influence of short-time linear recurrences on correlations and fluctuations at long times is emphasized. We…
There are many scales at which to quantify stability in spatial and ecological networks. Local-scale analyses focus on specific nodes of the spatial network, while regional-scale analyses consider the whole network. Similarly, species- and…
We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
The one-dimensional quantum breakdown model, which features spatially asymmetric fermionic interactions simulating the electrical breakdown phenomenon, exhibits an exponential U(1) symmetry and a variety of dynamical phases including…