Related papers: Dynamical Quantum Multigraphs
Tensor field theory (TFT) focuses on quantum field theory aspects of random tensor models, a quantum-gravity-motivated generalisation of random matrix models. The TFT correlation functions have been shown to be classified by graphs that…
The thermodynamical properties of a generalized Dicke model are calculated and related with the critical properties of its energy spectrum, namely the quantum phase transitions (QPT) and excited state quantum phase transitions (ESQPT). The…
Dynamics of large complex systems, such as relaxation towards equilibrium in classical statistical mechanics, often obeys a master equation. The equation significantly simplifies the complexities but describes essential information of…
Statistical models on infinite graphs may exhibit inhomogeneous thermodynamic behaviour at macroscopic scales. This phenomenon is of geometrical origin and may be properly described in terms of spectral partitions into subgraphs with well…
We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit…
The notion of entanglement is the most well-known nonclassical correlation in quantum mechanics and a fundamental resource in quantum information and computation. This correlation, which is displayed by certain classes of quantum states, is…
Graph states provide a powerful framework for describing multipartite entanglement in quantum information science. In their standard formulation, graph states are generated by controlled-$Z$ interactions and naturally encode symmetric…
Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for generating unbiased and independent samples from graphical models remains an active research…
Particle transport and energy flow are central for our understanding of a wealth of phenomena in physics and the natural sciences. Interactions are generically expected to promote ergodicity and diffusive behavior, yet quantum interference…
Let a general quantum many-body system at a low temperature adiabatically cross through the vicinity of the system's quantum critical point. We show that the system's temperature is significantly suppressed due to both the entropy…
Gauge theory and thermalization are both foundations of physics and nowadays are both topics of essential importance for modern quantum science and technology. Simulating lattice gauge theories (LGTs) realized recently with ultracold atoms…
The holographic principle and the thermodynamics of de Sitter space suggest that the total number of fundamental degrees of freedom associated with any finite-volume region of space may be finite. The naive picture of a short distance…
We present a detailed account of the isomonodromic quantization of dimensionally reduced Einstein gravity with two commuting Killing vectors. This theory constitutes an integrable ``midi-superspace" version of quantum gravity with…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
Thermalization of an isolated quantum system has been a nontrivial problem since the early days of quantum mechanics. In generic isolated quantum systems, nonequilibrium dynamics is expected to result in thermalization, indicating the…
The schematic model of interacting spins is introduced, which combines the symmetry of hypercube with the simplicity of random regular graph with degree three, i.e. the random cubic graph. We study the localization transition in this model,…
Demonstrating the ability of existing quantum platforms to perform certain computational tasks intractable to classical computers represents a cornerstone in quantum computing. Despite the growing number of such proposed "quantum supreme"…
Simulating non-equilibrium phenomena in strongly-interacting quantum many-body systems, including thermalization, is a promising application of near-term and future quantum computation. By performing experiments on a digital quantum…
In loop quantum gravity (LQG), states of the gravitational field are represented by labeled graphs called spin networks. Their dynamics can be described by a Hamiltonian constraint, { which acts on the spin network states modifying both…
We investigate the entanglement properties of quantum states associated with directed graphs. Using a measure derived from the Fubini-Study metric, we quantitatively relate multipartite entanglement to the local connectivity of the graph.…