Related papers: Quantum Simulations of Loop Quantum Gravity
This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of…
We present a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. Given any fixed background state representing a non-compact spatial geometry, we use the Gel'fand-Naimark-Segal…
Loop Quantum Gravity is a background independent, nonperturbative approach to the quantization of General Relativity. Its application to models of interest in cosmology and astrophysics, known as Loop Quantum Cosmology, has led to new and…
We explore the classical setting for the U(N) framework for SU(2) intertwiners for loop quantum gravity (LQG) and describe the corresponding phase space in terms of spinors with appropriate constraints. We show how its quantization leads…
The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic…
In this paper we calculated the spectral dimension of loop quantum gravity (LQG) using the scaling property of the area operator spectrum on spin-network states and using the scaling property of the volume and length operators on Gaussian…
We report the first simulations of the dynamics of quantum logic operations with a large number of qubits (up to 1000). A nuclear spin chain in which selective excitations of spins is provided by the gradient of the external magnetic field…
Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
The relation between Loop Quantum Gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the Barrett-Crane vertex amplitude is known to be related to the Regge action. In…
$SU(\infty)$-QGR is a quantum approach to Universe and gravity. Its main assumption is infinite mutually commuting observables in the Universe, leading to representation of $SU(\infty)$ by its Hilbert spaces and those of its subsystems. The…
Two desireable properties of a quantum dynamics for Loop Quantum Gravity (LQG) are that its generators provide an anomaly free representation of the classical constraint algebra and that physical states which lie in the kernel of these…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
We discuss how to simulate simple quantum logic operations with a large number of qubits. These simulations are needed for experimental testing of scalable solid-state quantum computers. Quantum logic for remote qubits is simulated in a…
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable…
Tensor networks provide a powerful tool for studying many-body quantum systems, particularly making quantum simulations more efficient. In this article, we construct a tensor network representation of the spin network states, which…
Quantum gravity is expected to require modifications of the notions of space and time. I discuss and clarify how this happens in Loop Quantum Gravity.
An important challenge in loop quantum gravity is to find semiclassical states - states that are as close to classical as quantum theory allows. This is difficult because the states in the Hilbert space used in LQG are excitations over a…
We highlight the structure and properties of an abstract approach to quantum cosmology and gravity, dubbed $SU(\infty)$-QGR. Beginning from the concept of the Universe as an isolated quantum system, the main axiom of is the existence of an…
We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasise that the off-shell (`strong') closure of the constraint algebra is a…