scholarly journals Prelude to Simulations of Loop Quantum Gravity on Adiabatic Quantum Computers

2021 ◽  
Vol 8 ◽  
Author(s):  
Jakub Mielczarek
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Planck Scale ◽  
Quantum Computers ◽  
Hamiltonian Constraint ◽  
Spin Network ◽  
Quantum Processor ◽  
Network States ◽  
D Wave ◽  
Planck Scale Physics

The article addresses the possibility of implementing spin network states, used in the loop quantum gravity approach to Planck scale physics on an adiabatic quantum computer. The discussion focuses on applying currently available technologies and analyzes a concrete example of a D-Wave machine. It is introduced a class of simple spin network states which can be implemented on the Chimera graph architecture of the D-Wave quantum processor. However, extension beyond the currently available quantum processor topologies is required to simulate more sophisticated spin network states. This may inspire new generations of adiabatic quantum computers. A possibility of simulating loop quantum gravity is discussed, and a method of solving a graph non-changing scalar (Hamiltonian) constraint with the use of adiabatic quantum computations is proposed. The presented results establish a basis for the future simulations of Planck scale physics, specifically quantum cosmological configurations, on quantum annealers.

scholarly journals MULTI-PLAQUETTE SOLUTIONS FOR DISCRETIZED ASHTEKAR GRAVITY

1996 ◽  
Vol 11 (05) ◽  
pp. 349-356 ◽  
Author(s):  
KIYOSHI EZAWA
Keyword(s):  
Quantum Gravity ◽  
Heat Kernel ◽  
Gauge Theories ◽  
Hamiltonian Constraint ◽  
Spin Network ◽  
Connected Set ◽  
Network States ◽  
Canonical Quantum Gravity ◽  
Canonical Quantum

A discretized version of canonical quantum gravity proposed by Loll is investigated. After slightly modifying Loll’s discretized Hamiltonian constraint, we encode its action on the spin network states in terms of combinatorial topological manipulations of the lattice loops. Using this topological formulation we find new solutions to the discretized Wheeler-DeWitt equation. These solutions have their support on the connected set of plaquettes. We also show that these solutions are not normalizable with respect to the induced heat-kernel measure on SL(2, C) gauge theories.

scholarly journals Curvatures and discrete Gauss–Codazzi equation in (2 + 1)-dimensional loop quantum gravity

2015 ◽  
Vol 12 (10) ◽  
pp. 1550112
Author(s):  
Seramika Ariwahjoedi ◽  
Jusak Sali Kosasih ◽  
Carlo Rovelli ◽  
Freddy P. Zen
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Dimensional Manifold ◽  
Plane Angle ◽  
Codazzi Equation ◽  
Spin Network ◽  
3 Dimensional ◽  
Network States

We derive the Gauss–Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss–Codazzi equation for a discrete (2 + 1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to write operators acting on spin network states in (2 + 1)-dimensional loop quantum gravity, representing the 3-dimensional intrinsic, 2-dimensional intrinsic, and 2-dimensional extrinsic curvatures.

Gauge formulation of general relativity using conformal and spin symmetries

2008 ◽  
Vol 366 (1871) ◽  
pp. 1867-1874 ◽  
Author(s):  
Charles H.-T Wang
Keyword(s):  
General Relativity ◽  
Gauge Symmetry ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Conformal Factor ◽  
Gauge Field Theories ◽  
Hamiltonian Constraint ◽  
Spin Network ◽  
Free Construction ◽  
Modern Physics

The gauge symmetry inherent in Maxwell's electromagnetics has a profound impact on modern physics. Following the successful quantization of electromagnetics and other higher order gauge field theories, the gauge principle has been applied in various forms to quantize gravity. A notable development in this direction is loop quantum gravity based on the spin-gauge treatment. This paper considers a further incorporation of the conformal gauge symmetry in canonical general relativity. This is a new conformal decomposition in that it is applied to simplify recently formulated parameter-free construction of spin-gauge variables for gravity. The resulting framework preserves many main features of the existing canonical framework for loop quantum gravity regarding the spin network representation and Thiemann's regularization. However, the Barbero–Immirzi parameter is converted into the conformal factor as a canonical variable. It behaves like a scalar field but is somehow non-dynamical since the Hamiltonian constraint does not depend on its momentum. The essential steps of the mathematical derivation of this parameter-free framework for the spin-gauge variables of gravity are spelled out. The implications for the loop quantum gravity programme are briefly discussed.

scholarly journals Hidden messenger from quantum geometry: Towards information conservation in quantum gravity

2018 ◽  
Vol 33 (18) ◽  
pp. 1850103 ◽  
Author(s):  
Xiao-Kan Guo ◽  
Qing-Yu Cai
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Information Loss ◽  
Quantum Geometry ◽  
Spin Network ◽  
General Derivation ◽  
Black Hole Information ◽  
Network States ◽  
Quantum Geometries

The back reactions of Hawking radiation allow nontrivial correlations between consecutive Hawking quanta, which gives a possible way of resolving the paradox of black hole information loss known as the hidden messenger method. In a recent work of Ma et al. [ arXiv:1711.10704 ], this method is enhanced by a general derivation using small deviations of the states of Hawking quanta off canonical typicality. In this paper, we use this typicality argument to study the effects of generic back reactions on the quantum geometries described by spin network states, and discuss the viability of entropy conservation in loop quantum gravity. We find that such back reactions lead to small area deformations of quantum geometries including those of quantum black holes. This shows that the hidden-messenger method is still viable in loop quantum gravity, which is a first step towards resolving the paradox of black hole information loss in quantum gravity.

scholarly journals Black Hole Interior from Loop Quantum Gravity

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Leonardo Modesto
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Event Horizon ◽  
Loop Quantum Gravity ◽  
Planck Scale ◽  
Semiclassical Analysis ◽  
Schwarzschild Solution ◽  
Quantum Black Hole ◽  
Minimum Value ◽  
Black Hole Interior

We calculate modifications to the Schwarzschild solution by using a semiclassical analysis of loop quantum black hole. We obtain a metric inside the event horizon that coincides with the Schwarzschild solution near the horizon but that is substantially different at the Planck scale. In particular, we obtain a bounce of theS2sphere for a minimum value of the radius and that it is possible to have another event horizon close to ther=0point.

scholarly journals PROPOSAL OF A SECOND GENERATION OF QUANTUM-GRAVITY-MOTIVATED LORENTZ-SYMMETRY TESTS: SENSITIVITY TO EFFECTS SUPPRESSED QUADRATICALLY BY THE PLANCK SCALE

2003 ◽  
Vol 12 (09) ◽  
pp. 1633-1639 ◽  
Author(s):  
GIOVANNI AMELINO-CAMELIA
Keyword(s):  
Quantum Gravity ◽  
Second Generation ◽  
Loop Quantum Gravity ◽  
Planck Scale ◽  
Cosmic Ray ◽  
Lorentz Symmetry ◽  
Planck Length ◽  
Satisfactory Description ◽  
Symmetry Tests ◽  
Quantum Spacetime

Over the last few years the study of possible Planck-scale departures from classical Lorentz symmetry has been one of the most active areas of quantum-gravity research. We now have a satisfactory description of the fate of Lorentz symmetry in the most popular noncommutative spacetimes and several studies have been devoted to the fate of Lorentz symmetry in loop quantum gravity. Remarkably there are planned experiments with enough sensitivity to reveal these quantum-spacetime effects, if their magnitude is only linearly suppressed by the Planck length. Unfortunately, in some quantum-gravity scenarios even the strongest quantum-spacetime effects are suppressed by at least two powers of the Planck length, and many authors have argued that it would be impossible to test these quadratically-suppressed effects. I here observe that advanced cosmic-ray observatories and neutrino observatories can provide the first elements of an experimental programme testing the possibility of departures from Lorentz symmetry that are quadratically Planck-length suppressed.

scholarly journals POLYMER GEOMETRY AT PLANCK SCALE AND QUANTUM EINSTEIN EQUATIONS

1996 ◽  
Vol 05 (06) ◽  
pp. 629-648 ◽  
Author(s):  
ABHAY ASHTEKAR
Keyword(s):  
Quantum Gravity ◽  
Planck Scale ◽  
Coarse Graining ◽  
Space Structure ◽  
Einstein Equations ◽  
Hamiltonian Constraint ◽  
Recent Approach ◽  
Canonical Approach ◽  
Background Fields ◽  
Discrete Spectra

Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge equivalent connections. This calculus does not use any background fields (such as a metric) and thus well-suited to a fully non-perturbative treatment of quantum gravity. Using this framework, quantum geometry is examined. Fundamental excitations turn out to be one-dimensional, rather like polymers. Geometrical observables such as areas of surfaces and volumes of regions are purely discrete spectra. Continuum picture arises only upon coarse graining of suitable semi-classical states. Next, regulated quantum diffeomorphism constraints can be imposed in an anomaly-free fashion and the space of solutions can be given a natural Hilbert space structure. Progress has also been made on the quantum Hamiltonian constraint in a number of directions. In particular, there is a recent approach based on a generalized .Wick transformation which maps solutions to the Euclidean quantum constraints to those of the Lorentzian theory. These developments are summarized. Emphasis is on conveying the underlying ideas and overall pictures rather than technical details.

scholarly journals ENTROPY AND AREA IN LOOP QUANTUM GRAVITY

2005 ◽  
Vol 14 (12) ◽  
pp. 2301-2305
Author(s):  
JOHN SWAIN
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Maximum Entropy ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Black Hole Entropy ◽  
Black Hole Thermodynamics ◽  
Three Dimensions ◽  
Spin Network

Black hole thermodynamics suggests that the maximum entropy that can be contained in a region of space is proportional to the area enclosing it rather than its volume. We argue that this follows naturally from loop quantum gravity and a result of Kolmogorov and Bardzin' on the the realizability of networks in three dimensions. This represents an alternative to other approaches in which some sort of correlation between field configurations helps limit the degrees of freedom within a region. It also provides an approach to thinking about black hole entropy in terms of states inside rather than on its surface. Intuitively, a spin network complicated enough to imbue a region with volume only lets that volume grow as quickly as the area bounding it.

Fermions, q-deformed diffeomorphism and the evolution of spin networks

2015 ◽  
Vol 24 (10) ◽  
pp. 1550074 ◽  
Author(s):  
L. Mullick ◽  
P. Bandyopadhyay
Keyword(s):  
Quantum Gravity ◽  
Gauge Group ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Closed Loop ◽  
Direction Vector ◽  
Spin Networks ◽  
Spin Network ◽  
Diffeomorphism Invariance ◽  
Diffeomorphism Symmetry

We have considered here the emergence of diffeomorphism symmetry in quantum gravity in the framework of the quantization of a fermion. It is pointed out that a closed loop having the holonomy associated with the SU(2) gauge group is realized from the rotation of the direction vector associated with the quantization of a fermion depicting spin degrees of freedom which appear as SU(2) gauge bundle. During the formation of a loop, a noncyclic path with open ends can be mapped onto a closed loop when the holonomy involves q-deformed gauge group SUq(2). This gives rise to q-deformed diffeomorphism and helps to realize diffeomorphism invariance in quantum gravity through a sequence of q-deformed diffeomorphism in the limit q = 1. We can consider adiabatic iteration such that the quasispin associated with the quantum group SUq(2) gradually evolves as the time dependent deformation parameter q changes and in the limit q = 1, we achieve the standard spin. This essentially depicts the evolution of spin network as the loop is being formed and links fermionic degrees of freedom with loop quantum gravity.

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