Related papers: Three Lectures on Complexity and Black Holes
This is the first of three PiTP lectures on complexity and its role in black hole physics.
We give arguments for the existence of a thermodynamics of quantum complexity that includes a "Second Law of Complexity". To guide us, we derive a correspondence between the computational (circuit) complexity of a quantum system of $K$…
This is the written version of a lecture given at KITP in Oct 2014 on Black Holes and quantum complexity. I've included (in boldface) various questions that came up during the lecture and discussions the following day, as well as the…
These are lecture notes from a weeklong course in quantum complexity theory taught at the Bellairs Research Institute in Barbados, February 21-25, 2016. The focus is quantum circuit complexity---i.e., the minimum number of gates needed to…
This review gives an introduction to various attempts to understand the quantum nature of black holes. The first part focuses on thermodynamics of black holes, Hawking radiation, and the interpretation of entropy. The second part is devoted…
We propose the use of a gravitational uncertainty principle for gravitation. We define the corresponding gravitational Planck's constant and the gravitational quantum of mass. We define entropy in terms of the quantum of gravity with the…
The ultimate limits of computation are not just logical, but physical. We investigate the physical resources -- time, energy, entropy, and free energy -- required to perform computational work. We apply the resulting measures of physical…
These notes introduce basic aspects of black hole thermodynamics. I review the classical laws of black hole mechanics, give a brief introduction to the essential concepts of quantum field theory in curved spacetime, and derive the Unruh and…
We show that counting different configurations that give rise to black hole entropy in loop quantum gravity is related to partitions in number theory.
A School on Loop Quantum Gravity was held at the IMSc during Sept 8 -- 18, 2009. In the first week a basic introduction to LQG was provided while in the second week the focus was on the two main application, to cosmology (LQC) and to the…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…
An introduction to generalized thermodynamics of quantum black holes, in the one-loop approximation, is given. The material is aimed at graduate students. The topics include: quantum evaporation of black holes, Euclidean formulation of…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards…
I present a viewpoint on black hole thermodynamics according to which the entropy: derives from horizon "degrees of freedom"; is finite because the deep structure of spacetime is discrete; is "objective" thanks to the distinguished coarse…
A brief review of the confrontation between black hole physics and quantum-mechanical unitarity is presented. Possibile reconciliations are modifying the laws of physics to allow fundamental loss of information, escape of information during…
This thesis is entirely devoted to black hole physics as a natural arena to study quantum gravity related questions. The five main Chapters present the results already published in arXiv:1512.04566 [gr-qc], arXiv:1604.07222 [gr-qc],…
First, the relation between black holes and limitations on information of other systems is developed. After reviewing the relation of entropy to information, we derive the entropy bound, review its applications to cosmology and its…
Black holes have often provided profound insights into the nature of gravity and the structure of space-time. The study of the mathematical properties of black objects is a major research theme of contemporary theoretical physics. This…
Many fundamental issues remain for black hole thermodynamics after almost half a century of its conception. For example, what are the underlying degrees of freedom of a black hole horizon that give rise to said thermodynamical properties?…