Related papers: Black Holes and Complexity Classes
In the early 1970s it is was realized that there is a striking formal analogy between the Laws of black-hole mechanics and the Laws of classical thermodynamics. Before the discovery of Hawking radiation, however, it was generally thought…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's…
This is a review of the results on black hole physics in the framework of loop quantum gravity. The key feature underlying the results is the discreteness of geometric quantities at the Planck scale predicted by this approach to quantum…
A pedagogical discussion is given of some aspects of \lq\lq quantum black holes", primarily using recently developed two-dimensional models. After a short preliminary concerning classical black holes, we give several motivations for…
Quantum computing promises transformational gains for solving some problems, but little to none for others. For anyone hoping to use quantum computers now or in the future, it is important to know which problems will benefit. In this paper,…
We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and…
This thesis develops recent work on the so called Volume-Complexity and Action-Complexity conjectures. According to this family of proposals, geometric quantities can be defined in some holographic gravitational theories that can be mapped…
We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the probabilistic quantum class BQP. 1. BQP is low for PP, i.e.,…
Getting the mathematical rules for quantised black holes correctly is far from straightforward. Many earlier treatises got it not quite correctly. The general relativistic transformation linking the distant observer (who only detects…
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…
Bringing gravity into a quantum-mechanical framework is likely the most profound remaining problem in fundamental physics. The "unitarity crisis" for black hole evolution appears to be a key facet of this problem, whose resolution will…
We discuss the limitations on space time measurement in the Schwarzchild metric. We find that near the horizon the limitations on space time measurement are of the order of the black hole radius. We suggest that it indicates that a large…
In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on…
The notion of quantum-mechanical completeness is adapted to situations where the only adequate description is in terms of quantum field theory in curved space-times. It is then shown that Schwarzschild black holes, although geodesically…
A novel perspective on defining black holes designed to be more broadly applicable outside of asymptotically flat spacetimes, in the context of classical general relativity, is presented, discussed, and characterized. The construction…
We study aspects of black holes and quantum chaos through the behavior of computational costs, which are distance notions in the manifold of unitaries of the theory. To this end, we enlarge Nielsen geometric approach to quantum computation…
Our earlier paper "Complexity Equals Action" conjectured that the quantum computational complexity of a holographic state is given by the classical action of a region in the bulk (the "Wheeler-DeWitt" patch). We provide calculations for the…
Understanding the fate of semi-classical black hole solutions at very late times is one of the most important open questions in quantum gravity. In this paper, we provide a path integral definition of the volume of the black hole interior…
It is a tantalising possibility that quantum gravity (QG) states remaining coherent at astrophysical, galactic and cosmological scales could exist and that they could play a crucial role in understanding macroscopic gravitational effects.…