Related papers: Quantum Computational Complexity -- From Quantum I…
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…
Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…
We study the complexity of computational problems from quantum physics. Typically, they are studied using the complexity class QMA (quantum counterpart of NP) but some natural computational problems appear to be slightly harder than QMA. We…
We study the influence of angular momentum on quantum complexity for CFT states holographically dual to rotating black holes. Using the holographic complexity=action (CA) and complexity=volume (CV) proposals, we study the full time…
We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…
I give a critical review of the holographic hypothesis, which posits that a universe with gravity can be described by a quantum field theory in fewer dimensions. I first recall how the idea originated from considerations on black hole…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
We study circuit complexity for spatial regions in holographic field theories. We study analogues based on the entanglement wedge of the bulk quantities appearing in the "complexity = volume" and "complexity = action" conjectures. We…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
The discovery of the fact that black holes radiate particles and eventually evaporate led Hawking to pose the well-known information loss paradox. This paradox caused a long and serious debate since it claims that the fundamental laws of…
Loop Quantum Gravity is a theory that attempts to describe the quantum mechanics of the gravitational field based on the canonical quantization of General Relativity. According to Loop Quantum Gravity, in a gravitational field, geometric…
The holographic state of matter exists in the quantum gravitational regime, with black holes as the example. In this essay, we provide a microscopic derivation to the holographic thermodynamics and further discuss its implications for…
The rate of complexification of a quantum state is conjectured to be bounded from above by the average energy of the state. A different conjecture relates the complexity of a holographic CFT state to the on-shell gravitational action of a…
According to the holographic principle, the information content assigned to a gravitational region is processed by its lower dimensional boundary. As an example setup compatible with this principle, the AdS/CFT correspondence relies on the…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
A coarse-grained description for the formation and evaporation of a black hole is given within the framework of a unitary theory of quantum gravity preserving locality, without dropping the information that manifests as macroscopic…
Quantum state tomography (QST) is a fundamental task in quantum information science that aims to reconstruct unknown quantum states from measurement data. However, the exponential growth of Hilbert-space dimension with system size makes…
State transformation problems such as compressing quantum information or breaking quantum commitments are fundamental quantum tasks. However, their computational difficulty cannot easily be characterized using traditional complexity theory,…
According to the pioneering work of Nielsen and collaborators, the length of the minimal geodesic in a geometric realization of a suitable operator space provides a measure of the quantum complexity of an operation. Compared with the…