Related papers: Quantum Computational Complexity -- From Quantum I…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
We consider the holographic complexity conjectures for de-Sitter invariant states in a quantum field theory on de Sitter space, dual to asymptotically anti-de Sitter geometries with de Sitter boundaries. The bulk holographic duals include…
We argue that complex systems science and the rules of quantum physics are intricately related. We discuss a range of quantum phenomena, such as cryptography, computation and quantum phases, and the rules responsible for their complexity.…
Recent proposals suggest that a notion of generalized complexity, analogous to generalized entropy, may be necessary for understanding the dynamics of holographic complexity in settings where quantum effects are non-negligible, such as…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
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 $K$…
A longstanding question in quantum gravity regards the localization of quantum information; one way to formulate this question is to ask how subsystems can be defined in quantum-gravitational systems. The gauge symmetry and necessity of…
This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of…
Significant advances in the development of computing devices based on quantum effects and the demonstration of their use to solve various problems have rekindled interest in the nature of the "quantum computational advantage." Although…
The aim of this paper is to enlight the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of…
Analyzing some well established facts, we give a model-independent parameterization of black hole quantum computing in terms of a set of macro and micro quantities and their relations. These include the relations between the…
We summarize basic features of quantum gravity states and processes, common to a number of related quantum gravity formalisms, and sharing a purely combinatorial and algebraic language, and a discrete geometric interpretation. We emphasize…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
This chapter gives an overview of the quantum aspects of black holes, focusing on the black hole information problem, the counting of black hole entropy in string theory, and the emergence of spacetime in holography. It is aimed at a broad…
Quantum computers are expected to revolutionize our ability to process information. The advancement from classical to quantum computing is a product of our advancement from classical to quantum physics -- the more our understanding of the…
Using the ``complexity equals action''(CA) conjecture, for an ordinary charged system, it has been shown that the late-time complexity growth rate is given by a difference between the value of $\Phi_{H}Q+\Omega_H J$ on the inner and outer…
I review some of the concepts at the crossroads of gravitational thermodynamics, holography and quantum mechanics. First, the origin of gravitational thermodynamics due to coarse graining of quantum information is exemplified using the…
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.…
A relativistic framework for the description of bound states consisting of a large number of quantum constituents is presented, and applied to black-hole interiors. At the parton level, the constituent distribution, number and energy…
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…