Related references
Note: Only part of the references are listed.
Article
Physics, Multidisciplinary
Adam R. Brown
Summary: Differential geometry has a long history in its applications in physics, especially in general relativity and related fields. Recently, Nielsen proposed using the tools of differential geometry to bound the complexity of quantum operations in the unitary group. The Bishop-Gromov bound, a result in differential geometry, gives an upper bound on the growth rate of geodesic ball volumes in terms of Ricci curvature. This paper applies the Bishop-Gromov bound to Nielsen's complexity geometry to establish lower bounds on the quantum complexity of a typical unitary, showing exponential growth in the number of qubits for a broad class of models.
Article
Physics, Particles & Fields
Mohsen Alishahiha et al.
Summary: In this work, we use the modified replica trick to compute the late-time behavior of complexity in JT gravity with N = 1 and N = 2 supersymmetries. For the N = 1 theory, we find that complexity saturates at a constant value with time-independent variance. For the N = 2 theory, complexity exhibits late-time linear growth. However, we speculate on the expectation of late-time saturation by considering the trumpet partition function and non-perturbative corrections to the spectral correlation.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Particles & Fields
Shira Chapman et al.
Summary: Quantum computational complexity is important in both quantum computation and black hole information processing. This article presents the geometric approach to complexity, discusses the relation between complexity, gravitational quantities, and chaos, and highlights open problems and future directions.
EUROPEAN PHYSICAL JOURNAL C
(2022)
Article
Physics, Multidisciplinary
Nicolas Chagnet et al.
Summary: The study explores the circuit complexity of conformal field theory states in arbitrary dimensions, with circuits moving along a unitary representation of the Lorentzian conformal group. Different choices of distance functions are understood in terms of the geometry of coadjoint orbits of the conformal group. The study explicitly relates circuits to timelike geodesics in anti-de Sitter space, and the complexity metric to distances between these geodesics, extending the method to circuits in other symmetry groups using a group theoretic generalization of coherent states concept.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Alexandre Belin et al.
Summary: This paper presents a new infinite class of gravitational observables in asymptotically anti-de Sitter space living on codimension-one slices of the geometry, the most famous of which is the volume of the maximal slice. The authors show that these observables display universal features for the thermofield-double state, growing linearly in time at late times and reproducing the switchback effect in shock wave geometries. They argue that any member of this class of observables is an equally viable candidate as the extremal volume for a gravitational dual of complexity.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Particles & Fields
Edgar Shaghoulian
Summary: This paper explores whether the central dogma of cosmological horizons has any support and proposes consistent answers with the quantum theory of de Sitter space, including a vanishing total entropy, an entropy of A/4G(N) on a single static patch, increasing entropy of a subregion as the region size grows, an island-like transition at half the horizon size, and a de Sitter version of the Hartman-Maldacena transition.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Multidisciplinary
Jonas Haferkamp et al.
Summary: The complexity of quantum states, which is key in quantum computing and black hole theory, has been shown to grow linearly over time under random operations. This study investigates how the complexity of random quantum circuits increases by constructing unitary operations from random two-qubit quantum gates. It is proven that the complexity grows linearly until it saturates at a threshold that is exponentially related to the number of qubits.
Article
Physics, Particles & Fields
Shira Chapman et al.
Summary: We computed the length of spacelike geodesics in certain double-sided flow geometries in two dimensions. The results showed that in geometries with black hole horizons, the geodesic length exhibits linear growth at late times, while in flow geometries with de Sitter horizons, geodesics with finite length only exist for short times and do not exhibit linear growth. These results have implications for understanding the holographic proposal for quantum complexity and the holographic nature of the de Sitter horizon.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Eivind Jorstad et al.
Summary: We study holographic complexity in de Sitter spacetime and find that it exhibits universal behavior in different approaches. Specifically, holographic complexity shows 'hyperfast' growth and appears to diverge with a universal power law at a finite critical time. We introduce a cutoff surface to regulate this divergence, and the subsequent growth of holographic complexity is linear in time.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Andrew Svesko et al.
Summary: This paper studies the semi-classical thermodynamics of two-dimensional de Sitter space in Jackiw-Teitelboim gravity, coupled with conformal matter. The study derives the quasi-local energy and the generalized entropy by introducing a timelike boundary in the static patch. The findings provide a first principles derivation of the island rule for U(1) symmetric dS(2) backgrounds.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Luca V. Iliesiu et al.
Summary: Understanding the fate of semi-classical black hole solutions at very late times is an important open question in quantum gravity. In this paper, the authors provide a path integral definition of the volume of the black hole interior and study its evolution at arbitrarily late times. They find that, after a linear growth, the length of the interior saturates at a time and value that is exponentially large in the entropy of the black hole, which supports the complexity equals volume proposal.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Mohsen Alishahiha et al.
Summary: In this paper, we investigate the complexity of a single-sided AdS black hole modelled by an end-of-the-world brane. We provide multi-boundary partition functions and matter correlation functions for such a setting. By computing the complexity using a modified replica trick, we find that the complexity saturates to a constant value following a period of linear growth at late times. Furthermore, we show an improved result for the variance of complexity, which is time-independent in the late time regime.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Edgar Shaghoulian et al.
Summary: This paper expands on two recent proposals to generalize the Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulas to de Sitter space, referred to as the monolayer and bilayer proposals. These proposals replace the boundary of AdS with the boundaries of static-patches or event horizons. The paper applies the rules of each proposal to various cases and demonstrates that they produce expected results. While the monolayer and bilayer proposals often yield the same results, they disagree in one specific situation. A better understanding of the thermodynamic limit of holographic systems is needed to definitively decide between the two.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Multidisciplinary
Johanna Erdmenger et al.
Summary: In this study, we construct the exact gravity dual to circuits performing local conformal transformations in general two-dimensional conformal field theories. Our findings establish the foundation for studying exact gravity duals to circuit costs from first principles.
Article
Astronomy & Astrophysics
Pablo Basteiro et al.
Summary: In this paper, we propose a new approach to defining complexity for quantum field theories by mapping Nielsen operator complexity for SU(N) gates to two-dimensional hydrodynamics. We develop a tractable large N limit that results in regular geometries on the manifold of unitaries as N tends to infinity. By introducing a basis of noncommutative plane waves for the su(N) algebra and defining a metric with polynomial penalty factors, we identify incompressible inviscid hydrodynamics on the two-torus as a novel effective theory of large-qudit operator complexity through the Euler-Arnold approach.
Article
Physics, Particles & Fields
Juan Maldacena et al.
Summary: This study focuses on aspects of the de Sitter version of Jackiw-Teitelboim gravity, exploring the boundary mode's gravitational corrections to cosmological observables and examining contributions from different topologies. By computing no-boundary wavefunctions and probability measures, the research also highlights the dominance of two-dimensional nearly de Sitter gravity dynamics on certain observables.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Shao-Kai Jian et al.
Summary: The concepts of operator size and computational complexity play key roles in the study of quantum chaos and holographic duality, helping characterize the structure of time-evolving Heisenberg operators. The study shows that complexity, well defined in both quantum systems and gravity theories, can serve as a useful measure of operator evolution, exhibiting exponential-to-linear growth behavior in some cases both at early and late times.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Juan Hernandez et al.
Summary: In this study, holographic complexity in the doubly holographic model was examined to focus on the holographic complexity=volume (CV) proposal for boundary subregions in the island phase. By deriving the leading contributions to the complexity and interpreting them in terms of the generalized volume of the island, a generalization of the CV proposal for higher curvature theories of gravity was proposed. Consistency checks were provided by investigating Gauss-Bonnet gravity and f(Script capital R) gravity in the bulk.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Astronomy & Astrophysics
Leonard Susskind
Summary: The Goheer-Kleban-Susskind no-go theorem highlights the incompatibility between the symmetry of de Sitter space and finite entropy. Recent developments suggest that eternal de Sitter space, if it exists, may just be an ensemble average.
Article
Astronomy & Astrophysics
Gustavo J. Turiaci et al.
Summary: A large class of two-dimensional dilaton-gravity theories in asymptotically AdS(2) spacetimes are holographically dual to a matrix integral, interpreted as an ensemble average over Hamiltonians. Extending this duality to include conical defects with small deficit angles, the theories are shown to be equal to the large p limit of a natural deformation of the (2, p) minimal string theory.
CLASSICAL AND QUANTUM GRAVITY
(2021)
Article
Astronomy & Astrophysics
Roberto Auzzi et al.
Summary: The study focuses on quantum computational complexity and its applications in holographic understanding of the black hole interior. By choosing penalty factors, negative curvatures are achieved to reproduce desired features in holography. The relationship between operator and state complexities is analyzed, providing a direct relation between geodesics and curvatures and a closed-form expression for the metric in terms of the operators.
Article
Physics, Particles & Fields
Rong-Gen Cai et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2020)
Article
Physics, Particles & Fields
Mario Flory et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2020)
Article
Physics, Multidisciplinary
Mario Flory et al.
PHYSICAL REVIEW RESEARCH
(2020)
Article
Physics, Particles & Fields
Johanna Erdmenger et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2020)
Article
Physics, Particles & Fields
Kanato Goto et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2019)
Article
Physics, Particles & Fields
Alexandre Belin et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2019)
Article
Physics, Particles & Fields
Mohsen Alishahiha
EUROPEAN PHYSICAL JOURNAL C
(2019)
Article
Physics, Particles & Fields
Dionysios Anninos et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2019)
Article
Astronomy & Astrophysics
Adam R. Brown et al.
Article
Astronomy & Astrophysics
Dionysios Anninos et al.
CLASSICAL AND QUANTUM GRAVITY
(2018)
Article
Physics, Multidisciplinary
Shira Chapman et al.
PHYSICAL REVIEW LETTERS
(2018)
Article
Physics, Particles & Fields
Lucas Hackl et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2018)
Article
Physics, Particles & Fields
Amin Akhavan et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2018)
Article
Physics, Multidisciplinary
Pawel Caputa et al.
PHYSICAL REVIEW LETTERS
(2017)
Article
Physics, Particles & Fields
Josiah Couch et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2017)
Article
Physics, Particles & Fields
Mohsen Alishahiha et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2017)
Article
Physics, Particles & Fields
Shira Chapman et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2017)
Article
Physics, Particles & Fields
Dean Carmi et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2017)
Article
Physics, Particles & Fields
Dean Carmi et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2017)
Article
Physics, Particles & Fields
Robert A. Jefferson et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2017)
Article
Physics, Multidisciplinary
Leonard Susskind
FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS
(2016)
Article
Physics, Multidisciplinary
Leonard Susskind
FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS
(2016)
Article
Astronomy & Astrophysics
Krishnamohan Parattu et al.
GENERAL RELATIVITY AND GRAVITATION
(2016)
Article
Physics, Multidisciplinary
Adam R. Brown et al.
PHYSICAL REVIEW LETTERS
(2016)
Article
Astronomy & Astrophysics
Juan Maldacena et al.
Article
Astronomy & Astrophysics
Mohsen Alishahiha
Article
Astronomy & Astrophysics
Douglas Stanford et al.
Article
Physics, Particles & Fields
Thomas Hartman et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2013)
Review
Physics, Nuclear
Dionysios Anninos
INTERNATIONAL JOURNAL OF MODERN PHYSICS A
(2012)
Article
Physics, Particles & Fields
Veronika E. Hubeny et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2007)
Article
Physics, Particles & Fields
Shinsei Ryu et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2006)
Article
Astronomy & Astrophysics
V Balasubramanian et al.
CLASSICAL AND QUANTUM GRAVITY
(2002)
Article
Astronomy & Astrophysics
R Bousso et al.
Article
Physics, Particles & Fields
A Strominger
JOURNAL OF HIGH ENERGY PHYSICS
(2001)
