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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
Farzad Omidi
Summary: In this paper, the authors investigate the generalized volume-complexity C-gen for a two-sided uncharged HV black brane in d+ 2 dimensions. They numerically calculate the growth rate of C-gen for different values of the hyperscaling violation exponent 0 and dynamical exponent z, and find that C-gen always grows linearly at late times with properly chosen lambda. The authors also examine the dependence of the growth rate on d, theta, z, and lambda, and calculate the complexity of formation obtained from volume-complexity. They show that it is not UV divergent and examine its dependence on the thermal entropy and temperature of the black brane. Furthermore, they numerically calculate the growth rate of C-gen for a linear combination of higher curvature corrections and show that the late time growth rate is again linear for appropriate values of the coupling constants.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Particles & Fields
Alexandre Belin et al.
Summary: We extend previous research to introduce a new class of gravitational observables in asymptotically Anti-de Sitter space, which exist in general codimension-zero regions of the bulk spacetime. These observables can be simplified to well-studied holographic complexity proposals and exhibit key universal features. We argue that any member of this new class of observables is a viable candidate as a gravitational dual of complexity. Using the Peierls construction, we demonstrate that variations of these observables can be encoded in the gravitational symplectic form on the semi-classical phase-space and mapped to the CFT.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Particles & Fields
Venkatesa Chandrasekaran et al.
Summary: We present an algebra of observables for a static patch in de Sitter space, where the operators are gravitationally dressed according to the observer's worldline. This algebra belongs to the Type II1 von Neumann algebra. The state of this algebra has a natural concept of entropy, with a maximum entropy state corresponding to empty de Sitter space. The entropy of any semiclassical state of the Type II1 algebras agrees, up to an arbitrary additive constant, with the expected generalized entropy S-gen = (A/4G(N)) + S-out.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Astronomy & Astrophysics
Chitraang Murdia et al.
Summary: This article describes two different but equivalent semiclassical views, both of which can accommodate the equivalence principle and unitarity. In one view, unitarity is inherently built-in, while the black hole interior only emerges effectively as a collective phenomenon involving horizon (and possibly other) degrees of freedom. In the other, more widely studied approach, the existence of the interior is manifest, but the unitarity of the underlying dynamics can only be captured indirectly by incorporating certain nonperturbative effects of gravity. These two pictures correspond to a distant description and a description based on entanglement islands/replica wormholes, respectively. The existence of these two approaches is rooted in the two formulations of quantum mechanics: the canonical and path integral formalisms.
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, 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
Yasuaki Hikida et al.
Summary: We present a class of dS/CFT correspondence between two-dimensional CFTs and three-dimensional de Sitter spaces. We argue that this correspondence includes various gravity limits and dualities associated with SU(2) and SU(N) WZW models. We confirm the correctness of this correspondence and study two-point functions and entanglement entropy. We also discuss the possible spectrum and quantum corrections in the gravity theory.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Multidisciplinary
Anxo Biasi et al.
Summary: Cosmological acceleration is difficult to explain in theories involving supergravity and superstrings, but it is possible in theories with regular black holes. By placing this scenario in a global antide Sitter background, the formation of de Sitter bubbles can be enhanced, potentially leading to the creation of multiple accelerating universes. Numerical work in a two-dimensional dilaton-gravity model supports this idea.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Yasuaki Hikida et al.
Summary: This letter proposes a holographic duality for classical gravity on a three-dimensional de Sitter space and presents evidence in terms of classical partition function and conformal field theory.
PHYSICAL REVIEW LETTERS
(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, Particles & Fields
Roberto Auzzi et al.
Summary: In this paper, we study the time-dependence of holographic complexity in a class of models with hairy black holes. We find that the volume complexity can only probe a portion of the black hole interior that remains far away from the singularity, while the action complexity can probe a portion closer to the singularity. Furthermore, we discover that the Kasner exponent does not directly affect the details of the complexity divergence and the late-time behavior.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
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
Alice Bernamonti et al.
Summary: The study focuses on the influence of angular momentum on holographic complexity of rotating black holes, revealing similarities with charged black holes. The inclusion of counterterms in the calculation is crucial for understanding the effects, especially in early time dependence. In the grand canonical ensemble, complexity of formation exhibits linear relation with temperature and diverges in the speed of light angular velocity limit.
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
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, Multidisciplinary
Mario Flory et al.
PHYSICAL REVIEW RESEARCH
(2020)
Article
Physics, Particles & Fields
Johanna Erdmenger et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2020)
Article
Astronomy & Astrophysics
Yasunori Nomura
Article
Physics, Particles & Fields
Cesar A. Agon et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2019)
Article
Physics, Multidisciplinary
Pawel Caputa et al.
PHYSICAL REVIEW LETTERS
(2019)
Article
Physics, Particles & Fields
Dionysios Anninos et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2019)
Article
Physics, Particles & Fields
Run-Qiu Yang et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2019)
Article
Mathematics, Applied
Patrick Iglesias-Zemmour
JOURNAL OF GEOMETRY AND PHYSICS
(2019)
Article
Physics, Particles & Fields
Zicao Fu 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
Shira Chapman et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2018)
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Physics, Particles & Fields
Josiah Couch et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2018)
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Shira Chapman et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2018)
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Run-Qiu Yang et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2018)
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Brian Swingle et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2018)
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Subhash Mahapatra et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2018)
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Yasunori Nomura et al.
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Dionysios Anninos et al.
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(2017)
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(2017)
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(2017)
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(2016)
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Leonard Susskind
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(2016)
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FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS
(2016)
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Leonard Susskind
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(2006)
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Review
Multidisciplinary Sciences
S Lloyd
