Relevant bibliographies by topics / Lieb-Robinson bound

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Academic literature on the topic 'Lieb-Robinson bound'

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Published: 28 September 2024

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Journal articles on the topic "Lieb-Robinson bound"

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Matsuta, Takuro, Tohru Koma, and Shu Nakamura. "Improving the Lieb–Robinson Bound for Long-Range Interactions." Annales Henri Poincaré 18, no. 2 (October 20, 2016): 519–28. http://dx.doi.org/10.1007/s00023-016-0526-1.

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Woods, M. P., and M. B. Plenio. "Dynamical error bounds for continuum discretisation via Gauss quadrature rules—A Lieb-Robinson bound approach." Journal of Mathematical Physics 57, no. 2 (February 2016): 022105. http://dx.doi.org/10.1063/1.4940436.

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Mahoney, Brendan J., and Craig S. Lent. "The Value of the Early-Time Lieb-Robinson Correlation Function for Qubit Arrays." Symmetry 14, no. 11 (October 26, 2022): 2253. http://dx.doi.org/10.3390/sym14112253.

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The Lieb-Robinson correlation function is one way to capture the propagation of quantum entanglement and correlations in many-body systems. We consider arrays of qubits described by the tranverse-field Ising model and examine correlations as the expanding front of entanglement first reaches a particular qubit. Rather than a new bound for the correlation function, we calculate its value, both numerically and analytically. A general analytical result is obtained that enables us to analyze very large arrays of qubits. The velocity of the entanglement front saturates to a constant value, for which an analytic expression is derived. At the leading edge of entanglement, the correlation function is well-described by an exponential reduced by the square root of the distance. This analysis is extended to arbitrary arrays with general coupling and topologies. For regular two and three dimensional qubit arrays with near-neighbor coupling we find the saturation values for the direction-dependent Lieb-Robinson velocity. The symmetry of the underlying 2D or 3D lattice is evident in the shape of surfaces of constant entanglement, even as the correlations front expands over hundreds of qubits.
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Strasberg, Philipp, Kavan Modi, and Michalis Skotiniotis. "How long does it take to implement a projective measurement?" European Journal of Physics 43, no. 3 (March 28, 2022): 035404. http://dx.doi.org/10.1088/1361-6404/ac5a7a.

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Abstract According to the Schrödinger equation, a closed quantum system evolves continuously in time. If it is subject to a measurement however, its state changes randomly and discontinuously, which is mathematically described by the projection postulate. But how long does it take for this discontinuous change to occur? Based on simple estimates, whose validity rests solely on the fact that all fundamental forces in nature are finite-ranged, we show that the implementation of a quantum measurement requires a minimum time. This time scales proportionally with the diameter of the quantum mechanical object, on which the measured observable acts non-trivially, with the proportionality constant being around 10−5 s m−1. We confirm our bound by comparison with experimentally reported measurement times for different platforms. We give a pedagogical exposition of our argumentation introducing along the way modern concepts such as ancilla-based measurements, the quantum speed limit, and Lieb–Robinson velocity bounds.
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Moosavian, Ali Hamed, Seyed Sajad Kahani, and Salman Beigi. "Limits of Short-Time Evolution of Local Hamiltonians." Quantum 6 (June 27, 2022): 744. http://dx.doi.org/10.22331/q-2022-06-27-744.

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Evolutions of local Hamiltonians in short times are expected to remain local and thus limited. In this paper, we validate this intuition by proving some limitations on short-time evolutions of local time-dependent Hamiltonians. We show that the distribution of the measurement output of short-time (at most logarithmic) evolutions of local Hamiltonians are concentrated and satisfy an isoperimetric inequality. To showcase explicit applications of our results, we study the MAXCUT problem and conclude that quantum annealing needs at least a run-time that scales logarithmically in the problem size to beat classical algorithms on MAXCUT. To establish our results, we also prove a Lieb-Robinson bound that works for time-dependent Hamiltonians which might be of independent interest.
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Vershynina, Anna, and Elliott Lieb. "Lieb-Robinson bounds." Scholarpedia 8, no. 9 (2013): 31267. http://dx.doi.org/10.4249/scholarpedia.31267.

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Doyon, Benjamin. "Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems." Communications in Mathematical Physics 391, no. 1 (January 27, 2022): 293–356. http://dx.doi.org/10.1007/s00220-022-04310-3.

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AbstractOne of the most profound questions of mathematical physics is that of establishing from first principles the hydrodynamic equations in large, isolated, strongly interacting many-body systems. This involves understanding relaxation at long times under reversible dynamics, determining the space of emergent collective degrees of freedom (the ballistic waves), showing that projection occurs onto them, and establishing their dynamics (the hydrodynamic equations). We make progress in these directions, focussing for simplicity on one-dimensional systems. Under a model-independent definition of the complete space of extensive conserved charges, we show that hydrodynamic projection occurs in Euler-scale two-point correlation functions. A fundamental ingredient is a property of relaxation: we establish ergodicity of correlation functions along almost every direction in space and time. We further show that to every extensive conserved charge with a local density is associated a local current and a continuity equation; and that Euler-scale two-point correlation functions of local conserved densities satisfy a hydrodynamic equation. The results are established rigorously within a general framework based on Hilbert spaces of observables. These spaces occur naturally in the $$C^*$$ C ∗ algebra description of statistical mechanics by the Gelfand–Naimark–Segal construction. Using Araki’s exponential clustering and the Lieb–Robinson bound, we show that the results hold, for instance, in every nonzero-temperature Gibbs state of short-range quantum spin chains. Many techniques we introduce are generalisable to higher dimensions. This provides a precise and universal theory for the emergence of ballistic waves at the Euler scale and how they propagate within homogeneous, stationary states.
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Islambekov, Umar, Robert Sims, and Gerald Teschl. "Lieb–Robinson Bounds for the Toda Lattice." Journal of Statistical Physics 148, no. 3 (August 2012): 440–79. http://dx.doi.org/10.1007/s10955-012-0554-2.

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NACHTERGAELE, BRUNO, BENJAMIN SCHLEIN, ROBERT SIMS, SHANNON STARR, and VALENTIN ZAGREBNOV. "ON THE EXISTENCE OF THE DYNAMICS FOR ANHARMONIC QUANTUM OSCILLATOR SYSTEMS." Reviews in Mathematical Physics 22, no. 02 (March 2010): 207–31. http://dx.doi.org/10.1142/s0129055x1000393x.

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We construct a W*-dynamical system describing the dynamics of a class of anharmonic quantum oscillator lattice systems in the thermodynamic limit. Our approach is based on recently proved Lieb–Robinson bounds for such systems on finite lattices [19].
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Nachtergaele, Bruno, and Robert Sims. "Lieb-Robinson Bounds and the Exponential Clustering Theorem." Communications in Mathematical Physics 265, no. 1 (March 22, 2006): 119–30. http://dx.doi.org/10.1007/s00220-006-1556-1.

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Dissertations / Theses on the topic "Lieb-Robinson bound"

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Islambekov, Umar. "Lieb-Robinson Bounds for the Toda Lattice." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/294026.

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We study locality properties of the Toda lattice in terms of Lieb-Robinson bounds. The estimates we prove produce a finite Lieb-Robinson velocity depending on the initial condition. Then we establish analogous results for certain perturbations of the Toda system. Finally, we obtain generalizations of our main results in the setting of the Toda hierarchy.
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Braida, Arthur. "Analog Quantum Computing for NP-Hard Combinatorial Graph Problems." Electronic Thesis or Diss., Orléans, 2024. http://www.theses.fr/2024ORLE1017.

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L'objectif principal de cette thèse est de fournir un éclairage théorique de la complexité du calcul quantique en temps continu (QA et AQC), de la compréhension du phénomène physique (AC) qui conduit à l'échec de l'AQC jusqu'à des preuves de performance de QA en temps court et constant. Pour atteindre cet objectif, nous utilisons différents outils analytiques empruntés à la physique théorique, comme l'analyse perturbative des systèmes quantiques et la borne de Lieb-Robinson sur la vitesse de corrélation dans les systèmes quantiques. La manipulation des graphes et la théorie spectrale des graphes sont nécessaires pour obtenir des résultats sur des classes spécifiques de graphes. Nous avons également introduit une nouvelle version paramétrée du QA standard afin d'affiner l'analyse.Tout d'abord, nous souhaitons obtenir une définition mathématique d'un AC afin d'en faciliter la compréhension lors de l'étude d'une classe spécifique de graphes sur lesquels nous souhaitons résoudre le problème de Maximum Cut. En plus de l'appui analytique que nous développons, nous apportons une étude numérique pour justifier la nature plus générale de notre définition par rapport à la précédente. Grâce à une analyse perturbative, nous parvenons à montrer que sur les graphes bipartis, un gap de fermeture exponentielle peut apparaître si le graphe est suffisamment irrégulier. Notre nouvelle définition de l'AC nous permet de remettre en question l'efficacité de l'AQC pour le résoudre malgré le temps d'exécution exponentiellement long que le théorème adiabatique impose pour garantir la solution optimale. Le deuxième axe est consacré à la performance du QA en temps constant court. Bien que le QA soit intrinsèquement non-local, la borne de LR nous permet de l'approximer avec une évolution locale. Une première approche est utilisée pour développer la méthode et montrer la non trivialité du résultat, c'est-à-dire au-dessus du choix aléatoire. Ensuite, nous définissons une notion d'analyse locale en exprimant le ratio d'approximation avec la seule connaissance de la structure locale. Une borne LR fine et adaptative est développée, nous permettant de trouver une valeur numérique du ratio d'approximation surpassant les algorithmes quantiques et classiques (strictement) locaux. Tous ces travaux de recherche ont été poursuivis entre l'équipe QuantumLab d'Eviden et l'équipe Graphes, Algorithmes et Modèles de Calcul (GAMoC) du Laboratoire d'Informatique Fondamentale d'Orléans (LIFO). Le travail numérique a été implémenté en utilisant le langage de programmation Julia ainsi que Python avec le logiciel QAPTIVA d'Eviden pour simuler efficacement l'équation de Schrödinger
The main objective of this thesis is to provide theoretical insight into the computational complexity of continuous-time quantum computing (QA and AQC), from understanding the physical phenomenon (AC) that leads to AQC failure to proving short constant-time QA efficiency. To achieve this goal, we use different analytical tools borrowed from theoretical physics like perturbative analysis of quantum systems and the Lieb-Robinson bound on the velocity of correlation in quantum systems. Graph manipulation and spectral graph theory are necessary to derive results on a specific class of graph. We also introduced a new parametrized version of the standard QA to tighten the analysis. First, we want to obtain a mathematical definition of an AC to be easier to grasp when studying a specific class of graph on which we want to solve the Maximum Cut problem. We support our new definition with a proven theorem that links it to exponentially small minimum gap and numerical evidence is brought to justify its more general nature compared to the previous one. With a perturbative analysis, we manage to show that on bipartite graphs, exponentially closing gap can arise if the graph is irregular enough. Our new definition of AC allows us to question the efficiency of AQC to solve it despite the exponentially long runtime the adiabatic theorem imposes to guarantee the optimal solution. The second axis is dedicated to the performance of QA at short constant times. Even though QA is inherently non-local, the LR bound allows us to approximate it with a local evolution. A first approach is used to develop the method and to show the non-triviality of the result, i.e. above random guess. Then we define a notion of local analysis by expressing the approximation ratio with only knowledge of the local structure. A tight and adaptive LR bound is developed allowing us to find a numerical value outperforming quantum and classical (strictly) local algorithms. All this research work has been pursued between Eviden QuantumLab team and the Graphes, Algorithmes et Modèles de Calcul (GAMoC) team at the Laboratoire d'Informatique Fondamentale d'Orléans (LIFO). The numerical work has been implemented using Julia programming Language as well as Python with the QAPTIVA software of Eviden to efficiently simulate the Schrödinger equation
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Books on the topic "Lieb-Robinson bound"

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Bru, J. B., and W. de Siqueira Pedra. Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-45784-0.

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Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory. Springer, 2016.

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Bru, J. B., and W. de Siqueira Pedra. Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory. Springer, 2016.

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Book chapters on the topic "Lieb-Robinson bound"

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Naaijkens, Pieter. "Lieb-Robinson Bounds." In Quantum Spin Systems on Infinite Lattices, 109–23. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51458-1_4.

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Naaijkens, Pieter. "Applications of Lieb-Robinson Bounds." In Quantum Spin Systems on Infinite Lattices, 151–71. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51458-1_6.

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Bru, J. B., and W. de Siqueira Pedra. "Lieb–Robinson Bounds for Multi–commutators." In Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory, 31–61. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45784-0_4.

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Bru, J. B., and W. de Siqueira Pedra. "Lieb–Robinson Bounds for Non-autonomous Dynamics." In Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory, 63–87. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45784-0_5.

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Bru, J. B., and W. de Siqueira Pedra. "Introduction." In Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory, 1–4. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45784-0_1.

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Bru, J. B., and W. de Siqueira Pedra. "Algebraic Quantum Mechanics." In Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory, 5–15. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45784-0_2.

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Bru, J. B., and W. de Siqueira Pedra. "Algebraic Setting for Interacting Fermions on the Lattice." In Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory, 17–30. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45784-0_3.

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Bru, J. B., and W. de Siqueira Pedra. "Applications to Conductivity Measures." In Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory, 89–101. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45784-0_6.

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Kliesch, Martin, Christian Gogolin, and Jens Eisert. "Lieb-Robinson Bounds and the Simulation of Time-Evolution of Local Observables in Lattice Systems." In Many-Electron Approaches in Physics, Chemistry and Mathematics, 301–18. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06379-9_17.

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Cheneau, Marc. "Experimental tests of Lieb–Robinson bounds." In The Physics and Mathematics of Elliott Lieb, 225–45. EMS Press, 2022. http://dx.doi.org/10.4171/90-1/10.

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Conference papers on the topic "Lieb-Robinson bound"

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NACHTERGAELE, BRUNO. "LIEB–ROBINSON BOUNDS AND THE EXISTENCE OF INFINITE SYSTEM DYNAMICS." In XVIth International Congress on Mathematical Physics. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814304634_0028.

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SIMS, ROBERT. "LIEB-ROBINSON BOUNDS AND QUASI-LOCALITY FOR THE DYNAMICS OF MANY-BODY QUANTUM SYSTEMS." In Proceedings of the QMath11 Conference. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814350365_0007.

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