Stochastic Hydrodynamic Analogy of Quantum Mechanics
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Why Is M-Theory the Leading Candidate for Theory of Everything?
Quanta Magazine Why Is M-Theory the Leading Candidate for Theory of Everything? The mother of all string theories passes a litmus test that, so far, no other candidate theory of quantum gravity has been able to match. By Natalie Wolchover It’s not easy being a “theory of everything.” A TOE has the very tough job of fitting gravity into the quantum laws of nature in such a way that, on large scales, gravity looks like curves in the fabric of space-time, as Albert Einstein described in his general theory of relativity. Somehow, space-time curvature emerges as the collective effect of quantized units of gravitational energy — particles known as gravitons. But naive attempts to calculate how gravitons interact result in nonsensical infinities, indicating the need for a deeper understanding of gravity. String theory (or, more technically, M-theory) is often described as the leading candidate for the theory of everything in our universe. But there’s no empirical evidence for it, or for any alternative ideas about how gravity might unify with the rest of the fundamental forces. Why, then, is string/M- theory given the edge over the others? [abstractions] The theory famously posits that gravitons, as well as electrons, photons and everything else, are not point-particles but rather imperceptibly tiny ribbons of energy, or “strings,” that vibrate in different ways. Interest in string theory soared in the mid-1980s, when physicists realized that it gave mathematically consistent descriptions of quantized gravity. But the five known versions of string theory were all “perturbative,” meaning they broke down in some regimes. -
Simulating Quantum Field Theory with a Quantum Computer
Simulating quantum field theory with a quantum computer John Preskill Lattice 2018 28 July 2018 This talk has two parts (1) Near-term prospects for quantum computing. (2) Opportunities in quantum simulation of quantum field theory. Exascale digital computers will advance our knowledge of QCD, but some challenges will remain, especially concerning real-time evolution and properties of nuclear matter and quark-gluon plasma at nonzero temperature and chemical potential. Digital computers may never be able to address these (and other) problems; quantum computers will solve them eventually, though I’m not sure when. The physics payoff may still be far away, but today’s research can hasten the arrival of a new era in which quantum simulation fuels progress in fundamental physics. Frontiers of Physics short distance long distance complexity Higgs boson Large scale structure “More is different” Neutrino masses Cosmic microwave Many-body entanglement background Supersymmetry Phases of quantum Dark matter matter Quantum gravity Dark energy Quantum computing String theory Gravitational waves Quantum spacetime particle collision molecular chemistry entangled electrons A quantum computer can simulate efficiently any physical process that occurs in Nature. (Maybe. We don’t actually know for sure.) superconductor black hole early universe Two fundamental ideas (1) Quantum complexity Why we think quantum computing is powerful. (2) Quantum error correction Why we think quantum computing is scalable. A complete description of a typical quantum state of just 300 qubits requires more bits than the number of atoms in the visible universe. Why we think quantum computing is powerful We know examples of problems that can be solved efficiently by a quantum computer, where we believe the problems are hard for classical computers. -
Physical Vacuum Is a Special Superfluid Medium
Physical vacuum is a special superfluid medium Valeriy I. Sbitnev∗ St. Petersburg B. P. Konstantinov Nuclear Physics Institute, NRC Kurchatov Institute, Gatchina, Leningrad district, 188350, Russia; Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA 94720, USA (Dated: August 9, 2016) The Navier-Stokes equation contains two terms which have been subjected to slight modification: (a) the viscosity term depends of time (the viscosity in average on time is zero, but its variance is non-zero); (b) the pressure gradient contains an added term describing the quantum entropy gradient multiplied by the pressure. Owing to these modifications, the Navier-Stokes equation can be reduced to the Schr¨odingerequation describing behavior of a particle into the vacuum being as a superfluid medium. Vortex structures arising in this medium show infinitely long life owing to zeroth average viscosity. The non-zero variance describes exchange of the vortex energy with zero-point energy of the vacuum. Radius of the vortex trembles around some average value. This observation sheds the light to the Zitterbewegung phenomenon. The long-lived vortex has a non-zero core where the vortex velocity vanishes. Keywords: Navier-Stokes; Schr¨odinger; zero-point fluctuations; superfluid vacuum; vortex; Bohmian trajectory; interference I. INTRODUCTION registered. Instead, the wave function represents it existence within an experimental scene [13]. A dramatic situation in physical understand- Another interpretation was proposed by Louis ing of the nature emerged in the late of 19th cen- de Broglie [18], which permits to explain such an tury. Observed phenomena on micro scales came experiment. In de Broglie's wave mechanics and into contradiction with the general positions of the double solution theory there are two waves. -
Quantum State Complexity in Computationally Tractable Quantum Circuits
PRX QUANTUM 2, 010329 (2021) Quantum State Complexity in Computationally Tractable Quantum Circuits Jason Iaconis * Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA (Received 28 September 2020; revised 29 December 2020; accepted 26 January 2021; published 23 February 2021) Characterizing the quantum complexity of local random quantum circuits is a very deep problem with implications to the seemingly disparate fields of quantum information theory, quantum many-body physics, and high-energy physics. While our theoretical understanding of these systems has progressed in recent years, numerical approaches for studying these models remains severely limited. In this paper, we discuss a special class of numerically tractable quantum circuits, known as quantum automaton circuits, which may be particularly well suited for this task. These are circuits that preserve the computational basis, yet can produce highly entangled output wave functions. Using ideas from quantum complexity theory, especially those concerning unitary designs, we argue that automaton wave functions have high quantum state complexity. We look at a wide variety of metrics, including measurements of the output bit-string distribution and characterization of the generalized entanglement properties of the quantum state, and find that automaton wave functions closely approximate the behavior of fully Haar random states. In addition to this, we identify the generalized out-of-time ordered 2k-point correlation functions as a particularly use- ful probe of complexity in automaton circuits. Using these correlators, we are able to numerically study the growth of complexity well beyond the scrambling time for very large systems. As a result, we are able to present evidence of a linear growth of design complexity in local quantum circuits, consistent with conjectures from quantum information theory. -
Quantum Computation and Complexity Theory
Quantum computation and complexity theory Course given at the Institut fÈurInformationssysteme, Abteilung fÈurDatenbanken und Expertensysteme, University of Technology Vienna, Wintersemester 1994/95 K. Svozil Institut fÈur Theoretische Physik University of Technology Vienna Wiedner Hauptstraûe 8-10/136 A-1040 Vienna, Austria e-mail: [email protected] December 5, 1994 qct.tex Abstract The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applicationsto quantum computing. Standardinterferomeric techniques are used to construct a physical device capable of universal quantum computation. Some consequences for recursion theory and complexity theory are discussed. hep-th/9412047 06 Dec 94 1 Contents 1 The Quantum of action 3 2 Quantum mechanics for the computer scientist 7 2.1 Hilbert space quantum mechanics ..................... 7 2.2 From single to multiple quanta Ð ªsecondº ®eld quantization ...... 15 2.3 Quantum interference ............................ 17 2.4 Hilbert lattices and quantum logic ..................... 22 2.5 Partial algebras ............................... 24 3 Quantum information theory 25 3.1 Information is physical ........................... 25 3.2 Copying and cloning of qbits ........................ 25 3.3 Context dependence of qbits ........................ 26 3.4 Classical versus quantum tautologies .................... 27 4 Elements of quantum computatability and complexity theory 28 4.1 Universal quantum computers ....................... 30 4.2 Universal quantum networks ........................ 31 4.3 Quantum recursion theory ......................... 35 4.4 Factoring .................................. 36 4.5 Travelling salesman ............................. 36 4.6 Will the strong Church-Turing thesis survive? ............... 37 Appendix 39 A Hilbert space 39 B Fundamental constants of physics and their relations 42 B.1 Fundamental constants of physics ..................... 42 B.2 Conversion tables .............................. 43 B.3 Electromagnetic radiation and other wave phenomena ......... -
Bohmian Mechanics Versus Madelung Quantum Hydrodynamics
Ann. Univ. Sofia, Fac. Phys. Special Edition (2012) 112-119 [arXiv 0904.0723] Bohmian mechanics versus Madelung quantum hydrodynamics Roumen Tsekov Department of Physical Chemistry, University of Sofia, 1164 Sofia, Bulgaria It is shown that the Bohmian mechanics and the Madelung quantum hy- drodynamics are different theories and the latter is a better ontological interpre- tation of quantum mechanics. A new stochastic interpretation of quantum me- chanics is proposed, which is the background of the Madelung quantum hydro- dynamics. Its relation to the complex mechanics is also explored. A new complex hydrodynamics is proposed, which eliminates completely the Bohm quantum po- tential. It describes the quantum evolution of the probability density by a con- vective diffusion with imaginary transport coefficients. The Copenhagen interpretation of quantum mechanics is guilty for the quantum mys- tery and many strange phenomena such as the Schrödinger cat, parallel quantum and classical worlds, wave-particle duality, decoherence, etc. Many scientists have tried, however, to put the quantum mechanics back on ontological foundations. For instance, Bohm [1] proposed an al- ternative interpretation of quantum mechanics, which is able to overcome some puzzles of the Copenhagen interpretation. He developed further the de Broglie pilot-wave theory and, for this reason, the Bohmian mechanics is also known as the de Broglie-Bohm theory. At the time of inception of quantum mechanics Madelung [2] has demonstrated that the Schrödinger equa- tion can be transformed in hydrodynamic form. This so-called Madelung quantum hydrodynam- ics is a less elaborated theory and usually considered as a precursor of the Bohmian mechanics. The scope of the present paper is to show that these two theories are different and the Made- lung hydrodynamics is a better interpretation of quantum mechanics than the Bohmian me- chanics. -
Bounds on Errors in Observables Computed from Molecular Dynamics Simulations
Bounds on Errors in Observables Computed from Molecular Dynamics Simulations Vikram Sundar [email protected] Advisor: Dr. David Gelbwaser and Prof. Alan´ Aspuru-Guzik (Chemistry) Shadow Advisor: Prof. Martin Nowak Submitted in partial fulfillment of the honors requirements for the degree of Bachelor of Arts in Mathematics March 19, 2018 Contents Abstract iii Acknowledgments iv 1 Introduction1 1.1 Molecular Dynamics................................1 1.1.1 Why Molecular Dynamics?........................1 1.1.2 What is Molecular Dynamics?......................2 1.1.2.1 Force Fields and Integrators..................2 1.1.2.2 Observables...........................3 1.2 Structure of this Thesis...............................4 1.2.1 Sources of Error...............................4 1.2.2 Key Results of this Thesis.........................5 2 The St¨ormer-Verlet Method and Energy Conservation7 2.1 Symplecticity....................................8 2.1.1 Hamiltonian and Lagrangian Mechanics................8 2.1.2 Symplectic Structures on Manifolds...................9 2.1.3 Hamiltonian Flows are Symplectic.................... 10 2.1.4 Symplecticity of the Stormer-Verlet¨ Method............... 12 2.2 Backward Error Analysis.............................. 12 2.2.1 Symplectic Methods and Backward Error Analysis.......... 14 2.2.2 Bounds on Energy Conservation..................... 14 3 Integrable Systems and Bounds on Sampling Error 16 3.1 Integrable Systems and the Arnold-Liouville Theorem............. 17 3.1.1 Poisson Brackets and First Integrals................... 17 3.1.2 Liouville’s Theorem............................ 18 3.1.3 Action-Angle Coordinates......................... 20 3.1.4 Integrability and MD Force Fields.................... 22 3.2 Sampling Error................................... 23 3.2.1 Equivalence of Spatial and Time Averages............... 23 3.2.2 Bounding Sampling Error......................... 24 3.2.3 Reducing Sampling Error with Filter Functions........... -
Conformal Field Theory out of Equilibrium: a Review Denis Bernard
Conformal field theory out of equilibrium: a review Denis Bernard| and Benjamin Doyon♠ | Laboratoire de Physique Th´eoriquede l'Ecole Normale Sup´erieurede Paris, CNRS, ENS & PSL Research University, UMPC & Sorbonne Universit´es,France. ♠ Department of Mathematics, King's College London, London, United Kingdom. We provide a pedagogical review of the main ideas and results in non-equilibrium conformal field theory and connected subjects. These concern the understanding of quantum transport and its statistics at and near critical points. Starting with phenomenological considerations, we explain the general framework, illustrated by the example of the Heisenberg quantum chain. We then introduce the main concepts underlying conformal field theory (CFT), the emergence of critical ballistic transport, and the CFT scattering construction of non-equilibrium steady states. Using this we review the theory for energy transport in homogeneous one-dimensional critical systems, including the complete description of its large deviations and the resulting (extended) fluctuation relations. We generalize some of these ideas to one-dimensional critical charge transport and to the presence of defects, as well as beyond one-dimensional criticality. We describe non-equilibrium transport in free-particle models, where connections are made with generalized Gibbs ensembles, and in higher-dimensional and non-integrable quantum field theories, where the use of the powerful hydrodynamic ideas for non-equilibrium steady states is explained. We finish with a list of open questions. The review does not assume any advanced prior knowledge of conformal field theory, large-deviation theory or hydrodynamics. March 24, 2016 Contents 1 Introduction 1 2 Mesoscopic electronic transport: basics 3 2.1 Elementary phenomenology . -
Quantum Speedup for Aeroscience and Engineering
NASA/TM-2020-220590 Quantum Speedup for Aeroscience and Engineering Peyman Givi University of Pittsburgh, Pittsburgh, Pennsylvania Andrew J. Daley University of Strathclyde, Glasgow, United Kingdom Dimitri Mavriplis University of Wyoming, Laramie, Wyoming Mujeeb Malik Langley Research Center, Hampton, Virginia May 2020 NASA STI Program . in Profile Since its founding, NASA has been dedicated to • CONFERENCE PUBLICATION. Collected the advancement of aeronautics and space science. papers from scientific and technical The NASA scientific and technical information conferences, symposia, seminars, or other (STI) program plays a key part in helping NASA meetings sponsored or co-sponsored by maintain this important role. NASA. The NASA STI program operates under the • SPECIAL PUBLICATION. Scientific, auspices of the Agency Chief Information Officer. It technical, or historical information from collects, organizes, provides for archiving, and NASA programs, projects, and missions, often disseminates NASA’s STI. The NASA STI program concerned with subjects having substantial provides access to the NASA Aeronautics and Space public interest. Database and its public interface, the NASA Technical Report Server, thus providing one of the • TECHNICAL TRANSLATION. English- largest collections of aeronautical and space science language translations of foreign scientific and STI in the world. Results are published in both non- technical material pertinent to NASA’s NASA channels and by NASA in the NASA STI mission. Report Series, which includes the following report types: Specialized services also include creating custom thesauri, building customized databases, • TECHNICAL PUBLICATION. Reports of and organizing and publishing research results. completed research or a major significant phase of research that present the results of For more information about the NASA STI NASA programs and include extensive data or program, see the following: theoretical analysis. -
Stochastic Quantum Dynamics and Relativity
Stochastic quantum dynamics and relativity Autor(en): Gisin, N. Objekttyp: Article Zeitschrift: Helvetica Physica Acta Band (Jahr): 62 (1989) Heft 4 PDF erstellt am: 25.09.2021 Persistenter Link: http://doi.org/10.5169/seals-116034 Nutzungsbedingungen Die ETH-Bibliothek ist Anbieterin der digitalisierten Zeitschriften. Sie besitzt keine Urheberrechte an den Inhalten der Zeitschriften. Die Rechte liegen in der Regel bei den Herausgebern. Die auf der Plattform e-periodica veröffentlichten Dokumente stehen für nicht-kommerzielle Zwecke in Lehre und Forschung sowie für die private Nutzung frei zur Verfügung. Einzelne Dateien oder Ausdrucke aus diesem Angebot können zusammen mit diesen Nutzungsbedingungen und den korrekten Herkunftsbezeichnungen weitergegeben werden. Das Veröffentlichen von Bildern in Print- und Online-Publikationen ist nur mit vorheriger Genehmigung der Rechteinhaber erlaubt. Die systematische Speicherung von Teilen des elektronischen Angebots auf anderen Servern bedarf ebenfalls des schriftlichen Einverständnisses der Rechteinhaber. Haftungsausschluss Alle Angaben erfolgen ohne Gewähr für Vollständigkeit oder Richtigkeit. Es wird keine Haftung übernommen für Schäden durch die Verwendung von Informationen aus diesem Online-Angebot oder durch das Fehlen von Informationen. Dies gilt auch für Inhalte Dritter, die über dieses Angebot zugänglich sind. Ein Dienst der ETH-Bibliothek ETH Zürich, Rämistrasse 101, 8092 Zürich, Schweiz, www.library.ethz.ch http://www.e-periodica.ch Helvetica Physica Acta, Vol. 62 (1989) 363-371 0018-0238/89/040363-09$l .50 + 0.20/0 © 1989 Birkhäuser Verlag, Basel Stochastic quantum dynamics and relativity By N. Gisin Groupe de Physique Appliquée, Université de Genève, 20 rue de l'Ecole de Médecine, 1211 Genève 4, Switzerland (13. I. 1989) Abstract. Our aim is to unify the Schrödinger dynamics and the projection postulate. -
Entropic Phase Maps in Discrete Quantum Gravity
entropy Article Entropic Phase Maps in Discrete Quantum Gravity Benjamin F. Dribus Department of Mathematics, William Carey University, 710 William Carey Parkway, Hattiesburg, MS 39401, USA; [email protected] or [email protected]; Tel.: +1-985-285-5821 Received: 26 May 2017; Accepted: 25 June 2017; Published: 30 June 2017 Abstract: Path summation offers a flexible general approach to quantum theory, including quantum gravity. In the latter setting, summation is performed over a space of evolutionary pathways in a history configuration space. Discrete causal histories called acyclic directed sets offer certain advantages over similar models appearing in the literature, such as causal sets. Path summation defined in terms of these histories enables derivation of discrete Schrödinger-type equations describing quantum spacetime dynamics for any suitable choice of algebraic quantities associated with each evolutionary pathway. These quantities, called phases, collectively define a phase map from the space of evolutionary pathways to a target object, such as the unit circle S1 ⊂ C, or an analogue such as S3 or S7. This paper explores the problem of identifying suitable phase maps for discrete quantum gravity, focusing on a class of S1-valued maps defined in terms of “structural increments” of histories, called terminal states. Invariants such as state automorphism groups determine multiplicities of states, and induce families of natural entropy functions. A phase map defined in terms of such a function is called an entropic phase map. The associated dynamical law may be viewed as an abstract combination of Schrödinger’s equation and the second law of thermodynamics. Keywords: quantum gravity; discrete spacetime; causal sets; path summation; entropic gravity 1. -
Quantum General Relativity
1 An extended zero-energy hypothesis predicting negative GF potential energy. ZEUT explains that, during the the existence of negative-energy gravitons and inflation phase of our universe, energy flows from the (negative energy) GF to the (positive energy) inflation field possibly explaining the accelerated expansion of (IF) so that the total (negative) GF-energy decreases our universe (becoming more negative) and the total (positive) IF-energy increases (becoming more positive): however, the respective * [1] GF/IF energy densities remain constant and opposite since Andrei-Lucian Drăgoi , Independent researcher the region is inflating; consequently, IF explains the (Bucharest, Romania) cancellation between matter (including radiation) and GF DOI: 10.13140/RG.2.2.36245.99044 energies on cosmological scales, which is consistent with * astronomical observations (concordant with the observable Abstract universe being flat) [2]. The negative energy GF and the positive energy matter (and radiation) may exactly cancel out only if our universe is completely flat: such a zero-energy flat This paper proposes an extended (e) zero-energy universe can theoretically last forever. Tryon acknowledged hypothesis (eZEH) starting from the “classical” speculative zero-energy universe hypothesis (ZEUH) (first proposed by that his ZEUT was inspired by the general relativist Peter physicist Pascual Jordan), which mainly states that the total Bergmann, who showed (before Tryon) how a universe could amount of energy in our universe is exactly zero: its amount come from nothing without contradicting ECP (with the 1st of positive energy (in the form of matter and radiation) is law of thermodynamics being also an ECP version). The first exactly canceled out by its negative energy (in the form of documented mention of ZEUH (1934) (in the context of gravity).