全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用：99美元
投递稿件

查看量下载量

相关文章

更多...

Quantum Deep Learning Triuniverse

DOI: 10.4236/jqis.2016.64015, PP. 223-248

Keywords: Quantum Foundations, Cosmology, Evolution, Artificial Intelligence

Full-Text   Cite this paper   Add to My Lib

Abstract:

An original quantum foundations concept of a deep learning computational Universe is introduced. The fundamental information of the Universe (or Triuniverse) is postulated to evolve about itself in a Red, Green and Blue (RGB) tricoloured stable self-mutuality in three information processing loops. The colour is a non-optical information label. The information processing loops form a feedback-reinforced deep learning macrocycle with trefoil knot topology. Fundamental information processing is driven by ψ-Epistemic Drive, the Natural appetite for information selected for advantageous knowledge. From its substrate of Mathematics, the knotted information processing loops determine emergent Physics and thence the evolution of super-emergent Life (biological and artificial intelligence). RGB-tricoloured information is processed in sequence in an Elemental feedback loop (R), then an Operational feedback loop (G), then a Structural feedback loop (B) and back to an Elemental feedback loop (R), and so on around the trefoil in deep learning macrocycles. It is postulated that hierarchical information correspondence from Mathematics through Physics to Life is mapped and conserved within each colour. The substrate of Mathematics has RGB-tricoloured feedback loops which are respectively Algebra (R), Algorithms (G) and Geometry (B). In Mathematics, the trefoil macrocycle is Algebraic Algorithmic Geometry and its correlation system is a Tensor Neural Knot Network enabling Qutrit Entanglement. Emergent Physics has corresponding RGB-tricoloured feedback loops of Quantum Mechanics (R), Quantum Deep Learning (G) and Quantum Geometrodynamics (B). In Physics, the trefoil macrocycle is Quantum Intelligent Geometrodynamics and its correlation system is Quantum Darwinism. Super-emergent Life has corresponding RGB-tricoloured loops of Variation (R), Selection (G) and Heredity (B). In the evolution of Life, the trefoil macrocycle is Variational Selective Heredity and its correlation ecosystem is Darwin’s ecologically “Entangled Bank”.

 References

[1]  Darwin, C. (1859) The Origin of Species. Murray, London.
[2]  Van Wyhe, J. (2006) The Complete Work of Charles Darwin Online. Notes and Records of the Royal Society, 60, 87-89.
http://dx.doi.org/10.1098/rsnr.2005.0128
[3]  Wiebe, N., Kapoor, A. and Svore, K.M. (2014) Quantum Deep Learning. Arxiv:1412.3489
[4]  Aldrich, H.E., Hodgson, G.M., Hull, D.L., Knudsen, T., Mokyr, J. and Vanberg, V.J. (2008) In Defence of Generalized Darwinism. Journal of Evolutionary Economics, 18, 577-596.
http://dx.doi.org/10.1007/s00191-008-0110-z
[5]  Armstrong, S., Morizur, J.F., Janousek, J., Hage, B., Treps, N., Lam, P.K. and Bachor, H.A. (2012) Programmable Multimode Quantum Networks. Nature Communications, 3, Article No. 1026.
http://dx.doi.org/10.1038/ncomms2033
[6]  Bäck, T., Fogel, D.B. and Michalewicz, Z. (1997) Handbook of Evolutionary Computation. Institute of Physics Pub., Bristol, UK.
[7]  Basu, S., Pollack, R. and Roy, M.F.I. (2003) Algorithms in Real Algebraic Geometry. In: Algorithms and Computation in Mathematics, Springer, Berlin Heidelberg.
http://dx.doi.org/10.1007/978-3-662-05355-3
[8]  Barvinsky, A.O. (1986) Quantum Geometrodynamics: The Wheeler-Dewitt Equations for the Wave Function of the Universe. Physics Letters B, 175, 401-404.
http://dx.doi.org/10.1016/0370-2693(86)90612-X
[9]  Bianchi, M., Pradisi, G. and Sagnotti, A. (1992) Toroidal Compactification and Symmetry Breaking in Open-String Theories. Nuclear Physics B, 376, 365-386.
http://dx.doi.org/10.1016/0550-3213(92)90129-Y
[10]  Bickhard, M.H. and Campbell, D.T. (2003) Variations in Variation and Selection: The Ubiquity of the Variation-and-Selective-Retention Ratchet in Emergent Organizational Complexity. Foundations of Science, 8, 215-282.
http://dx.doi.org/10.1023/A:1025046917589
[11]  Campbell, J.O. (2016) Universal Darwinism as a Process of Bayesian inference. Frontiers in Systems Neuroscience, 10, 49.
http://dx.doi.org/10.3389/fnsys.2016.00049
[12]  Carroll, S.B. (2008) Evo-Devo and an Expanding Evolutionary Synthesis: A Genetic Theory of Morphological Evolution. Cell, 134, 25-36.
http://dx.doi.org/10.1016/j.cell.2008.06.030
[13]  Champagnat, N., Ferrière, R. and Méléard, S. (2006) Unifying Evolutionary Dynamics: from Individual Stochastic Processes to Macroscopic Models. Theoretical Population Biology, 69, 297-321.
http://dx.doi.org/10.1016/j.tpb.2005.10.004
[14]  Chastain, E., Livnat, A., Papadimitriou, C. and Vazirani, U. (2014) Algorithms, Games, and Evolution. Proceedings of the National Academy of Sciences of the United States of America, 111, 10620-10623.
http://dx.doi.org/10.1073/pnas.1406556111
[15]  Dawkins, R. (1983) Universal Darwinism. In: Bendall, D.S., Ed., Evolution from Molecules to Man, Cambridge University Press, New York.
[16]  Deutsch, D. and Jozsa, R. (1992) Rapid Solution of Problems by Quantum Computation. Proceedings of the Royal Society of London. Proceedings of the Royal Society A: Mathematical and Physical Sciences, 439, 553-558.
http://dx.doi.org/10.1098/rspa.1992.0167
[17]  Dobzhansky, T. (1949) Towards a Modern Synthesis. Evolution, 3, 376-377.
http://dx.doi.org/10.2307/2405724
[18]  Eldredge, N. (1985) Unfinished Synthesis: Biological Hierarchies and Modern Evolutionary Thought. Oxford University Press, New York.
[19]  Flores Martinez, C.L. (2014) SETI in the Light of Cosmic Convergent Evolution. Acta Astronautica, 104, 341-349.
http://dx.doi.org/10.1016/j.actaastro.2014.08.013
[20]  Fogel, D.B. (2006) Evolutionary Computation: Toward a New Philosophy of Machine Intelligence. John Wiley & Sons, Hoboken.
[21]  Georgiev, G. and Georgiev, I. (2002) The Least Action and the Metric of an Organized System. Open Systems & Information Dynamics, 9, 371-380.
http://dx.doi.org/10.1023/A:1021858318296
[22]  Gray, J., He, Y.-H. and Lukas, A. (2006) Algorithmic Algebraic Geometry and Flux Vacua. Journal of High Energy Physics, 2006, 31.
http://dx.doi.org/10.1088/1126-6708/2006/09/031
[23]  Han, K.H. and Kim, J.H. (2002) Quantum-Inspired Evolutionary Algorithm for a Class of Combinatorial Optimization. IEEE Transactions on Evolutionary Computation, 6, 580-593.
http://dx.doi.org/10.1109/TEVC.2002.804320
[24]  Hartshorne, R. (1977) Algebraic Geometry. In: Graduate Texts in Mathematics, Springer, Berkeley, California.
http://dx.doi.org/10.1007/978-1-4757-3849-0
[25]  Hormozi, L., Bonesteel, N.E. and Simon, S.H. (2009) Topological Quantum Computing with Read-Rezayi States. Physical Review Letters, 103, Article ID: 160501.
http://dx.doi.org/10.1103/PhysRevLett.103.160501
[26]  Kiefer, C. (2012) Quantum Geometrodynamics. In: Quantum Gravity, 3rd Edition, Oxford Science Publications, Oxford, 141-189.
http://dx.doi.org/10.1093/acprof:oso/9780199585205.003.0005
[27]  Koutník, J., Cuccu, G., Schmidhuber, J. and Gomez, F. (2013) Evolving Large-Scale Neural Networks for Vision-Based Reinforcement Learning. Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, Amsterdam, 6-10 July 2013, 1061-1068.
http://dx.doi.org/10.1145/2463372.2463509
[28]  Last, C. (2015) Big Historical Foundations for Deep Future Speculations: Cosmic Evolution, Atechnogenesis, and Technocultural Civilization. Foundations of Science, 1-86.
http://dx.doi.org/10.1007/s10699-015-9434-y
[29]  LeCun, Y., Bengio, Y. and Hinton, G. (2015) Deep Learning. Nature, 521, 436-444.
http://dx.doi.org/10.1038/nature14539
[30]  Peldán, P. (1996) A Modular Invariant Quantum Theory from the Connection Formulation of (2 + 1)-Gravity on the Torus. Classical and Quantum Gravity, 13, 221-224.
http://dx.doi.org/10.1088/0264-9381/13/2/010
[31]  Peldán, P. (1996) Large Diffeomorphisms in 2 + 1 Quantum Gravity on the Torus. Physical Review D, 53, 3147-3155.
http://dx.doi.org/10.1103/PhysRevD.53.3147
[32]  Marolf, D.M. (1993) Loop Representations for 2 + 1 Gravity on a Torus. Classical and Quantum Gravity, 10, 2625-2647.
http://dx.doi.org/10.1088/0264-9381/10/12/020
[33]  Meusburger, C. and Noui, K. (2010) Combinatorial Quantisation of the Euclidean Torus Universe. Nuclear Physics B, 841, 463-505.
http://dx.doi.org/10.1016/j.nuclphysb.2010.08.014
[34]  Narain, K.S., Sarmadi, M.H. and Witten, E. (1987) A Note on Toroidal Compactification of Heterotic String Theory. Nuclear Physics B, 279, 369-379.
http://dx.doi.org/10.1016/0550-3213(87)90001-0
[35]  Nielsen, M.A. and Chuang, I.L. (2010) Quantum Computation and Quantum Information. 10th Anniversary Edition, Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511976667
[36]  Padgett, M.J., O’Holleran, K., Leach, J., Courtial, J. and Dennis, M.R. (2006) The Topology of Vortex Lines in Light Beams. Topology in Ordered Phases. Proceedings of the 1st International Symposium on TOP, Sapporo, 7-10 March 2005, 287-294.
http://dx.doi.org/10.1142/9789812772879_0046
[37]  Pitkänen, M. (2009) Topological Geometrodynamics Inspired Quantum Model of Living Matter. NeuroQuantology, 7, 338-367.
http://dx.doi.org/10.14704/nq.2009.7.3.238
[38]  Powell, R. and Mariscal, C. (2015) Convergent Evolution as Natural Experiment: The Tape of Life Reconsidered. Interface Focus, 5, Article ID: 20150040.
http://dx.doi.org/10.1098/rsfs.2015.0040
[39]  Rickles, D. (2008) Quantum Gravity: A Primer for Philosophers. Ashgate, Aldershot.
[40]  Rovelli, C. and Smolin, L. (1995) Discreteness of Area and Volume in Quantum Gravity. Nuclear Physics B, 442, 593-619.
http://dx.doi.org/10.1016/0550-3213(95)00150-Q
[41]  Smolin, L. (2014) Linking Shape Dynamics and Loop Quantum Gravity. Physical Review D, 90, Article ID: 044070. http://dx.doi.org/10.1103/PhysRevD.90.044070
[42]  Schmidhuber, J. (2015) Deep Learning in Neural Networks: An Overview. Neural Networks, 61, 85-117.
http://dx.doi.org/10.1016/j.neunet.2014.09.003
[43]  Smart, J.M. (2009) Evo Devo Universe? A Framework for Speculations on Cosmic Culture. In: Dick, S.J. and Lupisella, M.L., Eds., Cosmos & Culture: Cultural Evolution in a Cosmic Context, Govt Printing Office, NASA SP-2009-4802, Washington DC, 201-295.
[44]  Smolin, L. (1992) Did the Universe Evolve? Classical and Quantum Gravity, 9, 173-191.
http://dx.doi.org/10.1088/0264-9381/9/1/016
[45]  Smolin, L. (1997) The Life of the Cosmos. Oxford University Press, Oxford, USA.
[46]  Smolin, L. (2004) Cosmological Natural Selection as the Explanation for the Complexity of the Universe. Physica A: Statistical Mechanics and Its Applications, 340, 705-713.
http://dx.doi.org/10.1016/j.physa.2004.05.021
[47]  Sterelny, K., Smith, K.C. and Dickison, M. (1996) The Extended Replicator. Biology and Philosophy, 11, 377-403.
http://dx.doi.org/10.1007/BF00128788
[48]  Thiemann, T. (2003) Lectures on Loop Quantum Gravity. In: Giulini. D.J.W., Kiefer, C. and Lämmerzahl, C., Eds., Quantum Gravity, Springer Berlin Heidelberg, 41-135.
http://dx.doi.org/10.1007/978-3-540-45230-0_3
[49]  Valiant, L. (2013) Probably Approximately Correct: Nature’s Algorithms for Learning and Prospering in a Complex World. Basic Books, New York.
[50]  Vidal, C. (2010) Introduction to the Special Issue on the Evolution and Development of the Universe. Foundations of Science, 15, 95-99.
http://dx.doi.org/10.1007/s10699-010-9176-9
[51]  Vidal, C. (2014) The Beginning and the End: The Meaning of Life in a Cosmological Perspective. Springer International Publishing, Switzerland.
http://dx.doi.org/10.1007/978-3-319-05062-1
[52]  Watson, R.A. (2012) Is Evolution by Natural Selection the Algorithm of Biological Evolution? Artificial Life, 13, 121-128.
[53]  Watson, R.A., Mills, R., Buckley, C.L., Kouvaris, K., Jackson, A., Powers, S.T., Cox, C., Tudge, S., Davies, A., Kounios, L. and Power, D. (2015) Evolutionary Connectionism: Algorithmic Principles Underlying the Evolution of Biological Organisation in Evo-Devo, Evo-Eco and Evolutionary Transitions. Evolutionary Biology, 1-29.
http://dx.doi.org/10.1007/s11692-015-9358-z
[54]  Watson, R.A. and Szathmary, E. (2016) How Can Evolution Learn? Trends in Ecology & Evolution, 31, 147-157.
http://dx.doi.org/10.1016/j.tree.2015.11.009
[55]  Watson, R.A., Ficici, S.G. and Pollack, J.B. (2002) Embodied Evolution: Distributing an Evolutionary Algorithm in a Population of Robots. Robotics and Autonomous Systems, 39, 1-18.
http://dx.doi.org/10.1016/S0921-8890(02)00170-7
[56]  Wheeler, J.A. (1957) On the Nature of Quantum Geometrodynamics. Annals of Physics, 2, 604-614.
http://dx.doi.org/10.1016/0003-4916(57)90050-7
[57]  Wheeler, J.A. (1968) Superspace and the Nature of Quantum Geometrodynamics. Topics in Nonlinear Physics, 615-724.
[58]  Zurek, W.H. (2003) Decoherence, Einselection, and the Quantum Origins of the Classical. Reviews of Modern Physics, 75, 715-775.
http://dx.doi.org/10.1103/RevModPhys.75.715
[59]  Zurek, W.H. (2003) Quantum Darwinism and Envariance. arXiv:quant-ph/0308163
[60]  Zurek, W.H. (2009) Quantum Darwinism. Nature Physics, 5, 181-188.
http://dx.doi.org/10.1038/nphys1202
[61]  Bousso, R. (2002) The Holographic Principle. Reviews of Modern Physics, 74, 825-874.
http://dx.doi.org/10.1103/RevModPhys.74.825
[62]  ‘t Hooft, G. (2005) The Holographic Mapping of the Standard Model onto the Black Hole Horizon: I. Abelian Vector Field, Scalar Field and BEH Mechanism. Classical and Quantum Gravity, 22, 4179-4188.
http://dx.doi.org/10.1088/0264-9381/22/20/001
[63]  Susskind, L. (1995) The World as a Hologram. Journal of Mathematical Physics, 36, 6377.
http://dx.doi.org/10.1063/1.531249
[64]  Witten, E. (1998) Anti De Sitter Space and Holography. Advances in Theoretical and Mathematical Physics, 2, 253-291.
http://dx.doi.org/10.4310/ATMP.1998.v2.n2.a2
[65]  Myung, Y.S. (2005) Holographic Principle and Dark Energy. Physics Letters B, 610, 18-22.
http://dx.doi.org/10.1016/j.physletb.2005.02.006
[66]  Bekenstein, J.D. (2003) Information in the Holographic Universe. Scientific American, 289, 58-65.
http://dx.doi.org/10.1038/scientificamerican0803-58
[67]  Turing, A.M. (1950) I.—Computing Machinery and Intelligence. Mind, LIX, 433-460.
http://dx.doi.org/10.1093/mind/LIX.236.433
[68]  Shannon, C.E. (1948) A Mathematical Theory of Communication. The Bell System Technical Journal, 27, 379-423.
http://dx.doi.org/10.1002/j.1538-7305.1948.tb01338.x
[69]  Shannon, C.E. (1948) A Mathematical Theory of Communication. The Bell System Technical Journal, 27, 623-656.
http://dx.doi.org/10.1002/j.1538-7305.1948.tb00917.x
[70]  Von Neumann, J. (1996) Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton.
[71]  Jaynes, E.T. (1957) Information Theory and Statistical Mechanics. Physical Review, 106, 620-630.
http://dx.doi.org/10.1103/PhysRev.106.620
[72]  Landauer, R. (1961) Irreversibility and Heat Generation in the Computing Process. IBM Journal of Research and Development, 5, 183-191.
http://dx.doi.org/10.1147/rd.53.0183
[73]  Zuse, K. (1993) The Computer—My Life. Springer Verlag, New York.
http://dx.doi.org/10.1007/978-3-662-02931-2
[74]  Bekenstein, J.D. (2005) How Does the Entropy/Information Bound Work? Foundations of Physics, 35, 1805-1823.
http://dx.doi.org/10.1007/s10701-005-7350-7
[75]  Blume-Kohout, R. and Zurek, W.H. (2005) A Simple Example of “Quantum Darwinism”: Redundant Information Storage in Many-Spin Environments. Foundations of Physics, 35, 1857-1876.
http://dx.doi.org/10.1007/s10701-005-7352-5
[76]  Deutsch, D. (1997) The Fabric of Reality: The Science of Parallel Universes—and Its Implications. Penguin Books, Penguin.
[77]  Deutsch, D. (2013) Constructor Theory. Synthese, 190, 4331-4359.
http://dx.doi.org/10.1007/s11229-013-0279-z
[78]  Esposito, M., Harbola, U. and Mukamel, S. (2009) Nonequilibrium Fluctuations, Fluctuation Theorems, and Counting Statistics in Quantum Systems. Reviews of Modern Physics, 81, 1665.
http://dx.doi.org/10.1103/RevModPhys.81.1665
[79]  Fredkin, E. (1990) An Informational Process Based on Reversible Universal Cellular Automata. Physica D: Nonlinear Phenomena, 45, 254-270.
http://dx.doi.org/10.1016/0167-2789(90)90186-S
[80]  Fredkin, E. (2003) An Introduction to Digital Philosophy. International Journal of Theoretical Physics, 42, 189-247.
http://dx.doi.org/10.1023/A:1024443232206
[81]  Freedman, M.H., Larsen, M. and Wang, Z. (2002) A Modular Functor Which Is Universal for Quantum Computation. Communications in Mathematical Physics, 227, 605-622.
http://dx.doi.org/10.1007/s002200200645
[82]  Freedman, M., Kitaev, A., Larsen, M. and Wang, Z. (2003) Topological Quantum Computation. Bulletin of the American Mathematical Society, 40, 31-38.
http://dx.doi.org/10.1090/S0273-0979-02-00964-3
[83]  ‘t Hooft, G. (1999) Quantum Gravity as a Dissipative Deterministic System. Classical and Quantum Gravity, 16, 3263-3279.
http://dx.doi.org/10.1088/0264-9381/16/10/316
[84]  ‘t Hooft, G. (2014) The Cellular Automaton Interpretation of Quantum Mechanics. A View on the Quantum Nature of our Universe, Compulsory or Impossible? arXiv:1405.1548
[85]  Kitaev, A.Y. (2003) Fault-Tolerant Quantum Computation by Anyons. Annals of Physics, 303, 2-30.
http://dx.doi.org/10.1016/S0003-4916(02)00018-0
[86]  Kitaev, A. (2006) Anyons in an Exactly Solved Model and Beyond. Annals of Physics, 321, 2-111.
http://dx.doi.org/10.1016/j.aop.2005.10.005
[87]  Lloyd, S. (2012) The Universe as Quantum Computer. In: Zenil, H., Ed., A Computable Universe: Understanding and Exploring Nature as Computation, World Scientific Publishing, 567-581. http://dx.doi.org/10.1142/9789814374309_0029
[88]  Mandal, D. and Jarzynski, C. (2012) Work and Information Processing in a Solvable Model of Maxwell’s Demon. Proceedings of the National Academy of Sciences of the United States of America, 109, 11641-11645.
http://dx.doi.org/10.1073/pnas.1204263109
[89]  Nayak, C., Simon, S.H., Stern, A., Freedman, M. and Das Sarma, S. (2008) Non-Abelian Anyons and Topological Quantum Computation. Reviews of Modern Physics, 80, 1083-1159. http://dx.doi.org/10.1103/RevModPhys.80.1083
[90]  Ogburn, R.W. and Preskill, J. (1999) Topological Quantum Computation. In: Williams, C.P., Ed., Quantum Computing and Quantum Communications, Springer, Berlin Heidelberg.
[91]  Pekola, J.P. (2015) Towards Quantum Thermodynamics in Electronic Circuits. Nature Physics, 11, 118-123.
http://dx.doi.org/10.1038/nphys3169
[92]  Sagawa, T. and Ueda, M. (2008) Second Law of Thermodynamics with Discrete Quantum Feedback Control. Physical Review Letters, 100, Article ID: 080403.
http://dx.doi.org/10.1103/PhysRevLett.100.080403
[93]  Sau, J.D., Lutchyn, R.M., Tewari, S. and Das Sarma, S. (2010) Generic New Platform for Topological Quantum Computation Using Semiconductor Heterostructures. Physical Review Letters, 104, Article ID: 040502.
http://dx.doi.org/10.1103/PhysRevLett.104.040502
[94]  Schmidhuber, J. (2000) Algorithmic Theories of Everything. arXiv:quant-ph/0011122
[95]  Toyabe, S., Sagawa, T., Ueda, M., Muneyuki, E. and Sano, M. (2010) Experimental Demonstration of Information-to-Energy Conversion and Validation of the Generalized Jarzynski Equality. Nature Physics, 6, 988-992.
http://dx.doi.org/10.1038/nphys1821
[96]  Wang, Z. (2010) Topological Quantum Computation. CBMS Regional Conference Series in Mathematics.
[97]  von Weizsäcker, C.F., Görnitz, T. and Lyre, H. (2006) The Structure of Physics. Springer, The Netherlands.
[98]  Wheeler, J.A. (1990) Information, Physics, Quantum: The Search for Links. The Proceedings of the 1988 Workshop on Complexity, Entropy, and the Physics of Information, May-June 1989, Westview Press, Santa Fe, New Mexico, Boulder, CO, USA.
[99]  Wolfram, S. (2002) A New Kind of Science. Wolfram Media, Champaign.
[100]  Zenil, H. (2013) A Computable Universe: Understanding and Exploring Nature as Computation. World Scientific, Hackensack, New Jersey.
[101]  Zizzi, P.A. (2006) Space-Time at the Planck Scale: The Quantum Computer View. In: Garola, C., Rossi, A. and Sozzo, S., Eds., The Foundations of Quantum Mechanics, World Scientific Publishing, 345-358.
http://dx.doi.org/10.1142/9789812773258_0030
[102]  Zurek, W.H. (2007) Relative States and the Environment: Einselection, Envariance, Quantum Darwinism, and the Existential Interpretation. Arxiv:0707.2832.
[103]  Barbour, J.B. (1974) Relative-Distance Machian Theories. Nature, 249, 328-329.
http://dx.doi.org/10.1038/249328a0
[104]  Barbour, J. (2003) Scale-Invariant Gravity: Particle Dynamics. Classical and Quantum Gravity, 20, 1543-1570.
http://dx.doi.org/10.1088/0264-9381/20/8/310
[105]  Barbour, J.B. and Bertotti, B. (1982) Mach’s Principle and the Structure of Dynamical Theories. Proceedings of the Royal Society A: Mathematical and Physical Sciences, 382, 295-306.
http://dx.doi.org/10.1098/rspa.1982.0102
[106]  Gryb, S. (2009) Implementing Mach’s Principle Using Gauge Theory. Physical Review D, 80, Article ID: 024018.
http://dx.doi.org/10.1103/PhysRevD.80.024018
[107]  Gomes, H., Gryb, S. and Koslowski, T. (2011) Einstein Gravity as a 3D Conformally Invariant Theory. Classical and Quantum Gravity, 28, Article ID: 045005.
http://dx.doi.org/10.1088/0264-9381/28/4/045005
[108]  Barbour, J., Koslowski, T. and Mercati, F. (2014) Identification of a Gravitational Arrow of Time. Physical Review Letters, 113, Article ID: 181101.
http://dx.doi.org/10.1103/PhysRevLett.113.181101
[109]  Carlip, S. (1998) Quantum Gravity in 2 + 1 Dimensions. Cambridge University Press, Cambridge.
[110]  Thomson, W. and Kelvin, L. (1867) On Vortex Atoms. Proceedings of the Royal Society of Edinburgh, VI, 94-105. (Reprinted in Philosophical Magazine, XXXIV, 15-24)
[111]  Arias, K.I., Zysman-Colman, E., Loren, J.C., Linden, A. and Siegel, J.S. (2011) Synthesis of a D3-Symmetric “Trefoil” Knotted Cyclophane. Chemical Communications, 47, 9588-9590.
http://dx.doi.org/10.1039/c1cc11209k
[112]  Atiyah, M. (1995) Quantum Physics and the Topology of Knots. Reviews of Modern Physics, 67, 977-981.
http://dx.doi.org/10.1103/RevModPhys.67.977
[113]  Berry, M. (2001) Knotted Zeros in the Quantum States of Hydrogen. Foundations of Physics, 31, 659-667. http://dx.doi.org/10.1023/A:1017521126923
[114]  Bilson-Thompson, S., Hackett, J. and Kauffman, L.H. (2009) Particle Topology, Braids, and Braided Belts. Journal of Mathematical Physics, 50, Article ID: 113505.
http://dx.doi.org/10.1063/1.3237148
[115]  Bonesteel, N.E., Hormozi, L., Zikos, G. and Simon, S.H. (2005) Braid Topologies for Quantum Computation. Physical Review Letters, 95, Article ID: 140503.
http://dx.doi.org/10.1103/PhysRevLett.95.140503
[116]  Dennis, M.R., King, R.P., Jack, B., O’Holleran, K. and Padgett, M.J. (2010) Isolated Optical Vortex Knots. Nature Physics, 6, 118-121.
http://dx.doi.org/10.1038/nphys1504
[117]  Dimofte, T. (2013) Quantum Riemann Surfaces in Chern-Simons Theory. Advances in Theoretical and Mathematical Physics, 17, 479-599.
http://dx.doi.org/10.4310/ATMP.2013.v17.n3.a1
[118]  Evans, M.E., Robins, V. and Hyde, S.T. (2015) Ideal Geometry of Periodic Entanglements. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 471, Article ID: 20150254.
http://dx.doi.org/10.1098/rspa.2015.0254
[119]  Faddeev, L. and Niemi, A.J. (1997) Stable Knot-Like Structures in Classical Field Theory. Nature, 387, 58-61.
http://dx.doi.org/10.1038/387058a0
[120]  Faddeev, L. and Niemi, A.J. (1999) Partially Dual Variables in SU(2) Yang-Mills Theory. Physical Review Letters, 82, 1624-1627.
http://dx.doi.org/10.1103/PhysRevLett.82.1624
[121]  Finkelstein, R.J. (2013) The Preon Sector of the SLq(2) Model and the Binding Problem. International Journal of Modern Physics A, 29, Article ID: 1450092.
http://dx.doi.org/10.1142/S0217751X14500924
[122]  Finkelstein, R.J. (2015) The SLq(2) Extension of the Standard Model. International Journal of Modern Physics A, 30, Article ID: 1530037.
http://dx.doi.org/10.1142/S0217751X15300379
[123]  Finkelstein, R.J. and Cadavid, A.C. (2006) Masses and Interactions of q-Fermionic Knots. International Journal of Modern Physics A, 21, 4269-4302.
http://dx.doi.org/10.1142/S0217751X06032496
[124]  Gambini, R., Lewandowski, J., Marolf, D. and Pullin, J. (1998) On the Consistency of the Constraint Algebra in Spin Network Quantum Gravity. International Journal of Modern Physics D, 7, 97-109.
http://dx.doi.org/10.1142/S0218271898000103
[125]  Garnerone, S., Marzuoli, A. and Rasetti, M. (2006) Quantum Knitting. Laser Physics, 16, 1582-1594. http://dx.doi.org/10.1134/S1054660X06110120
[126]  Garoufalidis, S., Morton, H. and Vuong, T. (2013) The SL3 Colored Jones Polynomial of the Trefoil. Proceedings of the American Mathematical Society, 141, 2209-2220.
http://dx.doi.org/10.1090/S0002-9939-2013-11582-0
[127]  Gelca, R. (2002) Non-Commutative Trigonometry and the A-Polynomial of the Trefoil Knot. Mathematical Proceedings of the Cambridge Philosophical Society, 133, 311-323.
[128]  Jehle, H. (1981) Topological Characterization of Leptons, Quarks and Hadrons. Physics Letters B, 104, 207-211.
http://dx.doi.org/10.1016/0370-2693(81)90592-X
[129]  Katritch, V., Bednar, J., Michoud, D., Scharein, R.G., Dubochet, J. and Stasiak, A. (1996) Geometry and Physics of Knots. Nature, 384, 142-145.
http://dx.doi.org/10.1038/384142a0
[130]  Kauffman, L.H. (2001) Knots and Physics. World Scientific, Singapore.
[131]  Kauffman, L.H. (2015) Rotational Virtual Knots and Quantum Link Invariants. Journal of Knot Theory and Its Ramifications, 24, Article ID: 1541008.
http://dx.doi.org/10.1142/S0218216515410084
[132]  Kauffman, L.H. (2015) Knot Logic: Logical Connection and Topological Connection. Arxiv:1508.06028
[133]  Kauffman, L.H. (2016) Knot Logic and Topological Quantum Computing with Majorana Fermions. In: Chubb, J., Eskandarian, A. and Harizanov, V., Eds., Logic and Algebraic Structures in Quantum Computing, Lecture Notes in Logic Vol. 45, Cambridge University Press, Cambridge, 223-336.
http://dx.doi.org/10.1017/CBO9781139519687.012
[134]  Kauffman, L.H. and Lomonaco Jr., S.J. (2002) Quantum Entanglement and Topological Entanglement. New Journal of Physics, 4, 73.
http://dx.doi.org/10.1088/1367-2630/4/1/373
[135]  Kauffman, L.H. and Lomonaco Jr., S.J. (2004) Braiding Operators are Universal Quantum Gates. New Journal of Physics, 6, 134.
http://dx.doi.org/10.1088/1367-2630/6/1/134
[136]  Kauffman, L.H. and Lomonaco Jr., S.J. (2004) Quantum Knots. Proceedings of SPIE 5436, Quantum Information and Computation II, 268.
http://dx.doi.org/10.1117/12.544072
[137]  Kleckner, D. and Irvine, W.T.M. (2013) Creation and Dynamics of Knotted Vortices. Nature Physics, 9, 253-258.
http://dx.doi.org/10.1038/nphys2560
[138]  Liu, X. and Ricca, R.L. (2016) Knots Cascade Detected by a Monotonically Decreasing Sequence of Values. Scientific Reports, 6, Article No. 24118.
http://dx.doi.org/10.1038/srep24118
[139]  Moffatt, H.K. (1996) Pulling the Knot Tight. Nature, 384, 114.
http://dx.doi.org/10.1038/384114a0
[140]  Pieranski, P. and Przybyl, S. (2001) Ideal Trefoil Knot. Physical Review E, 64, Article ID: 031801.
http://dx.doi.org/10.1103/PhysRevE.64.031801
[141]  Ponnuswamy, N., Cougnon, F.B., Clough, J.M., Pantos, G.D. and Sanders, J.K. (2012) Discovery of an Organic Trefoil Knot. Science, 338, 783-785.
http://dx.doi.org/10.1126/science.1227032
[142]  Ranada, A.F. (1990) Knotted Solutions of the Maxwell Equations in Vacuum. Journal of Physics A: Mathematical and General, 23, L815-L820.
http://dx.doi.org/10.1088/0305-4470/23/16/007
[143]  Sawin, S. (1996) Links, Quantum Groups and TQFTs. Bulletin of the American Mathematical Society, 33, 413-446.
[144]  Stasiak, A., Dubochet, J., Katritch, V. and Pieranski, P. (1998) Ideal Knots and Their Relation to the Physics of Real Knots. In: Kauffman, L.H., Ed., Series on Knots and Everything, Vol. 19, World Scientific Publishing, 1-19.
http://dx.doi.org/10.1142/9789812796073_0001
[145]  Tempone-Wiltshire, S.J., Johnstone, S.P. and Helmerson, K. (2016) Optical Vortex Knots— One Photon at a Time. Scientific Reports, 6, Article No. 24463.
http://dx.doi.org/10.1038/srep24463
[146]  Thompson, A., Swearngin, J. and Bouwmeester, D. (2014) Linked and Knotted Gravitational Radiation. Journal of Physics A: Mathematical and Theoretical, 47, Article ID: 355205.
http://dx.doi.org/10.1088/1751-8113/47/35/355205
[147]  Was, Z. (1998) Trefoil Knot and Ad-Hoc Classification of Elementary Fields in the Standard Model. Physics Letters B, 416, 369-372.
http://dx.doi.org/10.1016/S0370-2693(97)01346-4
[148]  Weisstein, E.W. (2016) Trefoil Knot. From Mathworld—A Wolfram Web Resource.
http://mathworld.wolfram.com/TrefoilKnot.html
[149]  Simon, S. (2010) Quantum Computing with a Twist. Physics World, 23, 35-40.
http://dx.doi.org/10.1088/2058-7058/23/09/37
[150]  Lyons, R.E. and Vanderkulk, W. (1962) The Use of Triple-Modular Redundancy to Improve Computer Reliability. IBM Journal of Research and Development, 6, 200-209.
http://dx.doi.org/10.1147/rd.62.0200
[151]  Griffiths, R.B. (2007) Types of Quantum Information. Physical Review A, 76, Article ID: 062320.
http://dx.doi.org/10.1103/PhysRevA.76.062320
[152]  Perez, J., Füzfa, A., Carletti, T., Mélot, L. and Guedezounme, L. (2014) The Jungle Universe: Coupled Cosmological Models in a Lotka-Volterra Framework. General Relativity and Gravitation, 46, 1753.
http://dx.doi.org/10.1007/s10714-014-1753-8
[153]  Leach, J., Dennis, M.R., Courtial, J. and Padgett, M.J. (2005) Vortex Knots in Light. New Journal of Physics, 7, 55.
http://dx.doi.org/10.1088/1367-2630/7/1/055
[154]  Caves, C.M. and Milburn, G.J. (2000) Qutrit Entanglement. Optics Communications, 179, 439-446.
http://dx.doi.org/10.1016/S0030-4018(99)00693-8
[155]  McConnell, R., Zhang, H., Hu, J., Cuk, S. and Vuletic, V. (2015) Entanglement with Negative Wigner Function of Almost 3,000 Atoms Heralded by One Photon. Nature, 519, 439-442.
http://dx.doi.org/10.1038/nature14293
[156]  Turing, A.M. (1937) On Computable Numbers, with an Application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, s2-42, 230-265.
http://dx.doi.org/10.1112/plms/s2-42.1.230
[157]  Dyson, G. (2012) Turing Centenary: The Dawn of Computing. Nature, 482, 459-460.
http://dx.doi.org/10.1038/482459a
[158]  Aleksandrova, A., Borish, V. and Wootters, W.K. (2013) Real-Vector-Space Quantum Theory with a Universal Quantum Bit. Physical Review A, 87, Article ID: 052106.
http://dx.doi.org/10.1103/PhysRevA.87.052106
[159]  Garcia-Morales, V. (2015) Quantum Mechanics and the Principle of Least Radix Economy. Foundations of Physics, 45, 295-332.
http://dx.doi.org/10.1007/s10701-015-9865-x
[160]  Khalidi, M.A. (2015) Natural Kinds as Nodes in Causal Networks. Synthese, 1-18.
http://dx.doi.org/10.1007/s11229-015-0841-y
[161]  Orús, R. (2014) A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States. Annals of Physics, 349, 117-158.
http://dx.doi.org/10.1016/j.aop.2014.06.013
[162]  Goyal, S.K., Simon, B.N., Singh, R. and Simon, S. (2011) Geometry of the Generalized Bloch Sphere for Qutrit. arXiv:1111.4427
[163]  Klimov, A.B., Guzmán, R., Retamal, J.C. and Saavedra, C. (2003) Qutrit Quantum Computer with Trapped Ions. Physical Review A, 67, Article ID: 062313.
http://dx.doi.org/10.1103/PhysRevA.67.062313
[164]  Li, B., Yu, Z.H. and Fei, S.M. (2013) Geometry of Quantum Computation with Qutrits. Scientific Reports, 3, Article No. 2594.
http://dx.doi.org/10.1038/srep02594
[165]  Sarbicki, G. and Bengtsson, I. (2012) Dissecting the Qutrit. Journal of Physics A: Mathematical and Theoretical, 46, Article ID: 035306.
http://dx.doi.org/10.1088/1751-8113/46/3/035306
[166]  Pusey, M.F., Barrett, J. and Rudolph, T. (2012) On the Reality of the Quantum State. Nature Physics, 8, 475-478.
http://dx.doi.org/10.1038/nphys2309
[167]  Colbeck, R. and Renner, R. (2012) Is a System’s Wave Function in One-to-One Correspondence with Its Elements of Reality? Physical Review Letters, 108, Article ID: 150402.
http://dx.doi.org/10.1103/PhysRevLett.108.150402
[168]  Hardy, L. (2013) Are Quantum States Real? International Journal of Modern Physics B, 27, Article ID: 1345012.
http://dx.doi.org/10.1142/S0217979213450124
[169]  Patra, M.K., Pironio, S. and Massar, S. (2013) No-Go Theorems for Psi-Epistemic Models Based on a Continuity Assumption. Physical Review Letters, 111, Article ID: 090402.
http://dx.doi.org/10.1103/PhysRevLett.111.090402
[170]  Leifer, M.S. (2014) Is the Quantum State Real? An Extended Review of Ψ-Ontology Theorems. Quanta, 3, 67-155.
http://dx.doi.org/10.12743/quanta.v3i1.22
[171]  Gao, S. (2015) An Argument for Ψ-Ontology in Terms of Protective Measurements. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 52, 198-202.
http://dx.doi.org/10.1016/j.shpsb.2015.07.006

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133