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”.
Darwin, C. (1859) The Origin of Species. Murray, London.
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
Wiebe, N., Kapoor, A. and Svore, K.M. (2014) Quantum Deep Learning. Arxiv:1412.3489
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
Bäck, T., Fogel, D.B. and Michalewicz, Z. (1997) Handbook of Evolutionary Computation. Institute of Physics Pub., Bristol, UK.
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
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
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
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
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
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
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
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
Dawkins, R. (1983) Universal Darwinism. In: Bendall, D.S., Ed., Evolution from Molecules to Man, Cambridge University Press, New York.
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
Dobzhansky, T. (1949) Towards a Modern Synthesis. Evolution, 3, 376-377. http://dx.doi.org/10.2307/2405724
Eldredge, N. (1985) Unfinished Synthesis: Biological Hierarchies and Modern Evolutionary Thought. Oxford University Press, New York.
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
Fogel, D.B. (2006) Evolutionary Computation: Toward a New Philosophy of Machine Intelligence. John Wiley & Sons, Hoboken.
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
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
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
Hartshorne, R. (1977) Algebraic Geometry. In: Graduate Texts in Mathematics, Springer, Berkeley, California. http://dx.doi.org/10.1007/978-1-4757-3849-0
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
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
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
LeCun, Y., Bengio, Y. and Hinton, G. (2015) Deep Learning. Nature, 521, 436-444. http://dx.doi.org/10.1038/nature14539
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
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
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
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
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
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
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
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
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
Rickles, D. (2008) Quantum Gravity: A Primer for Philosophers. Ashgate, Aldershot.
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
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
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
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.
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
Smolin, L. (1997) The Life of the Cosmos. Oxford University Press, Oxford, USA.
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
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
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
Valiant, L. (2013) Probably Approximately Correct: Nature’s Algorithms for Learning and Prospering in a Complex World. Basic Books, New York.
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
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
Watson, R.A. (2012) Is Evolution by Natural Selection the Algorithm of Biological Evolution? Artificial Life, 13, 121-128.
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
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
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
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
Wheeler, J.A. (1968) Superspace and the Nature of Quantum Geometrodynamics. Topics in Nonlinear Physics, 615-724.
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
Zurek, W.H. (2003) Quantum Darwinism and Envariance. arXiv:quant-ph/0308163
Bousso, R. (2002) The Holographic Principle. Reviews of Modern Physics, 74, 825-874. http://dx.doi.org/10.1103/RevModPhys.74.825
‘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
Susskind, L. (1995) The World as a Hologram. Journal of Mathematical Physics, 36, 6377. http://dx.doi.org/10.1063/1.531249
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
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
Bekenstein, J.D. (2003) Information in the Holographic Universe. Scientific American, 289, 58-65. http://dx.doi.org/10.1038/scientificamerican0803-58
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
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
Von Neumann, J. (1996) Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton.
Jaynes, E.T. (1957) Information Theory and Statistical Mechanics. Physical Review, 106, 620-630. http://dx.doi.org/10.1103/PhysRev.106.620
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
Zuse, K. (1993) The Computer—My Life. Springer Verlag, New York. http://dx.doi.org/10.1007/978-3-662-02931-2
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
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
Deutsch, D. (1997) The Fabric of Reality: The Science of Parallel Universes—and Its Implications. Penguin Books, Penguin.
Deutsch, D. (2013) Constructor Theory. Synthese, 190, 4331-4359. http://dx.doi.org/10.1007/s11229-013-0279-z
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
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
Fredkin, E. (2003) An Introduction to Digital Philosophy. International Journal of Theoretical Physics, 42, 189-247. http://dx.doi.org/10.1023/A:1024443232206
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
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
‘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
‘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
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
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
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
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
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
Ogburn, R.W. and Preskill, J. (1999) Topological Quantum Computation. In: Williams, C.P., Ed., Quantum Computing and Quantum Communications, Springer, Berlin Heidelberg.
Pekola, J.P. (2015) Towards Quantum Thermodynamics in Electronic Circuits. Nature Physics, 11, 118-123. http://dx.doi.org/10.1038/nphys3169
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
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
Schmidhuber, J. (2000) Algorithmic Theories of Everything. arXiv:quant-ph/0011122
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
Wang, Z. (2010) Topological Quantum Computation. CBMS Regional Conference Series in Mathematics.
von Weizsäcker, C.F., Görnitz, T. and Lyre, H. (2006) The Structure of Physics. Springer, The Netherlands.
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.
Wolfram, S. (2002) A New Kind of Science. Wolfram Media, Champaign.
Zenil, H. (2013) A Computable Universe: Understanding and Exploring Nature as Computation. World Scientific, Hackensack, New Jersey.
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
Zurek, W.H. (2007) Relative States and the Environment: Einselection, Envariance, Quantum Darwinism, and the Existential Interpretation. Arxiv:0707.2832.
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
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
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
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
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
Carlip, S. (1998) Quantum Gravity in 2 + 1 Dimensions. Cambridge University Press, Cambridge.
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
Garnerone, S., Marzuoli, A. and Rasetti, M. (2006) Quantum Knitting. Laser Physics, 16, 1582-1594. http://dx.doi.org/10.1134/S1054660X06110120
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
Gelca, R. (2002) Non-Commutative Trigonometry and the A-Polynomial of the Trefoil Knot. Mathematical Proceedings of the Cambridge Philosophical Society, 133, 311-323.
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
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
Kauffman, L.H. (2001) Knots and Physics. World Scientific, Singapore.
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
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
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
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
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
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
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
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
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
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
Sawin, S. (1996) Links, Quantum Groups and TQFTs. Bulletin of the American Mathematical Society, 33, 413-446.
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
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
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
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
Weisstein, E.W. (2016) Trefoil Knot. From Mathworld—A Wolfram Web Resource. http://mathworld.wolfram.com/TrefoilKnot.html
Simon, S. (2010) Quantum Computing with a Twist. Physics World, 23, 35-40. http://dx.doi.org/10.1088/2058-7058/23/09/37
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
Griffiths, R.B. (2007) Types of Quantum Information. Physical Review A, 76, Article ID: 062320. http://dx.doi.org/10.1103/PhysRevA.76.062320
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
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
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
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
Dyson, G. (2012) Turing Centenary: The Dawn of Computing. Nature, 482, 459-460. http://dx.doi.org/10.1038/482459a
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
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
Khalidi, M.A. (2015) Natural Kinds as Nodes in Causal Networks. Synthese, 1-18. http://dx.doi.org/10.1007/s11229-015-0841-y
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
Goyal, S.K., Simon, B.N., Singh, R. and Simon, S. (2011) Geometry of the Generalized Bloch Sphere for Qutrit. arXiv:1111.4427
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
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
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
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
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
Hardy, L. (2013) Are Quantum States Real? International Journal of Modern Physics B, 27, Article ID: 1345012. http://dx.doi.org/10.1142/S0217979213450124
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
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
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