The Computing Spacetime

  • Fotini Markopoulou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)


The idea that the Universe is a program in a giant quantum computer is both fascinating and suffers from various problems. Nonetheless, it can provide a unified picture of physics and this is very useful for the problem of Quantum Gravity where such a unification is necessary. We give an introduction to the idea of the universe as a quantum computation, the problem of Quantum Gravity, and Quantum Graphity, a simple way to model a dynamical spacetime as a quantum computation.


Black Hole Quantum Gravity Cellular Automaton Cellular Automaton Hubbard Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Ashtekar, A., Lewandowski, J.: Background independent quantum gravity: A status report, Class. Quant. Grav. 21, R53 (2004)Google Scholar
  2. 2.
    Ashtekar, A., Stachel, J.: Conceptual Problems of Quantum Gravity. Springer (1991)Google Scholar
  3. 3.
    Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for your Mathematical Plays. AK Peters Ltd. (2001)Google Scholar
  4. 4.
    Bilson-Thompson, S.O., Markopoulou, F., Smolin, L.: Quantum Gravity and the Standard Model. Class. Quant. Grav. 24, 3975 (2005)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Brandenberger, R.: Inflationary Cosmology: Progress and Problems, hep-ph/9910410Google Scholar
  6. 6.
    Caravelli, F., Hamma, A., Markopoulou, F., Riera, A.: Trapped surfaces and emergent curved space in the Bose-Hubbard model. Phys. Rev. D, arxiv:1108 (to appear, 2013)Google Scholar
  7. 7.
    Carroll, S.: The Cosmological Constant, astro-ph/0004075Google Scholar
  8. 8.
    Dennett, D.C.: Consciousness explained. Back Bay Books, Boston (2001)Google Scholar
  9. 9.
    Deutsch, D.: Physics, Philosophy and Quantum Technology. In: Shapiro, J.H., Hirota, O. (eds.) The Sixth International Conference on Quantum Communication, Measurement and Computing. Rinton Press, Princeton (2003)Google Scholar
  10. 10.
    Eisert, J., Osborne, T.J.: General Entanglement Scaling Laws from Time Evolution. Phys. Rev. Lett. 97, 150404 (2006)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Hamma, A., Markopoulou, F., Premont-Schwarz, I., Severini, S.: Lieb-Robinson bounds and the speed of light from topological order. Phys. Rev. Lett. 102, 017204, arXiv:0808.2495v2 [quant-ph]Google Scholar
  12. 12.
    Hamma, A., Markopoulou, F., Lloyd, S., Caravelli, F., Severini, S., Markstrom, K.: A quantum Bose-Hubbard model with evolving graph as toy model for emergent spacetime. Phys. Rev. D 81, 104032 (2010)CrossRefGoogle Scholar
  13. 13.
    Hawkins, E., Markopoulou, F., Sahlmann, H.: Algebraic Causal Histories. Class. Q. Grav. 20, 3839 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Hossenfelder, S.: Experimental Search for Quantum Gravity, arxiv:1010.3420Google Scholar
  15. 15.
    Isham, C.J.: Prima Facie Questions in Quantum Gravity, gr-qc/9310031Google Scholar
  16. 16.
    Konopka, T., Markopoulou, F., Severini, S.: Quantum Graphity: a model of emergent locality. Phys. Rev. D 77, 104029 (2008)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Levin, M., Wen, X.G.: Fermions, strings, and gauge fields in lattice spin models. Phys. Rev. B 67, 245316 (2003)CrossRefGoogle Scholar
  18. 18.
    Levin, M.A., Wen, X.G.: String-net condensation: A physical mechanism for topological phases. Phys. Rev. B 71, 045110 (2005)CrossRefGoogle Scholar
  19. 19.
    Levin, M., Wen, X.G.: Quantum ether: Photons and electrons from a rotor model. arXiv:hep-th/0507118Google Scholar
  20. 20.
    Lieb, E.H., Robinson, D.W.: The finite group velocity of quantum spin systems. Commun. Math. Phys. 28, 251–257 (1972)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Lloyd, S.: Programming the Universe: A Quantum Computer Scientist Takes On the Cosmos, Knopf (2006)Google Scholar
  22. 22.
    Markopoulou, F.: Quantum Causal Histories. Class. Q. Grav. 17, 2059 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds in Quantum Many-Body Physics. In: Sims, R., Ueltschi, D. (eds.) Entropy and the Quantum. Contemporary Mathematics, vol. 529, pp. 141–176. American Mathematical Society (2010)Google Scholar
  24. 24.
    Prémont-Schwarz, I., Hamma, A., Klich, I., Markopoulou-Kalamara, F.: Lieb-Robinson bounds for commutator-bounded operators, arXiv:0912.4544v1 [quant-ph]Google Scholar
  25. 25.
    Rovelli, C.: Quantum Gravity. Cambridge U. Press, New York (2004)zbMATHCrossRefGoogle Scholar
  26. 26.
    Susskind, L.: The Black Hole War, Little, Brown (2008)Google Scholar
  27. 27.
    Tegmark, M.: The Multiverse Hierarchy, arxiv:0905.1283Google Scholar
  28. 28.
    Wald, R.M.: The thermodynamics of black holes, gr-qc/9912119Google Scholar
  29. 29.
    Wheeler, J.A., Ford, K.: Geons, black holes and quantum foam: a life in physics. W.W. Norton Company, Inc., New York (1998)zbMATHGoogle Scholar
  30. 30.
    Zuse, K.: Rechnender Raum. Elektronische Datenverarbeitung 8, 336–344 (1967)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Fotini Markopoulou
    • 1
  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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