Skip to main content
Springer Nature Link
Log in

Towards a Quantum Game of Life

  • Chapter
Game of Life Cellular Automata

  • 4871 Accesses

Abstract

Cellular automata provide a means of obtaining complex behaviour from a simple array of cells and a deterministic transition function. They supply a method of computation that dispenses with the need for manipulation of individual cells and they are computationally universal. Classical cellular automata have proved of great interest to computer scientists but the construction of quantum cellular automata pose particular difficulties. We present a version of John Conway’s famous two-dimensional classical cellular automata Life that has some quantum-like features, including interference effects. Some basic structures in the new automata are given and comparisons are made with Conway’s game.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Amoroso, S., Patt, Y.N.: Decision procedures for surjectivity and injectivity of parallel maps for tessellation structures. J. Comput. Syst. Sci. 6, 448–464 (1972)

    MATH  MathSciNet  Google Scholar 

  2. Auon, B., Tarifi, M.: Introduction to quantum cellular automata. Eprint: arXiv:quant-ph/0401123 (2004)

  3. Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, J., Smolin J., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995)

    Article  Google Scholar 

  4. Bell, J.S.: On the Einstein–Podolsky–Rosen paradox. Physics 1, 195–200 (1964)

    Google Scholar 

  5. Benjamin, S.C.: Schemes for parallel quantum computation without local control of qubits. Phys. Rev. A 61, 020301 (2000)

    Article  Google Scholar 

  6. Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays, vol. 2. Academic Press, London (1982)

    MATH  Google Scholar 

  7. Dumke, R., Volk, M., Muether, T., Buchkremer, F.B.J., Birkl, G., Ertmer, W.: Microoptical realization of arrays of selectively addressable dipole traps: a scalable configuration for quantum computation with atomic qubits. Phys. Rev. Lett. 89, 097903 (2002)

    Article  Google Scholar 

  8. Dürr, C., Santha, M.: A decision procedure for well-formed unitary linear quantum cellular automata. SIAM J. Comput. 31, 1076–1089 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)

    Article  MATH  Google Scholar 

  10. Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982)

    Article  MathSciNet  Google Scholar 

  11. Gardner, M.: Mathematical games: The fantastic combinations of John Conway’s new solitaire game of “Life”. Sci. Am. 223(10), 120 (1970)

    Article  Google Scholar 

  12. Gardner, M.: Mathematical games: On cellular automata, self-reproduction, the Garden of Eden and the game of “Life”. Sci. Am. 224(2), 116 (1971)

    Google Scholar 

  13. Gardner, M.: Wheels, Life and Other Mathematical Amusements. Freeman, New York (1983)

    MATH  Google Scholar 

  14. Grössing, G., Zeilinger, A.: Quantum cellular automata. Complex Syst. 2, 197–208 (1988)

    MATH  Google Scholar 

  15. Grössing, G., Zeilinger, A.: Structures in quantum cellular automata. Physica B 151, 366–370 (1988)

    Article  MathSciNet  Google Scholar 

  16. Gruska, J.: Quantum Computing. McGraw Hill, Maidenhead (1999)

    Google Scholar 

  17. Kari, J.: Reversibility of two-dimensional cellular automata is undecidable. Physica D 45, 379–385 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  18. Kempe, J.: Quantum random walks: an introductory overview. Contemp. Phys. 44, 307–327 (2003)

    Article  Google Scholar 

  19. Konno, N.: Quantum Walks and Quantum Cellular Automata. Lecture Notes in Computer Science. Springer, Berlin/Heidelberg (2008)

    Google Scholar 

  20. Konno, N., Mistuda, K., Soshi, T., Yoo, H.J.: Quantum walks and reversible cellular automata. Phys. Lett. A 330, 408–417 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  21. Lloyd, S.: Obituary: Rolf Laundauer. Nature 400, 720 (1999)

    Article  Google Scholar 

  22. Mandel, D., Greiner, M., Widera, A., Rom, T., Hänsch, T.W., Bloch, I.: Coherent transport of neutral atoms in spin-dependent optical lattice potentials. Phys. Rev. Lett. 91, 010407 (2003)

    Article  Google Scholar 

  23. Meyer, D.A.: From quantum cellular automata to quantum lattice gases. J. Stat. Phys. 85, 551–574 (1996)

    Article  MATH  Google Scholar 

  24. Morita, K.: Reversible simulation of one-dimensional irreversible cellular automata. Theor. Comput. Sci. 148, 157–163 (1995)

    Article  MATH  Google Scholar 

  25. Morita, K., Harao, M.: Computation universality of one-dimensional reversible (injective) cellular automata. Trans. IEICE 72, 758–762 (1989)

    Google Scholar 

  26. Nielsen, M.A., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  27. Schumacher, B., Werner, R.F.: Reversible quantum cellular automata. Eprint: arXiv:quant-ph/0405174 (2004)

  28. Silver, S.A.: http://www.bitstorm.org/gameoflife/lexicon

  29. Toffoli, T.: Cellular automata mechanics. PhD thesis, The University of Michigan (1977)

    Google Scholar 

  30. Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55, 601–644 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  31. Wolfram, S.: Mathematica: A System for Doing Mathematics by Computer. Addison–Wesley, Redwood City (1988)

    MATH  Google Scholar 

  32. Wolfram, S.: A New Kind of Science. Wolfram Media, Champaign (2002)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Physics, University of Melbourne, Parkville, 3010, Australia

    Adrian P. Flitney

Authors
  1. Adrian P. Flitney
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Derek Abbott
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adrian P. Flitney .

Editor information

Editors and Affiliations

  1. Fac. of Computing, Engineering and, Mathematical Sciences (CEMS), University of the West of England, Coldharbour Lane, Bristol, BS16 1QY, United Kingdom

    Andrew Adamatzky

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag London Limited

About this chapter

Cite this chapter

Flitney, A.P., Abbott, D. (2010). Towards a Quantum Game of Life. In: Adamatzky, A. (eds) Game of Life Cellular Automata. Springer, London. https://doi.org/10.1007/978-1-84996-217-9_23

Download citation

  • DOI: https://doi.org/10.1007/978-1-84996-217-9_23

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84996-216-2

  • Online ISBN: 978-1-84996-217-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics