Skip to main content
SpringerLink
Log in
Book cover

NASA International Conference on Quantum Computing and Quantum Communications

QCQC 1998: Quantum Computing and Quantum Communications pp 34–60Cite as

Quantum Computation of Fluid Dynamics

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1509))

Abstract

Presented is a quantum lattice gas for Navier-Stokes fluid dynamics simulation. The quantum lattice-gas transport equation at the microscopic scale is presented as a generalization of the classical lattice-gas transport equation. A special type of quantum computer network is proposed that is suitable for implementing the quantum lattice gas. The quantum computer network undergoes a partial collapse of the wave-function at every time step of the dynamical evolution. Each quantum computer in the network comprises only a few qubits, which are entangled for only a short time period. A Chapman-Enskog type analysis of the quantum computer network indicates that the total system of qubits behaves exactly like a viscous lattice-gas fluid at the macroscopic scale. Because of the quantum mechanical nature of the scattering process, superposition of outgoing collisional possibilities occurs. The quantum lattice gas obeys detail balance in its collisions and is therefore an unconditionally stable algorithm for fluid dynamics simulation.

This work is supported under Task No. 2304CP of the Air Force Office of Scientific Research, Mathematical and Computational Sciences Directorate.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Wolfram, S.: Cellular automaton fluids 1: Basic theory. J. of Stat. Phys., 45, No. 3/4 (1986) 471–526

    Article  MATH  MathSciNet  Google Scholar 

  2. Frisch, U., Hasslacher, B., Pomeau, Y.: Lattice-gas automata for the navier-stokes equation. Phys. Rev. Lett., 56, No. 14 (1986) 1505–1508

    Article  Google Scholar 

  3. Yepez, J.: Lattice-gas quantum computation. Inter. J. Theor. Phys, To appear, (1998) Proceeding of the 7th International Conference on the Discrete Simulation of Fluids, University of Oxford.

    Google Scholar 

  4. Feynman, R. P.: Simulating physics with computers. Inter. J. Theor. Phys., 21, No. 6/7 (1982) 467–488

    Article  MathSciNet  Google Scholar 

  5. Benioff, P.: Quantum mechanical hamiltonian models of turing machines. J. of Stat. Phys., 29, No. 3 (1982) 515–547

    Article  MATH  MathSciNet  Google Scholar 

  6. Deutsch, D.: Quantum theory, the church-turing principle and the universal quantum computer. Proc. Roy. Soc., London, A400 (1985) 97

    MathSciNet  Google Scholar 

  7. Margolus, M.: Quantum computation. In Daniel Greenberger, editor, New Techniques and Ideas in Quantum Measurement Theory, Annals of the New York Academy 480 (1985) 487–497

    Google Scholar 

  8. Bennett, C. H.: Quantum information and computation. Physics Today, Oct (1995) 24–30

    Google Scholar 

  9. Hey, A.J.G., Allen, R.W., editors: Feynman Lectures on Computation. The Advanced Book Program. Addison-Wesley Publishing Company, Inc. (1996)

    Google Scholar 

  10. Cory, D.G., Fahmy, A.F., Havel, T.F.: Ensemble quantum computing by nuclear magnetic resonance spectroscopy. Harvard Univ. Center for Research in Comp. Tech., Aiken Comp. Lab., Tech Rep TR-10-96 (1996)

    Google Scholar 

  11. Calderbank, A.R., Shor. P.W.: Good quantum error correcting codes exist. LANL archive: quant-ph/9512032 (1995)

    Google Scholar 

  12. Seth Lloyd.: Quantum-mechanical computers. Physics Today, Oct (1995) 140–145

    Google Scholar 

  13. Ekert, A., Jozsa, R.: Quantum computation and shor’s factoring algorithm. Rev. of Mod. Phys., 68, No. 3 (1996) 733–753

    Article  MathSciNet  Google Scholar 

  14. Fredkin, E., Toffoli, T.: Conservative logic. Inter. J. Theor. Phys., 21, No. 3/4 (1982) 219–253

    Article  MATH  MathSciNet  Google Scholar 

  15. Bennett, C.H.: Logical reversibility of computation. IBM J. Res. Dev., 6 (1979) 525–532

    Google Scholar 

  16. Bennett, C.H.: Thermodynamics of computation —a review. Inter. J. of Theor. Phys., 21 (1982) 219–253

    Article  Google Scholar 

  17. Sauro Succi.: Lattice boltzmann equation for quantum mechanics. Physica D, 69 (1993) 327–332

    Article  MATH  MathSciNet  Google Scholar 

  18. Boghosian, B.M., Taylor, W.: A quantum lattice-gas model for the many-particle schrodinger equation in d-dimensions. Phys. Rev. E, 57, No. 1 (1998) 54–66

    Article  MathSciNet  Google Scholar 

  19. Yepez, J.: Lattice gas for superfluid helium ii. Inter. J. Theor. Phys. Accepted 1996. To Appear (1998). Presented at 6th Inter. Conf. on Discrete Models for Fluid Mech., Boston Univ. Center for Comp. Sci, Aug 1996.

    Google Scholar 

  20. Hénon, M.: Viscosity of a lattice gas. In Gary D. Doolean, editor, Lattice Gas Methods for Partial Differential Equations, Santa Fe Institute, Addison-Wesley Publishing Company (1990) 179–207

    Google Scholar 

  21. Frisch, U., d’Humiéres, D., Hasslacher, B., Lallemand, P., Pomeau, Y., Rivet, J.P.: Lattice gas hydrodynamics in two and three dimensions. Comp. Sys., 1 (1987) 649–707

    MATH  Google Scholar 

  22. Yepez, J.: Lattice gas dynamics: Volume 1 viscous fluids. Technical Report PL-TR-96-2122(I), Air Force Research Laboratory, AFRL/VSBE Hanscom AFB, MA, Nov (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Air Force Research Laboratory, Hanscom Field, MA 01731, USA

    Jeffrey Yepez

Authors
  1. Jeffrey Yepez
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Jet Propulsion Laboratory, California Institute of Technology Quantum Algorithms and Technologies Group Information and Computing Technologies Research Section, Mail Stop 126-347, Pasadena, CA, 91109-8099, USA

    Colin P. Williams

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yepez, J. (1999). Quantum Computation of Fluid Dynamics. In: Williams, C.P. (eds) Quantum Computing and Quantum Communications. QCQC 1998. Lecture Notes in Computer Science, vol 1509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49208-9_3

Download citation

  • DOI: https://doi.org/10.1007/3-540-49208-9_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65514-5

  • Online ISBN: 978-3-540-49208-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation