Skip to main content
SpringerLink
Log in

Gaussian quantum computation with oracle-decision problems

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We study a simple-harmonic-oscillator quantum computer solving oracle decision problems. We show that such computers can perform better by using nonorthogonal Gaussian wave functions rather than orthogonal top-hat wave functions as input to the information encoding process. Using the Deutsch–Jozsa problem as an example, we demonstrate that Gaussian modulation with optimized width parameter results in a lower error rate than for the top-hat encoding. We conclude that Gaussian modulation can allow for an improved trade-off between encoding, processing and measurement of the information.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cormen T.H., Leiserson C.E., Rivest R.L., Stein C.: Introduction to Algorithms. McGraw-Hill, Cambridge, MA (2001)

    MATH  Google Scholar 

  2. Sipser M.: Introduction to the Theory of Computation. PWS Publishing Company, Boston, MA (1997)

    MATH  Google Scholar 

  3. Jackson A.S.: Analog Computation. McGraw-Hill, New York, NY (1974)

    Google Scholar 

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

    MATH  Google Scholar 

  5. Braunstein S.L., Pati A.K.: Quantum Information with Continuous Variables. Kluwer, Dordrecht, NL (2003)

    Book  MATH  Google Scholar 

  6. Gottesman D., Kitaev A., Preskill J.: Encoding a qubit in an oscillator. Phys. Rev. A 64, 012310 (2001). doi:10.1103/PhysRevA.64.012310

    Article  ADS  Google Scholar 

  7. Deutsch D.: Quantum theory, the Church-Turing principle and the universal quantum compute. Proc. R. Soc. Lond. A 400, 97–117 (1985). doi:10.1098/rspa.1985.0070

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Deutsch D., Jozsa R.: Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553–558 (1992). doi:10.1098/rspa.1992.0167

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Adcock M.R.A., Høyer P., Sanders B.C.: Limitations on continuous variable quantum algorithms with Fourier transforms. New J. Phys. 11, 103035 (2009). doi:10.1088/1367-2630/11/10/103035

    Article  ADS  Google Scholar 

  10. Furusawa A., Sørensen J.L., Braunstein S.L., Fuchs C.A., Kimble H.J., Polzik E.S.: Unconditional quantum teleportation. Science 282, 706–709 (1998). doi:10.1126/science.282.5389.706

    Article  ADS  Google Scholar 

  11. Grosshans F., Grangier P.: Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88, 057902 (2002). doi:10.1103/PhysRevLett.88.057902

    Article  ADS  Google Scholar 

  12. Appel J., Figueroa E., Korystov D., Lobino M., Lvovsky A.I.: Quantum memory for squeezed light. Phys. Rev. Lett. 100, 093602 (2008). doi:10.1103/PhysRevLett.100.093602

    Article  ADS  Google Scholar 

  13. Akamatsu D., Yokoi Y., Arikawa M., Nagatsuka S., Tanimura T., Furusawa A., Kozuma M.: Ultraslow propagation of squeezed vacuum pulses with electromagnetically induced transparency. Phys. Rev. Lett. 99, 153602 (2007). doi:10.1103/PhysRevLett.99.153602

    Article  ADS  Google Scholar 

  14. Braunstein S.L.: Error correction for continuous quantum variables. Phys. Rev. Lett. 80, 4084–4087 (1998). doi:10.1103/PhysRevLett.80.4084

    Article  ADS  Google Scholar 

  15. Eisert J., Plenio M.B., Scheel S.: Distilling Gaussian states with Gaussian operations is impossible. Phys. Rev. Lett. 89, 137903 (2002). doi:10.1103/PhysRevLett.89.137903

    Article  MathSciNet  ADS  Google Scholar 

  16. Bartlett S.D., Sanders B.C., Braunstein S.L., Nemoto K.: Efficient classical simulation of continuous variable quantum information processes. Phys. Rev. Lett. 88, 09704 (2002). doi:10.1103/PhysRevLett.88.097904

    Article  Google Scholar 

  17. Bartlett S.D., Sanders B.C.: Efficient classical simulation of optical quantum information circuits. Phys. Rev. Lett. 89, 207903 (2002). doi:10.1103/PhysRevLett.89.207903

    Article  ADS  Google Scholar 

  18. Cerf, N., Høyer, P., Magnin, L., Sanders, B.C.: Quantum algorithms with continuous variables for black box problems. In: 3rd international workshop on physics and computation (P&C 2010) conference proceedings. Available at http://www.pc2010.uac.pt/ (2010)

  19. Leonhardt U.: Measuring the Quantum State of Light. Cambridge University Press, Cambridge UK (1997)

    Google Scholar 

  20. Zwierz M., Pérez-Delgado C.A., Kok P.: Unifying parameter estimation and the Deutsch–Jozsa algorithm for continuous variables. Phys. Rev. A 82, 042320 (2010). doi:10.1103/PhysRevA.82.042320

    Article  ADS  Google Scholar 

  21. Cleve R., Ekert A., Macchiavello C., Mosca M.: Quantum algorithms revisited. Proc. R. Soc. Lond. A 454, 339–354 (1998). doi:10.1098/rspa.1998.0164

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. Adcock, M.R.A., Høyer, P., Sanders, B.C.: Quantum computation with coherent spin states and the close Hadamard problem. Available at http://arxiv.org/abs/1112.1446 (2011)

  23. Arrechi F.T., Courtens E., Gilmore R., Thomas H.: Atomic coherent states in quantum optics. Phys. Rev. A 6, 2211–2237 (1972). doi:10.1103/PhysRevA.6.2211

    Article  ADS  Google Scholar 

  24. Perelomov A.: Generalized Coherent States and their Applications. Springer, New York, NY (1972)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Quantum Information Science, University of Calgary, Calgary, AB, T2N 1N4, Canada

    Mark R. A. Adcock, Peter Høyer & Barry C. Sanders

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., Calgary, AB, T2N 1N4, Canada

    Peter Høyer

Authors
  1. Mark R. A. Adcock
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Høyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Barry C. Sanders
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mark R. A. Adcock.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Adcock, M.R.A., Høyer, P. & Sanders, B.C. Gaussian quantum computation with oracle-decision problems. Quantum Inf Process 12, 1759–1779 (2013). https://doi.org/10.1007/s11128-012-0489-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-012-0489-1

Keywords

Search

Navigation