Quantum Information Processing

, Volume 14, Issue 6, pp 1777–1785 | Cite as

A different Deutsch–Jozsa

Article

Abstract

One of the early achievements of quantum computing was demonstrated by Deutsch and Jozsa (Proc R Soc Lond A Math Phys Sci 439(1907):553, 1992) regarding classification of a particular type of Boolean functions. Their solution demonstrated an exponential speedup compared to classical approaches to the same problem; however, their solution was the only known quantum algorithm for that specific problem so far. This paper demonstrates another quantum algorithm for the same problem, with the same exponential advantage compared to classical algorithms. The novelty of this algorithm is the use of quantum amplitude amplification, a technique that is the key component of another celebrated quantum algorithm developed by Grover (Proceedings of the twenty-eighth annual ACM symposium on theory of computing, ACM Press, New York, 1996). A lower bound for randomized (classical) algorithms is also presented which establishes a sound gap between the effectiveness of our quantum algorithm and that of any randomized algorithm with similar efficiency.

Keywords

Quantum algorithm Deutsch–Jozsa Amplitude amplification Lower bound Randomized algorithm 

References

  1. 1.
    Grover, L.K.: A fast quantum mechanical algorithm for database search. In:Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp.212–219. ACM Press, New York (1996). doi:10.1145/237814.237866
  2. 2.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484 (1997). doi:10.1137/S0097539795293172 CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Jordan, S.: Quantum Algorithm Zoo. http://math.nist.gov/quantum/zoo/
  4. 4.
    Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. A Math. Phys. Eng. Sci. 400(1818), 97 (1985). doi:10.1098/rspa.1985.0070 CrossRefADSMATHMathSciNetGoogle Scholar
  5. 5.
    Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. Proc. R. Soc. A Math. Phys. Eng. Sci. 439(1907), 553 (1992). doi:10.1098/rspa.1992.0167 CrossRefADSMATHMathSciNetGoogle Scholar
  6. 6.
    Brassard, G., Høyer, P.: An exact quantum polynomial-time algorithm for Simon’s problem. In: Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems. IEEE Computing Society (1997), pp. 12–23. doi:10.1109/ISTCS.1997.595153
  7. 7.
    Grover, L.: Quantum computers can search rapidly by using almost any transformation. Phys. Rev. Lett. 80(19), 4329 (1998). doi:10.1103/PhysRevLett.80.4329 CrossRefADSGoogle Scholar
  8. 8.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information (Cambridge Series on Information and the Natural Sciences), 1st edn. Cambridge University Press, (2004). doi:10.1017/CBO9780511976667
  9. 9.
    Cleve, R., Ekert, A., Macchiavello, C., Mosca, M.: Quantum algorithms revisited. Proc. R. Soc. A Math. Phys. Eng. Sci. 454(1969), 339 (1998). doi:10.1098/rspa.1998.0164 CrossRefADSMATHMathSciNetGoogle Scholar
  10. 10.
    Brassard, G., Hoyer, P., Mosca, M., Tapp, A.: Quantum amplitude amplification and estimation. In Quantum Computation and Quantum Information: A Millennium Volume, AMS Contemporary Mathematics Series, vol. 305. American Mathematical Society (2002) doi:10.1090/conm/305

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Indraprastha Institute of Information Technology (IIIT-D)New DelhiIndia

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