The quantum query complexity of the hidden subgroup problem is polynomial

Information Processing Letters

Volumn 91, Issue 1, 2004, Pages 43-48

  Ettinger, Mark ^a   Høyer, Peter ^b   Knill, Emanuel ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF CALGARY   (Canada)

Author keywords

Algorithms; Hidden subgroups; Quantum computation; Query complexity

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; POLYNOMIALS; QUERY LANGUAGES; SET THEORY; THEOREM PROVING;

HIDDEN SUBGROUPS; QUANTUM COMPUTATION; QUANTUM COMPUTERS; QUERY COMPLEXITY;

DATA PROCESSING;

EID: 2642588230     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ipl.2004.01.024     Document Type: Article

References (13)

1. Simon D.R. On the power of quantum computation. SIAM J. Comput. 26:1997;1474-1483.
2. Shor P.W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26:1997;1484-1509.
3. Kitaev A.Y. Quantum computations: Algorithms and error correction. Russian Math. Surveys. 52:1997;1191-1249.
4. Brassard G., Høyer P. An exact quantum polynomial-time algorithm for Simon's problem. Proc. of the 5th Israeli Symposium on Theory of Computing Systems, Israel. 1997;12-23.
5. Ettinger M., Høyer P. On quantum algorithms for noncommutative hidden subgroups. Adv. Appl. Math. 25:2000;239-251.
6. Grigni M., Schulman L., Vazirani M., Vazirani U. Quantum mechanical algorithms for the nonabelian hidden subgroup problem. Proc. of the 33rd Annual ACM Symposium on the Theory of Computation. 2001;68-74 ACM Press, New York.
7. Hallgren S., Russell A., Ta-Shma A. Normal subgroup reconstruction and quantum computation using group representations. Proc. of the 32nd Annual ACM Symposium on the Theory of Computation. 2000;627-635 ACM Press, New York.
8. Ivanyos G., Magniez F., Santha M. Efficient quantum algorithms for some instances of the non-Abelian hidden subgroup problem. Proc. of the 13th ACM Symposium on Parallel Algorithms. 2001;263-270 ACM Press, New York.
9. Rötteler M., Beth T. Polynomial-time solution to the hidden subgroup problem for a class of non-Abelian groups. quant-ph/0112086. 2001.
10. Zalka C. On a particular non-Abelian hidden subgroup problem. http://qso.lanl.gov/~zalka/QC/QC.html. 1999.
11. Aaronson S. Quantum lower bound for the collision problem. Proc. of the 34th Annual ACM Symposium on the Theory of Computation (STOC). 2002;635-642 ACM Press, New York.
12. Shi Y. Quantum lower bounds for the collision and the element distinctness problems. Proc. of the 43rd Annual Symposium on the Foundations of Computer Science. 2002;513-519.
13. Brassard G., Høyer P., Mosca M., Tapp A. Quantum amplitude amplification and estimation. Lomonaco J.S.J., Brandt H.E. Quantum Computation and Quantum Information: A Millennium Volume. AMS Contemporary Mathematics Series. 2002;53-74 Amer. Math. Soc. Providence, RI.