Any AND-OR formula of size N can be evaluated in time N1/2+o(1) on a quantum computer

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2007, Pages 363-372

  Ambainis, Andris ^a,b   Childs, Andrew M ^b,c   Reichardt, Ben W ^c   Špalek, Robert ^d   Zhang, Shengyu ^c  

^a UNIVERSITY OF LATVIA   (Latvia)

^b UNIVERSITY OF WATERLOO   (Canada)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN FUNCTIONS; COMPUTER SCIENCE; FIBER OPTIC CHEMICAL SENSORS; OPERATING ROOMS;

FOUNDATIONS;

EID: 46749125783     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2007.4389507     Document Type: Conference Paper

References (20)

1. A. Ambainis. Polynomial degree vs. quantum query complexity. J. Comput. Syst. Sci., 72(2):220-238, 2006.
2. A. Ambainis. A nearly optimal discrete query quantum algorithm for evaluating NAND formulas, quant-ph/0704.3628, 2007.
3. H. Barnum and M. Saks. A lower bound on the quantum query complexity of read-once functions. J. Comput. Syst. Sci., 69(2):244-258, 2004.
4. R. Beals, H. Buhrman, R. Cleve, M. Mosca, and R. de Wolf. Quantum lower bounds by polynomials. J. ACM, 48(4):778-797, 2001.
5. M. L. Bonet and S. R. Buss. Size-depth tradeoffs for Boolean formulae. Information Processing Letters, 49(3):151-155, 1994.
6. N. H. Bshouty, R. Cleve, and W. Eberly. Size-depth tradeoffs for algebraic formulae. In Proc. of 32nd IEEE FOCS, pages 334-341, 1991.
7. H. Buhrman, R. Cleve, and A. Wigderson. Quantum vs. classical communication and computation. In Proc. of 30th ACM STOC, pages 63-68, 1998.
8. A. M. Childs, R. Cleve, S. P. Jordan, and D. Yeung. Discrete-query quantum algorithm for NAND trees, quant-ph/0702160, 2007.
9. 1/2+ε) on a quantum computer, quant-ph/0703015, 2007.
10. R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca. Quantum algorithms revisited. Proc. R. Soc. London A, 454(1969):339-354, 1998.
11. E. Farhi, J. Goldstone, and S. Gutmann. A quantum algorithm for the Hamiltonian NAND tree, quant-ph/0702144, 2007.
12. L. K. Grover. A fast quantum mechanical algorithm for database search. In Proc. of 28th ACM STOC, pages 212-219, 1996.
13. L. K. Grover. Tradeoffs in the quantum search algorithm. quant-ph/0201152, 2002.
14. P. Høyer, M. Mosca, and R. d. Wolf. Quantum search on bounded-error inputs. In Proc. of 30th ICALP, pages 291-299, 2003, LNCS 2719.
15. A. Y. Kitaev, A. H. Shen, and M. N. Vyalyi. Classical and Quantum Computation, volume 47 of Graduate Studies in Mathematics. American Mathematical Society, Providence, Rhode Island, 2002.
16. S. Laplante, T. Lee, and M. Szegedy. The quantum adversary method and classical formula size lower bounds. Computational Complexity, 15:163-196, 2006. Earlier version in Complexity'05.
17. M. Saks and A. Wigderson. Probabilistic Boolean decision trees and the complexity of evaluating game trees. In Proc. of 27th IEEE FOCS, pages 29-38, 1986.
18. M. Santha. On the Monte Carlo decision tree complexity of read-once formulae. Random Structures and Algorithms, 6(1):75-87, 1995.
19. M. Snir. Lower bounds on probabilistic linear decision trees. Theoretical Computer Science, 38:69-82, 1985.
20. M. Szegedy. Quantum speed-up of Markov chain based algorithms. In Proc. of 45th IEEE FOCS, pages 32-41, 2004.