Quantum algorithms for learning and testing juntas

Quantum Information Processing

Volumn 6, Issue 5, 2007, Pages 323-348

  Atıcı, Alp ^a   Servedio, Rocco A ^b  

^a Citadel Investment Group   (United States)

^b Fu Foundation School of Engineering and Applied Science   (United States)

Author keywords

Computational learning theory; Juntas; Lower bounds; Quantum computation; Quantum property testing; Quantum query algorithms

Indexed keywords

ALGORITHMS; BOOLEAN FUNCTIONS; COMPUTATIONAL COMPLEXITY; LEARNING SYSTEMS; QUANTUM COMPUTERS; RANDOM PROCESSES;

COMPUTATIONAL LEARNING THEORY; JUNTAS; LOWER BOUNDS; QUANTUM PROPERTY TESTING; QUANTUM QUERY ALGORITHMS;

QUANTUM THEORY;

EID: 35248878549     PISSN: 15700755     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11128-007-0061-6     Document Type: Article

References (29)

1. Ambainis A., Iwama K., Kawachi A., Masuda H., Putra R.H., and Yamashita S., in Proceedings of STACS 2004, pp. 93-104 (2003).
2. AtIcI A., Servedio R.A. (2005). Quantum Information Process. 4, 355-386
3. Bshouty N.H., Jackson J.C. (1999). SIAM J. Comp. 28, 1136-1153
4. J. Castro, in Proceedings of 17th ALT, pp. 78-92 (2006).
5. M. Hunziker, Meyer D.A., J. Park, J. Pommersheim, and M. Rothstein, The Geometry of Quantum Learning, arXiv:quant-ph/0309059; Quantum Information Processing (to appear).
6. K. Iwama, A. Kawachi, R. Raymond, and S. Yamashita, Robust Quantum Algorithms for Oracle Identification, arXiv:quant-ph/0411204 (2005).
7. Servedio R.A., Gortler S.J. (2004). SIAM J. Comp. 33, 1067-1092
8. H. Buhrman, L. Fortnow, I. Newman, and H. Röhrig, in Proceedings of 14th SODA, pp. 480-488 (2003).
9. K. Friedl, F. Magniez, M. Santha, and P. Sen, in Proceedings of the 28th International Symposium on Mathematical Foundations of Computer Science, pp. 419-428.
10. F. Magniez and A. Nayak, in Proceedings of the 32nd International Colloquium on Automata, Languages and Programming, pp. 1312-1324 (2005).
11. Jackson J.C. (1997). J. Comput. Syst. Sci. 55, 414-440
12. Valiant L.G. (1984). Commun. Assoc. Comp. Machinery 27, 1134-1142
13. J. Arpe and R. Reischuk, in Proceedings of the 14th International Conference on Algorithmic Learning Theory, pp. 99-113 (2003).
14. J. Arpe and R. Reischuk, in Proceedings of the 3rd International Conference on Theory and Applications of Models of Computation, pp. 387-398 (2006).
15. A. Blum, in Proceedings of the 16th Annual Conference on Learning Theory and 7th Kernel Workshop, pp. 731-733 (2003).
16. Chockler H., Gutfreund D. (2004). Information Process. Lett. 90, 301-305
17. E. Fischer, G. Kindler, D. Ron, S. Safra, and A. Samorodnitsky, in Proceedings of the 43rd IEEE Symposium on Foundations of Computer Science, pp. 103-112 (2002).
18. R. Lipton, E. Markakis, A. Mehta, and N. Vishnoi, in Proceedings of the 20th Annual IEEE Conference on Computational Complexity, pp. 112-119 (2005).
19. Mossel E., O'Donnell R., Servedio R.A. (2004). J. Compu. Syst. Sci. 69, 421-434
20. J. Köbler and W. Lindner, Bull. EATCS 89 (2006).
21. Y. Mansour, Learning Boolean functions via the Fourier transform, in Theoretical Advances in Neural Computation and Learning (Kluwer Academic Publishers, 1994, pp. 391-424).
22. Kushilevitz E., Mansour Y. (1993). SIAM J. Comput. 22, 1331-1348
23. Goldreich O., Goldwasser S., Ron D. (1998). J. ACM 45, 653-750
24. Rubinfeld R., Sudan M. (1996). SIAM J. Comp. 25, 252-271
25. Kahn J., Kalai G., and Linial N., in Proceedings of the 29th IEEE Symposium on Foundations of Computer Science, pp. 68-80 (1988).
26. Bernstein E., Vazirani U. (1997). SIAM J. Comp 26, 1411-1473
27. R. O'Donnell and R. A. Servedio, J. Comp System Sci, to appear. Available at http://www.cs.columbia.edu/~rocco/papers/ccc03.htm.. Preliminary version appeared in Eighteenth Annual IEEE Conference on Computational Complexity, pp. 3-12 (2003).
28. Preliminary version appeared in Eighteenth Annual IEEE Conference on Computational Complexity, pp. 3-12 (2003).
29. Bshouty N., Cleve R., Gavaldà R., Kannan S., and Tamon C. (1996). J. Comp. Syst. Sci. 52, 421-433