How significant are the known collision and element distinctness quantum algorithms

Quantum Information and Computation

Volumn 4, Issue 3, 2004, Pages 201-206

  Grover, Lov ^a   Rudolph, Terry ^a  

^a LUCENT TECHNOLOGIES   (United States)

Author keywords

Collision; Element Distinctness; Quantum Algorithms

Indexed keywords

COMPUTATIONAL METHODS; INFORMATION SYSTEMS;

COLLISION; ELEMENT DISTINCTNESS; QUANTUM ALGORITHMS; QUANTUM SEARCH; QUANTUM SEARCH ALGORITHM; SEARCH SPACES; STRUCTURED PROBLEMS; TIME/SPACE COMPLEXITY;

QUANTUM THEORY;

EID: 4043095544     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. L. K. Grover, Quantum Mechanics helps in searching for a needle in a haystack, Phys. Rev. Letters, 78(2), 325, 1997, also at http://www.bell-labs. com/user/lkgrover/.
2. C. H. Bennett, E. Bernstein, G. Brassard & U.Vazirani, Strengths and weaknesses of quantum computing, SIAM Journal on Computing, 26, no. 5, Oct. 1997, p. 1510-1524.
3. C. Zalka, Graver's quantum searching is optimal, Phys. Rev. A 60, 2746 (1999).
4. L. K. Grover, Trade-offs in the quantum search algorithm, Phys. Rev. A 66, 052314 (2002).
5. L. K. Grover, Quantum computers can search rapidly by using almost any transformation, Phys. Rev. Letters, 80(19), 1998, 4329-4332; A framework for fast quantum mechanical algorithms, Proc. 30th ACM Symposium on Theory of Computing (STOC), 1998, 53-63.
6. L. K. Grover, Quantum computers can search rapidly by using almost any transformation, Phys. Rev. Letters, 80(19), 1998, 4329-4332; A framework for fast quantum mechanical algorithms, Proc. 30th ACM Symposium on Theory of Computing (STOC), 1998, 53-63.
7. G. Brassard, P. Hoeyer, M. Mosca and Alain Tapp, Quantum amplitude amplification and estimation, quant-ph/0005055; G. Brassard and P. Hoyer, quant-ph/9704027.
8. G. Brassard, P. Hoeyer, M. Mosca and Alain Tapp, Quantum amplitude amplification and estimation, quant-ph/0005055; G. Brassard and P. Hoyer, quant-ph/9704027.
9. S. Aaronson, Quantum lower bound for the collision problem, STOC '02, pp.635-642. Also quant-ph/0111102.
10. S. Kutin, Quantum lower bound for the collision problem, quant-ph/0304162.
11. A. Ambainis, Quantum Lower Bounds for Collision and Element Distinctness with Small Range, quant-ph/0305179.
12. Y. Shih, Quantum lower bounds for the collision and element distinctness problems, quant-ph/0112086.
13. G. Brassard, P. Hoyer & A. Tapp, Quantum Algorithms for the collision problem, SIGACT News, 28:14-19,1997. Also quant-ph/9705002
14. H. Buhrman et al, Quantum Algorithms for Element Distinctness, quant-ph/0007016.
15. Umesh Vazirani, private communication.