Quantum algorithms for subset finding

Quantum Information and Computation

Volumn 5, Issue 7, 2005, Pages 593-604

  Childs, Andrew M ^a,b   Eisenberg, Jason M ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Quantum computation; Quantum query complexity; Quantum walk

Indexed keywords

QUANTUM COMPUTERS; QUANTUM THEORY;

CONTINUOUS-TIME QUANTUM WALKS; DISCRETE TIME; LOWER BOUNDS; QUANTUM ALGORITHMS; QUANTUM QUERY COMPLEXITY; QUANTUM WALK; QUERY ALGORITHMS; QUERY COMPLEXITY;

CONTINUOUS TIME SYSTEMS;

EID: 29844458138     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. L. K. Grover, Quantum mechanics helps in searching for a needle in a haystack, Phys. Rev. Lett. 79, 325 (1997), quant-ph/9706033.
2. C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani, Strengths and weaknesses of quantum computing, SIAM J. Comput. 26, 1510 (1997), quant-ph/9701001.
3. H. Buhrman, C. Durr, M. Heiligman, P. Høyer, F. Magniez, M. Santha, and R. de Wolf, Quantum algorithms for element distinctness, in Proc. 16th IEEE Conference on Computational Complexity (2001), pp. 131-137, quant-ph/0007016.
4. A. Ambainis, Quantum walk algorithm for element distinctness, in Proc. 45th IEEE Symposium on Foundations of Computer Science (2004), pp. 22-31, quant-ph/0311001.
5. S. Aaronson, Quantum lower bound for the collision problem, in Proc. 34th ACM Symposium on Theory of Computing (2002), pp. 635-642, quant-ph/0111102.
6. Y. Shi, Quantum lower bounds for the collision and the element distinctness problems, in Proc. 43rd IEEE Symposium on Foundations of Computer Science (2002), pp. 513-519, quant-ph/0112086.
7. A. Ambainis, Polynomial degree and lower bounds in quantum complexity: Collision and element distinctness with small range, Theory of Computing 1, 37 (2005), quant-ph/0305179.
8. S. Kutin, Quantum lower bound for the collision problem with small range, Theory of Computing 1, 29 (2005), quant-ph/0304162.
9. D. A. Meyer, From quantum cellular automata to quantum lattice gasses, J. Stat. Phys. 85, 551 (1996), quant-ph/9604003.
10. J. Watrous, Quantum simulations of classical random walks and undirected graph connectivity, J. Computer and System Sciences 62, 376 (2001), cs.CC/9812012.
11. D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani, Quantum walks on graphs, in Proc. 33rd ACM Symposium on Theory of Computing (2001), pp. 50-59, quant-ph/0012090.
12. A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous, One-dimensional quantum walks, in Proc. 33rd ACM Symposium on Theory of Computing (2001), pp. 37-49.
13. 1.3) quantum algorithm for the triangle problem, quant-ph/0310134.
14. A. M. Childs J. Goldstone, Spatial search by quantum walk, Phys. Rev. A 70, 022314 (2004), quant-ph/0306054.
15. R. Bhatia, Matrix Analysis (Springer-Verlag, New York, 1997).
16. M. Szegedy, On the quantum query complexity of detecting triangles in graphs, quant-ph/0310107.
17. E. Farhi and S. Gutmann, Quantum computation and decision trees, Phys. Rev. A 58, 915 (1998), quant-ph/9706062.
18. A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. A. Spielman, Exponential algorithmic speedup by quantum walk, in Proc. 35th ACM Symposium on Theory of Computing (2003), pp. 59-68, quant-ph/0209131.
19. D. Aharonov and A. Ta-Shma, Adiabatic quantum state generation and statistical zero knowledge, in Proc. 35th ACM Symposium on Theory of Computing (2003), pp. 20-29, quant-ph/0301023.
20. N. Linial, Distributive graph algorithms - global solutions from local data, in Proc. 28th IEEE Symposium on Foundations of Computer Science (1987), pp. 331-335.
21. N. Linial, Locality in distributed graph algorithms, SIAM J. Comput. 21, 193 (1992).