-
2
-
-
0008690083
-
The graph isomorphism problem
-
Dept. of Computing Science, University of Alberta
-
S. Fortin, The graph isomorphism problem, Tech. Report TR 96-20, Dept. of Computing Science, University of Alberta, 1996.
-
(1996)
Tech. Report
, vol.TR 96-20
-
-
Fortin, S.1
-
3
-
-
84986520524
-
The graph isomorphism problem
-
X. Liu and D.J. Klein, The graph isomorphism problem, J. Comput. Chem. 12, 1243-1251 (1991).
-
(1991)
J. Comput. Chem.
, vol.12
, pp. 1243-1251
-
-
Liu, X.1
Klein, D.J.2
-
6
-
-
0020166327
-
Isomorphism of graphs of bounded valence can be tested in polynomial time
-
Luks, E.M., Isomorphism of graphs of bounded valence can be tested in polynomial time, J. Comput. Sys. Sci. 25, 42-65 (1982)
-
(1982)
J. Comput. Sys. Sci.
, vol.25
, pp. 42-65
-
-
Luks, E.M.1
-
9
-
-
0344349316
-
A linear-time algorithm for isomorphism of graphs of bounded average genus
-
J. Chen, A linear-time algorithm for isomorphism of graphs of bounded average genus, SIAM J. Disc. Math. 7, 614-631 (1994).
-
(1994)
SIAM J. Disc. Math.
, vol.7
, pp. 614-631
-
-
Chen, J.1
-
11
-
-
0001460788
-
A note on the graph isomorphism counting problem
-
R. Mathon, A note on the graph isomorphism counting problem, Information Processing Letters, 8, 131-132 (1979).
-
(1979)
Information Processing Letters
, vol.8
, pp. 131-132
-
-
Mathon, R.1
-
12
-
-
0023646410
-
Does co-NP have short interactive proofs?
-
R. Boppana, J. Hastad, and S. Zachos, Does co-NP have short interactive proofs? In Information Processing Letters 25, pp. 27-32, 1987.
-
(1987)
Information Processing Letters
, vol.25
, pp. 27-32
-
-
Boppana, R.1
Hastad, J.2
Zachos, S.3
-
13
-
-
0024128620
-
Graph isomorphism is in the low hierarchy
-
U. Schöning, Graph isomorphism is in the low hierarchy, J. Computer and System Sciences 37, 312-323 (1988).
-
(1988)
J. Computer and System Sciences
, vol.37
, pp. 312-323
-
-
Schöning, U.1
-
14
-
-
23744436646
-
-
note
-
Perhaps the best-known example of a problem believed to be neither in P nor NP-complete is factorization, for which no classical polynomial algorithm is known but which can be solved in polynomial time on a quantum computer [15].
-
-
-
-
15
-
-
0142051871
-
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
-
P.W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. Sci. Statis. Comput. 26, 1484 (1997).
-
(1997)
SIAM J. Sci. Statis. Comput.
, vol.26
, pp. 1484
-
-
Shor, P.W.1
-
16
-
-
0034819348
-
Quantum mechanical algorithms for the non-abelian hidden subgroup problem
-
M. Grigni, L. J. Schulman, M. Vazirani, and U. Vazirani, Quantum mechanical algorithms for the non-abelian hidden subgroup problem, in Proc. 33rd Annual ACM symposium on theory of computing, pp. 68-74 (2001).
-
(2001)
Proc. 33rd Annual ACM Symposium on Theory of Computing
, pp. 68-74
-
-
Grigni, M.1
Schulman, L.J.2
Vazirani, M.3
Vazirani, U.4
-
17
-
-
0141534114
-
The hidden subgroup problem and quantum computation using group representations
-
S. Hallgren, A. Russell, and A. Ta-Shma, The hidden subgroup problem and quantum computation using group representations, SIAM J. Comput. 32, 916-934 (2003).
-
(2003)
SIAM J. Comput.
, vol.32
, pp. 916-934
-
-
Hallgren, S.1
Russell, A.2
Ta-Shma, A.3
-
20
-
-
0036036708
-
Quantum lower bound for the collision problem
-
Aaronson Quantum Lower Bound for the Collision Problem in Proc. ACM Symp. on Theory of Computing, 635-642 (2002).
-
(2002)
Proc. ACM Symp. on Theory of Computing
, pp. 635-642
-
-
Aaronson1
-
21
-
-
23744475526
-
-
note
-
A well-known quantum algorithm motivated by physical processes is the adiabatic algorithm proposed by Farhi and collaborators [22, 23, 24]. The algorithms we examine are clearly different than the adiabatic algorithm, but the philosophy underlying the scheme is analogous.
-
-
-
-
22
-
-
0035917832
-
A quantum adiabatic algorithm applied to random instances of an NP-complete problem
-
E. Farhi et al., A quantum adiabatic algorithm applied to random instances of an NP-complete problem, Science 292, 472-475 (2001).
-
(2001)
Science
, vol.292
, pp. 472-475
-
-
Farhi, E.1
-
23
-
-
0036146412
-
Robustness of adiabatic quantum computation
-
A.M. Childs, E. Farhi, and J. Preskill, Robustness of adiabatic quantum computation, Phys. Rev. A 65, 012322 (2002).
-
(2002)
Phys. Rev. A
, vol.65
, pp. 012322
-
-
Childs, A.M.1
Farhi, E.2
Preskill, J.3
-
24
-
-
0036542418
-
Quantum search by local adiabatic evolution
-
J. Roland and N.J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65, 042308 (2002).
-
(2002)
Phys. Rev. A
, vol.65
, pp. 042308
-
-
Roland, J.1
Cerf, N.J.2
-
33
-
-
0037770172
-
Adiabatic quantum state generation and statistical zero knowledge
-
Aharonov and Ta-Shma, Adiabatic Quantum State Generation and Statistical Zero Knowledge, in Proc. ACM Symp. on Theory of Computing, 20-29 (2003).
-
(2003)
Proc. ACM Symp. on Theory of Computing
, pp. 20-29
-
-
Aharonov1
Ta-Shma2
-
34
-
-
85111345508
-
-
note
-
p > 2.
-
-
-
|