-
1
-
-
0004342981
-
-
American Mathematical Society, Boston, MA
-
A. Kitaev, A. Shen, and M. Vyalyi, Classical and Quantum Computation (American Mathematical Society, Boston, MA, 2002).
-
(2002)
Classical and Quantum Computation
-
-
Kitaev, A.1
Shen, A.2
Vyalyi, M.3
-
2
-
-
51249180339
-
-
IJTPBM 0020-7748 10.1007/BF02650179
-
R. P. Feynman, Int. J. Theor. Phys. IJTPBM 0020-7748 10.1007/BF02650179 21, 467 (1982)
-
(1982)
Int. J. Theor. Phys.
, vol.21
, pp. 467
-
-
Feynman, R.P.1
-
3
-
-
5344230456
-
-
FNDPA4 0015-9018 10.1007/BF01886518
-
R. P. Feynman, Found. Phys. FNDPA4 0015-9018 10.1007/BF01886518 16, 507 (1986).
-
(1986)
Found. Phys.
, vol.16
, pp. 507
-
-
Feynman, R.P.1
-
4
-
-
4344570203
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.93.040502
-
G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.040502 93, 040502 (2004).
-
(2004)
Phys. Rev. Lett.
, vol.93
, pp. 040502
-
-
Vidal, G.1
-
5
-
-
33746708722
-
-
PRLAAZ 0950-1207 10.1098/rspa.1998.0164
-
R. Cleve, A. Ekert, Ch. Macchiavello, and M. Mosca, Proc. R. Soc. London, Ser. A PRLAAZ 0950-1207 10.1098/rspa.1998.0164 454, 339 (1998).
-
(1998)
Proc. R. Soc. London, Ser. A
, vol.454
, pp. 339
-
-
Cleve, R.1
Ekert, A.2
MacChiavello, Ch.3
Mosca, M.4
-
6
-
-
0036757946
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.66.032316
-
G. Giedke and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.032316 66, 032316 (2002).
-
(2002)
Phys. Rev. A
, vol.66
, pp. 032316
-
-
Giedke, G.1
Cirac, J.I.2
-
8
-
-
0036508628
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.65.032325
-
B. M. Terhal and D. P. DiVincenzo, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032325 65, 032325 (2002).
-
(2002)
Phys. Rev. A
, vol.65
, pp. 032325
-
-
Terhal, B.M.1
Divincenzo, D.P.2
-
10
-
-
0035963060
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.86.5188
-
R. Raussendorf and H.-J. Briegel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.5188 86, 5188 (2001).
-
(2001)
Phys. Rev. Lett.
, vol.86
, pp. 5188
-
-
Raussendorf, R.1
Briegel, H.-J.2
-
11
-
-
34547722211
-
-
arXiv:quant-ph/0603266, Int. Colloq. Automata, Languages Programm. (to be published).
-
N. de Beaudrap, V. Danos, and E. Kashefi, e-print arXiv:quant-ph/0603266, Int. Colloq. Automata, Languages Programm. (to be published).
-
-
-
De Beaudrap, N.1
Danos, V.2
Kashefi, E.3
-
12
-
-
34547707557
-
-
arXiv:quant-ph/0512130, Quantum Inf. Comput. (to be published).
-
W. Hall, e-print arXiv:quant-ph/0512130, Quantum Inf. Comput. (to be published).
-
-
-
Hall, W.1
-
13
-
-
34547311239
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.98.220503
-
D. Gross and J. Eisert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.220503 98, 220503 (2007).
-
(2007)
Phys. Rev. Lett.
, vol.98
, pp. 220503
-
-
Gross, D.1
Eisert, J.2
-
14
-
-
18444380214
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.71.032318
-
A. M. Childs, D. W. Leung, and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.032318 71, 032318 (2005).
-
(2005)
Phys. Rev. A
, vol.71
, pp. 032318
-
-
Childs, A.M.1
Leung, D.W.2
Nielsen, M.A.3
-
15
-
-
33749989342
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.97.150504
-
M. Van den Nest, A. Miyake, W. Dür, and H. Briegel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.150504 97, 150504 (2006).
-
(2006)
Phys. Rev. Lett.
, vol.97
, pp. 150504
-
-
Van Den Nest, M.1
Miyake, A.2
Dür, W.3
Briegel, H.4
-
16
-
-
34547694993
-
-
arXiv:quant-ph/0504097, Rev. Math. Phys. (to be published).
-
M. A. Nielsen, e-print arXiv:quant-ph/0504097, Rev. Math. Phys. (to be published).
-
-
-
Nielsen, M.A.1
-
17
-
-
0037268624
-
-
APNYA6 0003-4916 10.1016/S0003-4916(02)00018-0
-
A. Kitaev, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/S0003-4916(02) 00018-0 303, 2 (2003).
-
(2003)
Ann. Phys. (N.Y.)
, vol.303
, pp. 2
-
-
Kitaev, A.1
-
18
-
-
34547704465
-
-
arXiv:quant-ph/9811052.
-
S. Bravyi and A. Kitaev, e-print arXiv:quant-ph/9811052.
-
-
-
Bravyi, S.1
Kitaev, A.2
-
20
-
-
0035981729
-
-
JMAPAQ 0022-2488 10.1063/1.1499754
-
E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1499754 43, 4452 (2002).
-
(2002)
J. Math. Phys.
, vol.43
, pp. 4452
-
-
Dennis, E.1
Kitaev, A.2
Landahl, A.3
Preskill, J.4
-
21
-
-
14644419012
-
-
PYLAAG 0375-9601 10.1016/j.physleta.2005.01.060
-
A. Hamma, R. Ionicioiu, and P. Zanardi, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2005.01.060 337, 22 (2005).
-
(2005)
Phys. Lett. A
, vol.337
, pp. 22
-
-
Hamma, A.1
Ionicioiu, R.2
Zanardi, P.3
-
22
-
-
33846679636
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.75.012337
-
M. Van den Nest, W. Dür, G. Vidal, and H. J. Briegel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.012337 75, 012337 (2007).
-
(2007)
Phys. Rev. A
, vol.75
, pp. 012337
-
-
Van Den Nest, M.1
Dür, W.2
Vidal, G.3
Briegel, H.J.4
-
24
-
-
34547718317
-
-
A. Kitaev (private communication).
-
-
-
Kitaev, A.1
-
26
-
-
0001051761
-
-
JPHAC5 0305-4470 10.1088/0305-4470/15/10/028
-
F. Barahona, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/15/10/028 15, 3241 (1982).
-
(1982)
J. Phys. A
, vol.15
, pp. 3241
-
-
Barahona, F.1
-
27
-
-
0000113399
-
-
0031-8914
-
P. Kasteleyn, Physica 27, 1209 (1961). 0031-8914
-
(1961)
Physica
, vol.27
, pp. 1209
-
-
Kasteleyn, P.1
-
29
-
-
34547724463
-
-
Note that at each step of MQC only some part of a qubit is measured. To compute probabilities of outcomes of such partial measurements we have to consider arbitrary subgraphs of the square lattice.
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Note that at each step of MQC only some part of a qubit is measured. To compute probabilities of outcomes of such partial measurements we have to consider arbitrary subgraphs of the square lattice.
-
-
-
-
30
-
-
34547694992
-
-
One can easily check that projecting a qubit onto a state |0 or |1 effectively removes this qubit from the lattice leading to a state | GE on a modified planar graph. One can use this observation to avoid the cases αe =0.
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One can easily check that projecting a qubit onto a state |0 or |1 effectively removes this qubit from the lattice leading to a state | GE on a modified planar graph. One can use this observation to avoid the cases αe =0.
-
-
-
-
31
-
-
0001184263
-
-
JMAPAQ 0022-2488 10.1063/1.1724294
-
B. Zumino, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1724294 3, 1055 (1962).
-
(1962)
J. Math. Phys.
, vol.3
, pp. 1055
-
-
Zumino, B.1
-
32
-
-
34547722210
-
-
arXiv:quant-ph/0511069, SIAM J. Comput. (to be published).
-
I. Markov and Y.-Y. Shi, arXiv:quant-ph/0511069, SIAM J. Comput. (to be published).
-
-
-
Markov, I.1
Shi, Y.-Y.2
-
33
-
-
33747637170
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.74.022320
-
Y.-Y. Shi, L.-M. Duan, and G. Vidal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.022320 74, 022320 (2006).
-
(2006)
Phys. Rev. A
, vol.74
, pp. 022320
-
-
Shi, Y.-Y.1
Duan, L.-M.2
Vidal, G.3
-
34
-
-
69349107393
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.93.056402
-
J. K. Pachos and M. B. Plenio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.056402 93, 056402 (2004).
-
(2004)
Phys. Rev. Lett.
, vol.93
, pp. 056402
-
-
Pachos, J.K.1
Plenio, M.B.2
-
35
-
-
0036149982
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.65.012308
-
D. Schlingemann and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.012308 65, 012308 (2001).
-
(2001)
Phys. Rev. A
, vol.65
, pp. 012308
-
-
Schlingemann, D.1
Werner, R.F.2
-
37
-
-
34547722962
-
-
M. Hein, Proceedings of the International School of Physics "Enrico Fermi" on "Quantum Computers, Algorithms and Chaos," Varenna, Italy, 2005 (to be published);
-
(2005)
-
-
Hein, M.1
-
38
-
-
34547719152
-
-
e-print arXiv:quant-ph/0602096
-
e-print arXiv:quant-ph/0602096.
-
-
-
-
39
-
-
34547712991
-
-
Ph.D. thesis, Princeton University
-
S.-I. Oum, Ph.D. thesis, Princeton University, 2005.
-
(2005)
-
-
Oum, S.-I.1
-
40
-
-
34547716729
-
-
Although the definition of a surface code state does not involve any surface, we have chosen this term to avoid them being confused with graph states-generalizations of the cluster state.
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Although the definition of a surface code state does not involve any surface, we have chosen this term to avoid them being confused with graph states-generalizations of the cluster state.
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