-
1
-
-
0035917832
-
A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem
-
Farhi E, Goldstone J, Gutmann S, Lapan J, Lundgren A, Preda D. A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science (2001) 292:472. doi: 10.1126/science.1057726
-
(2001)
Science
, vol.292
, pp. 472
-
-
Farhi, E.1
Goldstone, J.2
Gutmann, S.3
Lapan, J.4
Lundgren, A.5
Preda, D.6
-
2
-
-
52249083005
-
Colloquium: Quantum annealing and analog quantum computation
-
Das A, Chakrabarti BK. Colloquium: quantum annealing and analog quantum computation. Rev Mod Phy. (2008) 80:1061. doi: 10.1103/RevModPhys.80.1061
-
(2008)
Rev Mod Phy
, vol.80
, pp. 1061
-
-
Das, A.1
Chakrabarti, B.K.2
-
3
-
-
77955454198
-
Anderson localization makes adiabatic quantum optimization fail
-
Altshuler B, Krovi H, Roland J. Anderson localization makes adiabatic quantum optimization fail. Proc Natl Acad Sci USA. (2010) 107:12446. doi: 10.1073/pnas.1002116107
-
(2010)
Proc Natl Acad Sci USA
, vol.107
-
-
Altshuler, B.1
Krovi, H.2
Roland, J.3
-
4
-
-
79551620062
-
Does adiabatic quantum optimization fail for NP-complete problems?
-
Dickson NG, Amin MHS. Does adiabatic quantum optimization fail for NP-complete problems?. Phys Rev Lett. (2011) 106:050502. doi: 10.1103/PhysRevLett.106.050502
-
(2011)
Phys Rev Lett
, vol.106
-
-
Dickson, N.G.1
Amin, M.H.S.2
-
5
-
-
84873096101
-
The quantum adiabatic algorithm applied to random optimization problems: The quantum spin glass perspective
-
Bapst V, Foini L, Krzakala F, Semerjian G, Zamponi F. The quantum adiabatic algorithm applied to random optimization problems: the quantum spin glass perspective. Phys Rep. (2013) 523:127. doi: 10.1016/j.physrep.2012.10.002
-
(2013)
Phys Rep
, vol.523
, pp. 127
-
-
Bapst, V.1
Foini, L.2
Krzakala, F.3
Semerjian, G.4
Zamponi, F.5
-
6
-
-
80051711497
-
Unstructured randomness, small gaps and localization
-
Farhi E, Goldstone J, Gosset D, Gutmann S, Shor P. Unstructured randomness, small gaps and localization. Quantum Comput Inform. (2011) 11:840. Available online at:http://arxiv.org/abs/1010.0009
-
(2011)
Quantum Comput Inform
, vol.11
, pp. 840
-
-
Farhi, E.1
Goldstone, J.2
Gosset, D.3
Gutmann, S.4
Shor, P.5
-
7
-
-
84870547073
-
The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
-
Farhi E, Gosset D, Hen I, Sandvik AW, Shor P, Young AP, et al. The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs. Phys Rev. (2012) A86:052334. doi: 10.1103/PhysRevA.86.052334
-
(2012)
Phys Rev
, vol.A86
-
-
Farhi, E.1
Gosset, D.2
Hen, I.3
Sandvik, A.W.4
Shor, P.5
Young, A.P.6
-
8
-
-
84855396260
-
Exponential complexity of the quantum adiabatic algorithm for certain satisfiability problems
-
Hen I, Young AP. Exponential complexity of the quantum adiabatic algorithm for certain satisfiability problems. Phys Rev. (2011) E84:061152. doi: 10.1103/PhysRevE.84.061152
-
(2011)
Phys Rev
, vol.E84
-
-
Hen, I.1
Young, A.P.2
-
9
-
-
77953083534
-
First-order transitions and the performance of quantum algorithms in random optimization problems
-
Jorg T, Krzakala F, Semerjian G, Zamponi F. First-order transitions and the performance of quantum algorithms in random optimization problems. Phys Rev Lett. (2010) 104:207206. doi: 10.1103/PhysRevLett.104.207206
-
(2010)
Phys Rev Lett
, vol.104
-
-
Jorg, T.1
Krzakala, F.2
Semerjian, G.3
Zamponi, F.4
-
10
-
-
0037192472
-
Theory of quantum annealing of an Ising spin glass
-
Santoro GE, Martonak R, Tosatti E, Car R. Theory of quantum annealing of an Ising spin glass. Science (2002) 295:2427. doi: 10.1126/science.1068774
-
(2002)
Science
, vol.295
, pp. 2427
-
-
Santoro, G.E.1
Martonak, R.2
Tosatti, E.3
Car, R.4
-
11
-
-
84884693855
-
Experimental signature of programmable quantum annealing
-
Boixo S, Albash T, Spedalieri FM, Chancellor N, Lidar DA. Experimental signature of programmable quantum annealing. Nat Commun. (2013) 4:3067. doi: 10.1038/ncomms3067
-
(2013)
Nat Commun
, vol.4
, pp. 3067
-
-
Boixo, S.1
Albash, T.2
Spedalieri, F.M.3
Chancellor, N.4
Lidar, D.A.5
-
12
-
-
84891045946
-
-
Boixo S, Rønnow TF, Isakov SV, Wang Z, Wecker D, Lidar DA, et al. Quantum annealing with more than one hundred qubits (2013). Available online at: http://arxiv.org/abs/1304.4595
-
(2013)
Quantum annealing with more than one hundred qubits
-
-
Boixo, S.1
Rønnow, T.F.2
Isakov, S.V.3
Wang, Z.4
Wecker, D.5
Lidar, D.A.6
-
13
-
-
79955917132
-
Quantum annealing with manufactured spins
-
Johnson MW, Amin MHS, Gildert S, Lanting T, Hamze F, Dickson N, et al. Quantum annealing with manufactured spins. Nature (2011) 473:194. doi: 10.1038/nature10012
-
(2011)
Nature
, vol.473
, pp. 194
-
-
Johnson, M.W.1
Amin, M.H.S.2
Gildert, S.3
Lanting, T.4
Hamze, F.5
Dickson, N.6
-
15
-
-
48349143593
-
Realizable Hamiltonians for universal adiabatic quantum computers
-
Biamonte JD, Love PJ. Realizable Hamiltonians for universal adiabatic quantum computers. Phys Rev. (2008) A78:012352. doi: 10.1103/PhysRevA.78.012352
-
(2008)
Phys Rev
, vol.A78
-
-
Biamonte, J.D.1
Love, P.J.2
-
17
-
-
0001051761
-
On the computational complexity of Ising spin glass models
-
Barahona F. On the computational complexity of Ising spin glass models. J Phys. (1982)A15:3241.
-
(1982)
J Phys
, vol.A15
, pp. 3241
-
-
Barahona, F.1
-
18
-
-
0003037529
-
Reducibility among combinatorial problems
-
Miller RE, Thatcher JW, and Bohlinger JD, editors., New York, NY: Plenum Press
-
Karp RM. Reducibility among combinatorial problems. In: Miller RE, Thatcher JW, and Bohlinger JD, editors. Complexity of Computer Computations. New York, NY: Plenum Press (1972), p. 85. doi: 10.1007/978-1-4684-2001-2_9
-
(1972)
Complexity of Computer Computations
-
-
Karp, R.M.1
-
20
-
-
36149036022
-
Application of statistical mechanics to NP-complete problems in combinatorial optimisation
-
Fu Y, Anderson PW. Application of statistical mechanics to NP-complete problems in combinatorial optimisation. J Phys. (1986) A19:1605.
-
(1986)
J Phys
, vol.A19
, pp. 1605
-
-
Fu, Y.1
Anderson, P.W.2
-
23
-
-
26444479778
-
Optimization by simulated annealing
-
Kirkpatrick S, Gelatt CD, Vecchi MP. Optimization by simulated annealing. Science (1983)220:671. doi: 10.1126/science.220.4598.671
-
(1983)
Science
, vol.220
, pp. 671
-
-
Kirkpatrick, S.1
Gelatt, C.D.2
Vecchi, M.P.3
-
25
-
-
0023449962
-
Spin glasses and the statistical mechanics of protein folding
-
Bryngelson JD, Wolynes PG. Spin glasses and the statistical mechanics of protein folding. Proc Natl Acad Sci USA. (1987) 84:7524. doi: 10.1073/pnas.84.21.7524
-
(1987)
Proc Natl Acad Sci USA
, vol.84
, pp. 7524
-
-
Bryngelson, J.D.1
Wolynes, P.G.2
-
26
-
-
0031897962
-
Protein folding in the hydrophobic-hydrophilic (HP) model is NP-complete
-
Berger B, Leighton T. Protein folding in the hydrophobic-hydrophilic (HP) model is NP-complete. J Comput Biol. (1998) 5:27. doi: 10.1089/cmb.1998.5.27
-
(1998)
J Comput Biol
, vol.5
, pp. 27
-
-
Berger, B.1
Leighton, T.2
-
27
-
-
0020118274
-
Neural networks and physical systems with emergent collective computational abilities
-
Hopfield JJ. Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci USA. (1982) 79:2554. doi: 10.1073/pnas.79.8.2554
-
(1982)
Proc Natl Acad Sci USA
, vol.79
, pp. 2554
-
-
Hopfield, J.J.1
-
28
-
-
84875597374
-
Crises and collective socio-economic phenomena: Simple models and challenges
-
Bouchaud JP. Crises and collective socio-economic phenomena: simple models and challenges. J Stat Phys. (2013) 151:567. doi: 10.1007/s10955-012-0687-3
-
(2013)
J Stat Phys
, vol.151
, pp. 567
-
-
Bouchaud, J.P.1
-
29
-
-
84875498991
-
Multistable binary decision making on networks
-
Lucas A, Lee CH. Multistable binary decision making on networks. Phys Rev. (2013)E87:032806. doi: 10.1103/PhysRevE.87.032806. Available online at:http://arxiv.org/abs/1210.6044
-
(2013)
Phys Rev
, vol.E87
-
-
Lucas, A.1
Lee, C.H.2
-
30
-
-
84859309090
-
Quantum factorization of 143 on a dipolar-coupling nuclear magnetic resonance system
-
[Erratum (2012)109:269902E]
-
Xu N, Zhu J, Lu D, Zhou X, Peng X, Du J. Quantum factorization of 143 on a dipolar-coupling nuclear magnetic resonance system. Phys Rev Lett. (2012) 108:130501 [Erratum (2012)109:269902E]. doi: 10.1103/PhysRevLett.108.130501
-
(2012)
Phys Rev Lett
, vol.108
-
-
Xu, N.1
Zhu, J.2
Lu, D.3
Zhou, X.4
Peng, X.5
Du, J.6
-
31
-
-
84884683911
-
Experimental determination of Ramsey numbers
-
Bian Z, Chudak F, Macready WG, Clark L, Gaitan F. Experimental determination of Ramsey numbers. Phys Rev Lett. (2013) 111:130505. doi: 10.1103/PhysRevLett.111.130505
-
(2013)
Phys Rev Lett
, vol.111
-
-
Bian, Z.1
Chudak, F.2
Macready, W.G.3
Clark, L.4
Gaitan, F.5
-
32
-
-
84866056973
-
Finding low-energy conformations of lattice protein models by quantum annealing
-
Perdomo-Ortiz A, Dickson N, Drew-Brook M, Rose G, Aspuru-Guzik A. Finding low-energy conformations of lattice protein models by quantum annealing. Sci Rep. (2012) 2:571. doi: 10.1038/srep00571
-
(2012)
Sci Rep
, vol.2
, pp. 571
-
-
Perdomo-Ortiz, A.1
Dickson, N.2
Drew-Brook, M.3
Rose, G.4
Aspuru-Guzik, A.5
-
36
-
-
0042456012
-
The max-cut problem and quadratic 0-1 optimization; polyhedral aspects, relaxations and bounds
-
Boros E, Hammer PL. The max-cut problem and quadratic 0-1 optimization; polyhedral aspects, relaxations and bounds. Annal Operat Res. (1991) 33:151. doi: 10.1007/BF02115753
-
(1991)
Annal Operat Res
, vol.33
, pp. 151
-
-
Boros, E.1
Hammer, P.L.2
-
37
-
-
31244435415
-
Pseudo-Boolean optimization
-
Boros E, Hammer PL. Pseudo-Boolean optimization. Discrete Appl Math. (2002) 123:155. doi: 10.1016/S0166-218X(01)00341-9
-
(2002)
Discrete Appl Math
, vol.123
, pp. 155
-
-
Boros, E.1
Hammer, P.L.2
-
39
-
-
0024683063
-
A decomposition method for minimizing quadratic pseudo-Boolean functions
-
Billionnet A, Jaumard B. A decomposition method for minimizing quadratic pseudo-Boolean functions. Operat Res Lett. (1989) 8:161. doi: 10.1016/0167-6377(89)90043-6
-
(1989)
Operat Res Lett
, vol.8
, pp. 161
-
-
Billionnet, A.1
Jaumard, B.2
-
40
-
-
44349194348
-
Non-perturbative k-body to two-body commuting conversion Hamiltonians and embedding problem instances into Ising spins
-
Biamonte JD. Non-perturbative k-body to two-body commuting conversion Hamiltonians and embedding problem instances into Ising spins. Phys Rev. (2008) A77:052331. doi: 10.1103/PhysRevA.77.052331
-
(2008)
Phys Rev
, vol.A77
-
-
Biamonte, J.D.1
-
41
-
-
84894503191
-
Resource efficient gadgets for compiling adiabatic quantum optimization problems
-
Babbush R, O'Gorman B, Aspuru-Guzik A. Resource efficient gadgets for compiling adiabatic quantum optimization problems. Annal. Phys. (2013) 525:877. doi: 10.1002/andp.201300120
-
(2013)
Annal. Phys
, vol.525
, pp. 877
-
-
Babbush, R.1
O'Gorman, B.2
Aspuru-Guzik, A.3
-
42
-
-
57149102082
-
A quantum adiabatic algorithm for factorization and its experimental implementation
-
Peng X, Liao Z, Xu N, Qin G, Zhou X, Suter D, et al. A quantum adiabatic algorithm for factorization and its experimental implementation. Phys Rev Lett. (2008) 101:220405. doi: 10.1103/PhysRevLett.101.220405
-
(2008)
Phys Rev Lett
, vol.101
-
-
Peng, X.1
Liao, Z.2
Xu, N.3
Qin, G.4
Zhou, X.5
Suter, D.6
-
43
-
-
55849152053
-
Minor-embedding in adiabatic quantum computation: I the parameter setting problem
-
Choi V. Minor-embedding in adiabatic quantum computation: I the parameter setting problem. Quantum Inform Process. (2008) 7:193. doi: 10.1007/s11128-008-0082-9
-
(2008)
Quantum Inform Process
, vol.7
, pp. 193
-
-
Choi, V.1
-
44
-
-
79956145817
-
Minor-embedding in adiabatic quantum computation: II Minor-universal graph design
-
Choi V. Minor-embedding in adiabatic quantum computation: II Minor-universal graph design. Quantum Inform Process. (2011) 10:343. doi: 10.1007/s11128-010-0200-3
-
(2011)
Quantum Inform Process
, vol.10
, pp. 343
-
-
Choi, V.1
-
45
-
-
85168935073
-
Adiabatic quantum programming: Minor embedding with hard faults
-
Klymko C, Sullivan BD, Humble TS. Adiabatic quantum programming: minor embedding with hard faults. Quantum Inform Process. Available online at: http://arxiv.org/abs/1210.8395
-
Quantum Inform Process
-
-
Klymko, C.1
Sullivan, B.D.2
Humble, T.S.3
-
46
-
-
0032221884
-
Finding a large hidden clique in a random graph
-
Alon N, Krivelevich M, Sudakov B. Finding a large hidden clique in a random graph. Random Struct Algorith. (1998) 13:457. doi: 10.1002/(SICI)1098-2418(199810/12)13:3/4<457::AID-RSA14>3.3.CO;2-K
-
(1998)
Random Struct Algorith
, vol.13
, pp. 457
-
-
Alon, N.1
Krivelevich, M.2
Sudakov, B.3
-
51
-
-
0042492825
-
The Potts model
-
Wu FY. The Potts model. Rev Mod Phys. (1982) 54:1. doi: 10.1103/RevModPhys.54.235
-
(1982)
Rev Mod Phys
, vol.54
, pp. 1
-
-
Wu, F.Y.1
-
52
-
-
84972498411
-
Every planar map is four colorable I: Discharging
-
Appel K, Haken W. Every planar map is four colorable I: discharging. Illinois J Math. (1977)21:429.
-
(1977)
Illinois J Math
, vol.21
, pp. 429
-
-
Appel, K.1
Haken, W.2
-
53
-
-
84972500815
-
Every planar map is four colorable II Reducibility
-
Appel K, Haken W, Koch J. Every planar map is four colorable II Reducibility. Illinois J Math. (1977) 21:491.
-
(1977)
Illinois J Math
, vol.21
, pp. 491
-
-
Appel, K.1
Haken, W.2
Koch, J.3
-
54
-
-
84888342332
-
Spin glass approach to the feedback vertex set problem
-
Zhou HJ. Spin glass approach to the feedback vertex set problem. Eur Phys J (2013) B86:455. doi: 10.1140/epjb/e2013-40690-1
-
(2013)
Eur Phys J
, vol.B86
, pp. 455
-
-
Zhou, H.J.1
-
55
-
-
33748035771
-
The NP-completeness column
-
Johnson DS. The NP-completeness column. ACM Trans Algorith. (2005) 1:160. doi: 10.1145/1077464.1077476
-
(2005)
ACM Trans Algorith
, vol.1
, pp. 160
-
-
Johnson, D.S.1
-
56
-
-
84867316019
-
Solving the graph isomorphism problem with a quantum annealer
-
Hen I, Young AP. Solving the graph isomorphism problem with a quantum annealer. Phys Rev. (2012) A86:042310. doi: 10.1103/PhysRevA.86.042310
-
(2012)
Phys Rev
, vol.A86
-
-
Hen, I.1
Young, A.P.2
-
60
-
-
0025720957
-
A random polynomial-time algorithm for approximating the volume of convex bodies
-
Dyer M, Frieze A, Kannan R. A random polynomial-time algorithm for approximating the volume of convex bodies. J ACM. (1991) 38:1. doi: 10.1145/102782.102783
-
(1991)
J ACM
, vol.38
, pp. 1
-
-
Dyer, M.1
Frieze, A.2
Kannan, R.3
-
62
-
-
38049173092
-
Randomized algorithms for the low-rank approximation of matrices
-
Liberty E, Woolfe F, Martinsson PG, Rokhlin V, Tygert M. Randomized algorithms for the low-rank approximation of matrices. Proc Natl Acad Sci USA. (2007) 104:20167. doi: 10.1073/pnas.0709640104
-
(2007)
Proc Natl Acad Sci USA
, vol.104
-
-
Liberty, E.1
Woolfe, F.2
Martinsson, P.G.3
Rokhlin, V.4
Tygert, M.5
-
63
-
-
79960425522
-
Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
-
Halko N, Martinsson P, Tropp JA. Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. SIAM Rev. (2011) 53:217. doi: 10.1137/090771806
-
(2011)
SIAM Rev
, vol.53
, pp. 217
-
-
Halko, N.1
Martinsson, P.2
Tropp, J.A.3
-
64
-
-
85168936862
-
Parallel implementation of a fast randomized algorithm for the decomposition of low rank matrices
-
(accepted)
-
Lucas A, Stalzer M, Feo J. Parallel implementation of a fast randomized algorithm for the decomposition of low rank matrices. Parallel Process Lett. (accepted). Available online at:http://arxiv.org/abs/1205.3830
-
Parallel Process Lett
-
-
Lucas, A.1
Stalzer, M.2
Feo, J.3
|