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Volumn 2, Issue , 2014, Pages 1-14

Ising formulations of many NP problems

Author keywords

Adiabatic quantum computation; Algorithms; Complexity theory; NP; Spin glasses

Indexed keywords

COMPUTATIONAL COMPLEXITY; QUANTUM COMPUTERS; SPIN GLASS;

EID: 84937141373     PISSN: None     EISSN: 2296424X     Source Type: Journal    
DOI: 10.3389/fphy.2014.00005     Document Type: Article
Times cited : (2478)

References (64)
  • 1
    • 0035917832 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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
  • 15
    • 48349143593 scopus 로고    scopus 로고
    • 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 scopus 로고
    • 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 scopus 로고
    • 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 scopus 로고
    • 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 scopus 로고
    • 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 scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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
  • 32
    • 84866056973 scopus 로고    scopus 로고
    • 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 scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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
  • 47
    • 0011497393 scopus 로고    scopus 로고
    • Finding cliques by quantum adiabatic evolution
    • Childs AM, Farhi E, Goldstone J, Gutmann S. Finding cliques by quantum adiabatic evolution. Quantum Inform Comput. (2002) 2:181. Available online at: http://arxiv.org/abs/quant-ph/0012104
    • (2002) Quantum Inform Comput , vol.2 , pp. 181
    • Childs, A.M.1    Farhi, E.2    Goldstone, J.3    Gutmann, S.4
  • 51
    • 0042492825 scopus 로고
    • 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 scopus 로고
    • 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 scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고
    • 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
  • 63
    • 79960425522 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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


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