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Volumn 38, Issue 3, 2008, Pages 963-981

Simulating quantum computation by contracting tensor networks

Author keywords

Classical simulation; Computational complexity; One way quantum computation; Quantum computation; Tensor network; Treewidth

Indexed keywords

CLASSICAL SIMULATION; MAXIMUM DEGREES; ONE-WAY QUANTUM COMPUTATION; PREPRINT; QUANTUM CIRCUITS; QUANTUM COMPUTATION; QUANTUM COMPUTATIONS; QUANTUM RESOURCES; RANDOMIZED ALGORITHMS; T GATES; TREE WIDTHS; TREEWIDTH; UNDERLYING GRAPHS;

EID: 54849416233     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/050644756     Document Type: Article
Times cited : (476)

References (41)
  • 1
    • 37649028493 scopus 로고    scopus 로고
    • Improved simulation of stabilizer circuits
    • S. AARONSON AND D. GOTTESMAN, Improved simulation of stabilizer circuits, Physical Rev. A, 70 (2004), p. 052328-1-052328-14.
    • (2004) Physical Rev. A , vol.70
    • AARONSON, S.1    GOTTESMAN, D.2
  • 4
    • 0037507853 scopus 로고    scopus 로고
    • Fixed parameter algorithms for dominating set and related problems on planar graphs
    • J. ALBER, H. L. BODLAENDER, H. FERNAU, T. KLOKS, AND R. NIEDERMEIER, Fixed parameter algorithms for dominating set and related problems on planar graphs, Algorithmica, 33 (2002), pp. 461-493.
    • (2002) Algorithmica , vol.33 , pp. 461-493
    • ALBER, J.1    BODLAENDER, H.L.2    FERNAU, H.3    KLOKS, T.4    NIEDERMEIER, R.5
  • 5
    • 0021787868 scopus 로고
    • Efficient algorithms for combinatorial problems on graphs with bounded decomposability - a survey
    • S. ARNBORG, Efficient algorithms for combinatorial problems on graphs with bounded decomposability - a survey, BIT, 25 (1985), pp. 2-23.
    • (1985) BIT , vol.25 , pp. 2-23
    • ARNBORG, S.1
  • 7
    • 0035137538 scopus 로고    scopus 로고
    • Persistent entanglement in arrays of interacting particles
    • H. J. BRIEGEL AND R. RAUSSENDORF, Persistent entanglement in arrays of interacting particles, Phys. Rev. Lett., 86 (2001), pp. 910-913.
    • (2001) Phys. Rev. Lett , vol.86 , pp. 910-913
    • BRIEGEL, H.J.1    RAUSSENDORF, R.2
  • 8
    • 55249122432 scopus 로고    scopus 로고
    • Treewidth: Characterizations, Applications, and Computations
    • Technical report UU-CS-2006-041, Universiteit Utrecht, Utrecht, The Netherlands
    • H. L. BODLAENDER, Treewidth: Characterizations, Applications, and Computations, Technical report UU-CS-2006-041, Universiteit Utrecht, Utrecht, The Netherlands, 2006.
    • (2006)
    • BODLAENDER, H.L.1
  • 9
    • 55249097875 scopus 로고    scopus 로고
    • On measurement-based quantum computation with the toric code states
    • preprint: quant-ph/0610102
    • S. BRAVYI AND R. RAUSSENDORF, On measurement-based quantum computation with the toric code states, preprint: quant-ph/0610102.
    • BRAVYI, S.1    RAUSSENDORF, R.2
  • 10
    • 26444484361 scopus 로고    scopus 로고
    • Width-based algorithms for SAT and Circuit-SAT (extended abstract)
    • Proceedings of the Sixth International Conference on Theory and Applications of Satisfiability Testing SAT 2003, Santa Margherita, Italy, Springer-Verlag
    • E. BROERING AND S. LOKAM, Width-based algorithms for SAT and Circuit-SAT (extended abstract), in Proceedings of the Sixth International Conference on Theory and Applications of Satisfiability Testing (SAT 2003), Santa Margherita, Italy, Lecture Notes in Comput. Sci. 2919, Springer-Verlag, 2004, pp. 162-171.
    • (2004) Lecture Notes in Comput. Sci , vol.2919 , pp. 162-171
    • BROERING, E.1    LOKAM, S.2
  • 11
    • 0033188982 scopus 로고    scopus 로고
    • Bucket elimination: A unifying framework for reasoning
    • R. DECHTER, Bucket elimination: A unifying framework for reasoning, Artificial Intelligence, 113 (1999), pp. 41-85.
    • (1999) Artificial Intelligence , vol.113 , pp. 41-85
    • DECHTER, R.1
  • 12
    • 55249099995 scopus 로고    scopus 로고
    • D. GOTTESMAN, The Heisenberg representation of quantum, computers, in Proceedings of the 22nd International Colloquium on Group Theoretical Methods in Physics, Group 22: S. P. Corney, R. Delbourgo, and P. D. Jarvis, eds., International Press, Cambridge, MA, 1999, pp. 32-43. Long version: quant-ph/9807006.
    • D. GOTTESMAN, The Heisenberg representation of quantum, computers, in Proceedings of the 22nd International Colloquium on Group Theoretical Methods in Physics, Group 22: S. P. Corney, R. Delbourgo, and P. D. Jarvis, eds., International Press, Cambridge, MA, 1999, pp. 32-43. Long version: quant-ph/9807006.
  • 13
    • 26844539700 scopus 로고    scopus 로고
    • S. A. FENNER, F. GREEN, S. HOMER, AND Y. ZHANG, Bounds on the power of constant-depth quantum, circuits, in Proceedings of the 15th International Symposium on Fundamentals of Computation Theory (FCT), Lübeck, Germany, 2005, Lecture Notes in Comput. Sci. 3623, M. Liskiewicz and R. Reischuk, eds., Springer, Berlin, 2005, pp. 44-55.
    • S. A. FENNER, F. GREEN, S. HOMER, AND Y. ZHANG, Bounds on the power of constant-depth quantum, circuits, in Proceedings of the 15th International Symposium on Fundamentals of Computation Theory (FCT), Lübeck, Germany, 2005, Lecture Notes in Comput. Sci. 3623, M. Liskiewicz and R. Reischuk, eds., Springer, Berlin, 2005, pp. 44-55.
  • 15
    • 55249088744 scopus 로고    scopus 로고
    • On the simulation of quantum circuits
    • preprint: quant-ph/0603163
    • R. JOZSA, On the simulation of quantum circuits, preprint: quant-ph/0603163.
    • JOZSA, R.1
  • 16
    • 1542516146 scopus 로고    scopus 로고
    • R. JOZSA AND N. LINDEN, On the role of entanglement in quantum computational speed-up, Lond. Proc. R. Soc. Ser. A Math. Phys. Eng. Sci., 459, 2003, pp. 2011-2032.
    • R. JOZSA AND N. LINDEN, On the role of entanglement in quantum computational speed-up, Lond. Proc. R. Soc. Ser. A Math. Phys. Eng. Sci., 459, 2003, pp. 2011-2032.
  • 19
    • 37349111410 scopus 로고    scopus 로고
    • Simulating quantum computation by contracting tensor networks
    • preprint: quant-ph/0511069
    • I. L. MARKOV AND Y. SHI, Simulating quantum computation by contracting tensor networks, preprint: quant-ph/0511069.
    • MARKOV, I.L.1    SHI, Y.2
  • 21
    • 33846679636 scopus 로고    scopus 로고
    • M. VAN DEN NEST, W. DÜR, G VIDAL, AND H J. BRIEGEL, Classical simulation versus universality in measurement based quantum computation, Phys. Rev. A, 75 (2007), p. 012337.
    • M. VAN DEN NEST, W. DÜR, G VIDAL, AND H J. BRIEGEL, Classical simulation versus universality in measurement based quantum computation, Phys. Rev. A, 75 (2007), p. 012337.
  • 22
    • 33749989342 scopus 로고    scopus 로고
    • M. VAN DEN NEST, A. MIYAKE, W. DÜR AND H. J BRIEGEL, Universal resources for measurement-based quantum computation, Phys. Rev. Lett., 97 (2006), p. 150504.
    • M. VAN DEN NEST, A. MIYAKE, W. DÜR AND H. J BRIEGEL, Universal resources for measurement-based quantum computation, Phys. Rev. Lett., 97 (2006), p. 150504.
  • 24
    • 55249100499 scopus 로고    scopus 로고
    • Renormalization algorithm for the calculation of spectra of interacting quantum systems
    • preprint: cond-mat/0504717
    • D. PORRAS, F. VERSTRAETE, AND J. I. CIRAC, Renormalization algorithm for the calculation of spectra of interacting quantum systems, preprint: cond-mat/0504717.
    • PORRAS, D.1    VERSTRAETE, F.2    CIRAC, J.I.3
  • 25
    • 0035963060 scopus 로고    scopus 로고
    • A one-way quantum computer
    • R. RAUSSENDORF AND H. J. BRIEGEL, A one-way quantum computer, Phys. Rev. Lett., 86 (2001), pp. 5188-5191.
    • (2001) Phys. Rev. Lett , vol.86 , pp. 5188-5191
    • RAUSSENDORF, R.1    BRIEGEL, H.J.2
  • 28
    • 0001227241 scopus 로고    scopus 로고
    • N. ROBERTSON AND P. D. SEYMOUR, Graph minors. X. Obstructions to tree-decomposition, Journal of Comb. Theory Ser. B, 52 (1991), pp. 153-190.
    • N. ROBERTSON AND P. D. SEYMOUR, Graph minors. X. Obstructions to tree-decomposition, Journal of Comb. Theory Ser. B, 52 (1991), pp. 153-190.
  • 29
    • 0014928358 scopus 로고
    • Triangulated graphs and the elimination process
    • D. J. ROSE, Triangulated graphs and the elimination process, J. Math. Anal. Appl., 32 (1970), pp. 597-609.
    • (1970) J. Math. Anal. Appl , vol.32 , pp. 597-609
    • ROSE, D.J.1
  • 30
    • 0036242960 scopus 로고    scopus 로고
    • Quantum formulas: A lower bound and simulation
    • V. P. ROYCHOWDHURY AND F. VATAN, Quantum formulas: A lower bound and simulation, SIAM J. Comput., 31 (2001), pp. 460-476.
    • (2001) SIAM J. Comput , vol.31 , pp. 460-476
    • ROYCHOWDHURY, V.P.1    VATAN, F.2
  • 31
    • 0036508628 scopus 로고    scopus 로고
    • Classical simulation of noninteracting-fermion quantum circuits
    • B. M. TERHAL AND D. P. DIVINCENZO, Classical simulation of noninteracting-fermion quantum circuits, Phys. Rev. A, 65 (2002), pp. 32325-32334.
    • (2002) Phys. Rev. A , vol.65 , pp. 32325-32334
    • TERHAL, B.M.1    DIVINCENZO, D.P.2
  • 32
    • 2442419277 scopus 로고    scopus 로고
    • Adaptive quantum computation, constant depth quantum circuits and Arthur-Merlin games
    • B. M. TERHAL AND D. P. DIVINCENZO, Adaptive quantum computation, constant depth quantum circuits and Arthur-Merlin games, Quantum Inf. Comput., 4 (2004), pp. 134-145.
    • (2004) Quantum Inf. Comput , vol.4 , pp. 134-145
    • TERHAL, B.M.1    DIVINCENZO, D.P.2
  • 33
    • 0036519749 scopus 로고    scopus 로고
    • Quantum circuits that can be simulated classically in polynomial time
    • L. G. VALIANT, Quantum circuits that can be simulated classically in polynomial time, SIAM J. Comput., 31 (2002), pp. 1229-1254.
    • (2002) SIAM J. Comput , vol.31 , pp. 1229-1254
    • VALIANT, L.G.1
  • 34
    • 27144464282 scopus 로고    scopus 로고
    • Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
    • preprint: cond-mat/0407066
    • F. VERSTRAETE AND J. I. CIRAC, Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions, preprint: cond-mat/0407066.
    • VERSTRAETE, F.1    CIRAC, J.I.2
  • 35
    • 19744374448 scopus 로고    scopus 로고
    • Matrix product density operators: Simulation of finite-temperature and dissipative systems
    • F. VERSTRAETE, J. J. GARCIA-RIPOLL, AND J. I. CIRAC, Matrix product density operators: Simulation of finite-temperature and dissipative systems, Phys. Rev. Lett., 93 (2004), p. 207204.
    • (2004) Phys. Rev. Lett , vol.93 , pp. 207204
    • VERSTRAETE, F.1    GARCIA-RIPOLL, J.J.2    CIRAC, J.I.3
  • 36
    • 0242425255 scopus 로고    scopus 로고
    • Efficient classical simulation of slightly entangled quantum computations
    • G. VIDAL, Efficient classical simulation of slightly entangled quantum computations, Phys. Rev. Lett., 91 (2003), p. 147902.
    • (2003) Phys. Rev. Lett , vol.91 , pp. 147902
    • VIDAL, G.1
  • 37
    • 4344570203 scopus 로고    scopus 로고
    • Efficient simulation of one-dimensional quantum many-body systems
    • G. VIDAL, Efficient simulation of one-dimensional quantum many-body systems, Phys. Rev. Lett., 93 (2004), p. 040502.
    • (2004) Phys. Rev. Lett , vol.93 , pp. 040502
    • VIDAL, G.1
  • 38
    • 15244342458 scopus 로고    scopus 로고
    • P. WALTHER, K. J. RESCH. T. RUDOLPH, E. SCHENCK, H. WEINFURTER, V. VEDRAL, M. ASPELMEYER, AND A, ZEILINGER, Experimental one-way quantum computing, Nature, 434 (2005), pp. 169-176.
    • P. WALTHER, K. J. RESCH. T. RUDOLPH, E. SCHENCK, H. WEINFURTER, V. VEDRAL, M. ASPELMEYER, AND A, ZEILINGER, Experimental one-way quantum computing, Nature, 434 (2005), pp. 169-176.
  • 39
    • 35348823184 scopus 로고    scopus 로고
    • Efficient classical simulation of the approximate quantum Fourier transform
    • N. YORAN AND A. SHORT, Efficient classical simulation of the approximate quantum Fourier transform, Phys. Rev. A, 76 (2007), p. 042321.
    • (2007) Phys. Rev. A , vol.76 , pp. 042321
    • YORAN, N.1    SHORT, A.2
  • 41
    • 19744365684 scopus 로고    scopus 로고
    • Mixed-State dynamics in one-dimensional quantum lattice systems: A time-dependent superoperator renormalization algorithm
    • M. ZWOLAK AND G. VIDAL, Mixed-State dynamics in one-dimensional quantum lattice systems: A time-dependent superoperator renormalization algorithm, Phys. Rev. Lett., 93 (2004), p. 207205.
    • (2004) Phys. Rev. Lett , vol.93 , pp. 207205
    • ZWOLAK, M.1    VIDAL, G.2


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