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Volumn 6, Issue 3, 2006, Pages 213-262

A geometric approach to quantum circuit lower bounds

Author keywords

Finsler geometry; Lower bounds; Quantum circuits

Indexed keywords

DIFFERENTIAL EQUATIONS; GEODESY; GEOMETRY; INTEGRATED CIRCUIT MANUFACTURE; QUBITS; TIMING CIRCUITS;

EID: 33645778554     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (200)

References (68)
  • 1
    • 39149096969 scopus 로고    scopus 로고
    • Is P versus NP formally independent?
    • S. Aaronson. Is P versus NP formally independent? Bulletin of the EATCS, 81, 2003.
    • (2003) Bulletin of the EATCS , pp. 81
    • Aaronson, S.1
  • 2
    • 33645765511 scopus 로고    scopus 로고
    • Publicaciones de la Escuela Venezolana de Matematicas, Caracas, Venezuela
    • J. C. Álvarez and C. Durán. An introduction to Finsler geometry. Publicaciones de la Escuela Venezolana de Matematicas, Caracas, Venezuela, 1998. Available at http://www.math.poly.edu/research/finsler/.
    • (1998) An Introduction to Finsler Geometry
    • Álvarez, J.C.1    Durán, C.2
  • 4
    • 0004064083 scopus 로고
    • Mathematical methods of classical mechanics. Springer-Verlag, New York, 2nd edition
    • V. I. Arnold. Mathematical methods of classical mechanics, volume 60 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2nd edition, 1989.
    • (1989) Graduate Texts in Mathematics , vol.60
    • Arnold, V.I.1
  • 6
    • 0003647259 scopus 로고    scopus 로고
    • An introduction to Riemann-Finsler geometry. Springer, New York
    • D. Bao, S.-S. Chern, and Z. Shen. An introduction to Riemann-Finsler geometry, volume 200 of Graduate Texts in Mathematics. Springer, New York, 2000.
    • (2000) Graduate Texts in Mathematics , vol.200
    • Bao, D.1    Chern, S.-S.2    Shen, Z.3
  • 9
    • 0001063035 scopus 로고    scopus 로고
    • Strengths and weaknesses of quantum computing
    • arXiv:quant-ph/9701001
    • C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani. Strengths and weaknesses of quantum computing. SIAM J. Comp., 26(5):1510-1523, 1997. arXiv:quant-ph/9701001.
    • (1997) SIAM J. Comp. , vol.26 , Issue.5 , pp. 1510-1523
    • Bennett, C.H.1    Bernstein, E.2    Brassard, G.3    Vazirani, U.4
  • 12
    • 84953846236 scopus 로고    scopus 로고
    • chapter II in [13]. Chapman & Hall / CRC Press. arXiv:quant-ph/ 0108062
    • J. L. Brylinski and R. Brylinski. Universal quantum gates, chapter II in [13]. Chapman & Hall / CRC Press, 2002. arXiv:quant-ph/0108062.
    • (2002) Universal Quantum Gates
    • Brylinski, J.L.1    Brylinski, R.2
  • 13
    • 85060213774 scopus 로고    scopus 로고
    • R. K. Brylinski and G. Chen, editors. Computational Mathematics. Chapman & Hall / CRC Press
    • R. K. Brylinski and G. Chen, editors. Mathematics of Quantum Computation. Computational Mathematics. Chapman & Hall / CRC Press, 2002.
    • (2002) Mathematics of Quantum Computation
  • 16
    • 0942289430 scopus 로고    scopus 로고
    • Lower bounds on the complexty of simulating quantum gates
    • arXiv:quant-ph/0307190
    • A. M. Childs, H. L. Haselgrove, and M. A. Nielsen. Lower bounds on the complexty of simulating quantum gates. Phys. Rev. A, 68(5):052311, 2003. arXiv:quant-ph/0307190.
    • (2003) Phys. Rev. A , vol.68 , Issue.5 , pp. 052311
    • Childs, A.M.1    Haselgrove, H.L.2    Nielsen, M.A.3
  • 19
    • 0141689114 scopus 로고    scopus 로고
    • Reducing quantum computations to elementary unitary operations
    • G. Cybenko. Reducing quantum computations to elementary unitary operations. Computing in Science and Engineering, 3:27-32, 2001.
    • (2001) Computing in Science and Engineering , vol.3 , pp. 27-32
    • Cybenko, G.1
  • 22
    • 0036541322 scopus 로고    scopus 로고
    • Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries
    • arXiv:quant-ph/0106064
    • J. L. Dodd, M. A. Nielsen, M. J. Bremner, and R. T. Thew. Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries. Phys. Rev. A, 65(4):040301 (R), 2002. arXiv:quant-ph/0106064.
    • (2002) Phys. Rev. A , vol.65 , Issue.4
    • Dodd, J.L.1    Nielsen, M.A.2    Bremner, M.J.3    Thew, R.T.4
  • 24
    • 3142664609 scopus 로고    scopus 로고
    • Optimal smoothing for convex polytopes
    • M. Ghomi. Optimal smoothing for convex polytopes. Bull. London Math. Soc., 36:483-492, 2004.
    • (2004) Bull. London Math. Soc. , vol.36 , pp. 483-492
    • Ghomi, M.1
  • 25
    • 0000318382 scopus 로고    scopus 로고
    • Active control of the dynamics of atoms and molecules
    • R. J. Gordon and S. A. Rice. Active control of the dynamics of atoms and molecules. Annu. Rev. Phys. Chem., 48:601-541, 1997.
    • (1997) Annu. Rev. Phys. Chem. , vol.48 , pp. 601-1541
    • Gordon, R.J.1    Rice, S.A.2
  • 26
    • 0003932204 scopus 로고    scopus 로고
    • PhD thesis, California Institute of Technology, Pasadena, CA. arXiv:quant-ph/9705052
    • D. Gottesman. Stabilizer Codes and Quantum Error Correction. PhD thesis, California Institute of Technology, Pasadena, CA, 1997. arXiv:quant-ph/9705052.
    • (1997) Stabilizer Codes and Quantum Error Correction
    • Gottesman, D.1
  • 27
    • 0036992056 scopus 로고    scopus 로고
    • Characterization of non-local gates
    • arXiv:quant-ph/0205100
    • K. Hammerer, G. Vidal, and J. I. Cirac. Characterization of non-local gates. Phys. Rev. A, 66(06):062321, 2002. arXiv:quant-ph/0205100.
    • (2002) Phys. Rev. A , vol.66 , Issue.6 , pp. 062321
    • Hammerer, K.1    Vidal, G.2    Cirac, J.I.3
  • 28
    • 0002310121 scopus 로고
    • Die symbolische exponentialformel in der gruppentheorie
    • F. Hausdorff. Die symbolische Exponentialformel in der Gruppentheorie. Leipziger Berichte, 58:19-48, 1906.
    • (1906) Leipziger Berichte , vol.58 , pp. 19-48
    • Hausdorff, F.1
  • 29
    • 33645768496 scopus 로고    scopus 로고
    • Differential geometry, Lie groups, and symmetric spaces. Reprint edition published by the American Mathematical Society, Providence, Rhode Island
    • S. Helgason. Differential geometry, Lie groups, and symmetric spaces, volume 34 of Graduate Studies in Mathematics. Reprint edition published by the American Mathematical Society, Providence, Rhode Island, 2001.
    • (2001) Graduate Studies in Mathematics , vol.34
    • Helgason, S.1
  • 33
    • 0035280053 scopus 로고    scopus 로고
    • Time optimal control in spin systems
    • arXiv:quant-ph/0006114
    • N. Khaneja, R. Brockett, and S. J. Glaser. Time optimal control in spin systems. Phys. Rev. A, 63(3):032308, 2001. arXiv:quant-ph/0006114.
    • (2001) Phys. Rev. A , vol.63 , Issue.3 , pp. 032308
    • Khaneja, N.1    Brockett, R.2    Glaser, S.J.3
  • 34
    • 0035370922 scopus 로고    scopus 로고
    • n) and control of spin systems
    • arXiv:quant-ph/0010100
    • n) and control of spin systems. Chem. Physics, 267:11-23, 2001. arXiv:quant-ph/0010100.
    • (2001) Chem. Physics , vol.267 , pp. 11-23
    • Khaneja, N.1    Glaser, S.J.2
  • 35
    • 84983715460 scopus 로고    scopus 로고
    • Sub-Riemannian geometry and time optimal control of three spin systems: Quantum gates and coherence transfer
    • arXiv:quant-ph/0106099
    • N. Khaneja, S. J. Glaser, and R. Brockett. Sub-Riemannian geometry and time optimal control of three spin systems: Quantum gates and coherence transfer. Phys. Rev. A, 65(3):032301, 2002. arXiv:quant-ph/0106099.
    • (2002) Phys. Rev. A , vol.65 , Issue.3 , pp. 032301
    • Khaneja, N.1    Glaser, S.J.2    Brockett, R.3
  • 36
    • 0040052002 scopus 로고    scopus 로고
    • Quantum computations: Algorithms and error correction
    • A. Y. Kitaev. Quantum computations: algorithms and error correction. Russ. Math. Surv., 52(6):1191-1249, 1997.
    • (1997) Russ. Math. Surv. , vol.52 , Issue.6 , pp. 1191-1249
    • Kitaev, A.Y.1
  • 38
    • 0003647259 scopus 로고    scopus 로고
    • Riemannian manifolds: An introduction to curvature. Springer-Verlag, New York
    • J. M. Lee. Riemannian manifolds: An introduction to curvature, volume 176 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1997.
    • (1997) Graduate Texts in Mathematics , vol.176
    • Lee, J.M.1
  • 39
    • 0003647259 scopus 로고    scopus 로고
    • Introduction to smooth manifolds. Springer-Verlag, New York
    • J. M. Lee. Introduction to smooth manifolds, volume 218 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2003.
    • (2003) Graduate Texts in Mathematics , vol.218
    • Lee, J.M.1
  • 41
    • 0034437552 scopus 로고    scopus 로고
    • Sub-Finslerian metric associated to an optimal control system
    • C. López and E. Martínez. Sub-Finslerian metric associated to an optimal control system. SIAM J. Control Optim., 39(3):798-811, 2000.
    • (2000) SIAM J. Control Optim. , vol.39 , Issue.3 , pp. 798-811
    • López, C.1    Martínez, E.2
  • 42
    • 0009801975 scopus 로고    scopus 로고
    • A tour of subriemannian geometries, their geodesics and applications. American Mathematical Society, Providence, Rhode Island
    • R. Montgomery. A tour of subriemannian geometries, their geodesics and applications, volume 91 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, Rhode Island, 2002.
    • (2002) Mathematical Surveys and Monographs , vol.91
    • Montgomery, R.1
  • 44
    • 0036242861 scopus 로고    scopus 로고
    • Geometric complexity theory I: An approach to the P vs. NP and related problems
    • K. Mulmuley and M. Sahoni. Geometric complexity theory I: An approach to the P vs. NP and related problems. SIAM J. Comp., 31(2):496-526, 2002.
    • (2002) SIAM J. Comp. , vol.31 , Issue.2 , pp. 496-526
    • Mulmuley, K.1    Sahoni, M.2
  • 47
    • 33645755176 scopus 로고    scopus 로고
    • On linear matrix equations
    • Michael A. Nielsen. On linear matrix equations. Technical note 0401, available at www.qinfo.org/people/nielsen/blog/archive/000087.html, 2004.
    • (2004) Technical Note , vol.401
    • Nielsen, M.A.1
  • 48
    • 0037191441 scopus 로고    scopus 로고
    • Quantum computing by an optimal control algorithm for unitary transformations
    • J. P. Paolo and R. Kosloff. Quantum computing by an optimal control algorithm for unitary transformations. Phys. Rev. Lett., 89(18):188301, 2002.
    • (2002) Phys. Rev. Lett. , vol.89 , Issue.18 , pp. 188301
    • Paolo, J.P.1    Kosloff, R.2
  • 49
    • 1142268069 scopus 로고    scopus 로고
    • Optimal control theory for unitary transformations
    • arXiv:quant-ph/0309011
    • J. P. Paolo and R. Kosloff. Optimal control theory for unitary transformations. Phys. Rev. A, 68(6):062308, 2003. arXiv:quant-ph/0309011.
    • (2003) Phys. Rev. A , vol.68 , Issue.6 , pp. 062308
    • Paolo, J.P.1    Kosloff, R.2
  • 51
    • 0034607880 scopus 로고    scopus 로고
    • Chemistry - Whither the future of controlling quantum phenomena?
    • May 5
    • H. Rabitz, R. de Vive-Riedle, M. Motzkus, and K. Kompa. Chemistry - whither the future of controlling quantum phenomena? Science, 288(5467):824-828, May 5 2000.
    • (2000) Science , vol.288 , Issue.5467 , pp. 824-828
    • Rabitz, H.1    De Vive-Riedle, R.2    Motzkus, M.3    Kompa, K.4
  • 52
    • 0035439838 scopus 로고    scopus 로고
    • Optimally shaped terahertz pulses for phase retrieval in a Rydberg-atom data register
    • C. Rangan and P. H. Bucksbaum. Optimally shaped terahertz pulses for phase retrieval in a Rydberg-atom data register. Phys. Rev. A, 64(3):033417, 2001.
    • (2001) Phys. Rev. A , vol.64 , Issue.3 , pp. 033417
    • Rangan, C.1    Bucksbaum, P.H.2
  • 57
    • 84966240253 scopus 로고
    • On direct product matrices
    • W. E. Roth. On direct product matrices. Bull. Amer. Math. Soc., 40:461-468, 1934.
    • (1934) Bull. Amer. Math. Soc. , vol.40 , pp. 461-468
    • Roth, W.E.1
  • 63
    • 0037037873 scopus 로고    scopus 로고
    • Quantum computation with vibrationally excited molecules
    • C. M. Tesch and R. de Vivie-Riedle. Quantum computation with vibrationally excited molecules. Phys. Rev. Lett., 89(15):157901, 2002.
    • (2002) Phys. Rev. Lett. , vol.89 , Issue.15 , pp. 157901
    • Tesch, C.M.1    De Vivie-Riedle, R.2
  • 65
    • 0037054142 scopus 로고    scopus 로고
    • Interaction cost of non-local gates
    • arXiv:quant-ph/0112168
    • G. Vidal, K. Hammerer, and J. I. Cirac. Interaction cost of non-local gates. Phys. Rev. Lett., 88(23):237902, 2002. arXiv:quant-ph/0112168.
    • (2002) Phys. Rev. Lett. , vol.88 , Issue.23 , pp. 237902
    • Vidal, G.1    Hammerer, K.2    Cirac, J.I.3
  • 67
    • 0041528206 scopus 로고    scopus 로고
    • Exact two-qubit universal quantum circuit
    • arXiv:quant-ph/0212109
    • J. Zhang, J. Vala, S. Sastry, and K. B. Whaley. Exact two-qubit universal quantum circuit. Phys. Rev. Lett., 91(2):022903, 2003. arXiv:quant-ph/0212109.
    • (2003) Phys. Rev. Lett. , vol.91 , Issue.2 , pp. 022903
    • Zhang, J.1    Vala, J.2    Sastry, S.3    Whaley, K.B.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.