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Volumn 36, Issue 5-6, 2010, Pages 359-369

Matrix exponentials and parallel prefix computation in a quantum control problem

Author keywords

Chebyshev polynomials; Matrix exponential; Parallel matrix multiplication; Parallel prefix problem; Quantum control algorithm

Indexed keywords

CHEBYSHEV POLYNOMIALS; MATRIX EXPONENTIALS; PARALLEL MATRIX MULTIPLICATION; PARALLEL PREFIX; QUANTUM CONTROL ALGORITHM;

EID: 77953132134     PISSN: 01678191     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.parco.2010.01.006     Document Type: Article
Times cited : (15)

References (27)
  • 1
    • 77953130345 scopus 로고    scopus 로고
    • Parallelisation of block recursive matrix multiplication in prefix computations
    • C. Bischof et al, Eds, Parallel Computing: Architectures, Algorithms and Applications, Proceedings of the ParCo, Parallel Computing of
    • M. Bader, S. Hanigk, T. Huckle, Parallelisation of block recursive matrix multiplication in prefix computations, in: C. Bischof et al. (Eds.), Parallel Computing: Architectures, Algorithms and Applications, Proceedings of the ParCo, Parallel Computing 2007, vol. 38 of NIC Series, 2008.
    • (2007) NIC Series , vol.38
    • Bader, M.1    Hanigk, S.2    Huckle, T.3
  • 2
    • 0028530654 scopus 로고
    • PUMMA: parallel universal matrix multiplication algorithms on distributed memory concurrent computers
    • Choi J., Dongarra J., and Walker D. PUMMA: parallel universal matrix multiplication algorithms on distributed memory concurrent computers. Concurrency: Pract. Exp. 6 7 (1994) 543-570
    • (1994) Concurrency: Pract. Exp. , vol.6 , Issue.7 , pp. 543-570
    • Choi, J.1    Dongarra, J.2    Walker, D.3
  • 3
    • 4244043498 scopus 로고
    • Quantum-computing with cold trapped ions
    • Cirac J.I., and Zoller P. Quantum-computing with cold trapped ions. Phys. Rev. Lett 74 (1995) 4091-4094
    • (1995) Phys. Rev. Lett , vol.74 , pp. 4091-4094
    • Cirac, J.I.1    Zoller, P.2
  • 5
    • 4243807288 scopus 로고    scopus 로고
    • Quantum mechanics helps in searching for a needle in a haystack
    • Grover L.K. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79 (1997) 325-328
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 325-328
    • Grover, L.K.1
  • 8
    • 27144549311 scopus 로고    scopus 로고
    • The scaling and squaring method for the matrix exponential revisited
    • Higham N.J. The scaling and squaring method for the matrix exponential revisited. SIAM J. Matrix Anal. Appl. 26 4 (2005) 1179-1193
    • (2005) SIAM J. Matrix Anal. Appl. , vol.26 , Issue.4 , pp. 1179-1193
    • Higham, N.J.1
  • 10
    • 77953139158 scopus 로고    scopus 로고
    • T. Huckle, T. Schulte-Herbrüggen, A. Spörl, K. Waldherr, S. Glaser, Using the HLRB-II cluster as a quantum CISC-compiler, in: High Performance Computing in Science and Engineering, Garching 2007, Springer, 2008.
    • T. Huckle, T. Schulte-Herbrüggen, A. Spörl, K. Waldherr, S. Glaser, Using the HLRB-II cluster as a quantum CISC-compiler, in: High Performance Computing in Science and Engineering, Garching 2007, Springer, 2008.
  • 11
    • 10844258198 scopus 로고    scopus 로고
    • Communication lower bounds for distributed-memory matrix multiplication
    • Irony D., Toledo S., and Tiskin A. Communication lower bounds for distributed-memory matrix multiplication. J. Parallel Distrib. Comput. 64 9 (2004) 1017-1026
    • (2004) J. Parallel Distrib. Comput. , vol.64 , Issue.9 , pp. 1017-1026
    • Irony, D.1    Toledo, S.2    Tiskin, A.3
  • 12
    • 0032516155 scopus 로고    scopus 로고
    • A silicon-based nuclear spin quantum computer
    • Kane B.E. A silicon-based nuclear spin quantum computer. Nature (London) 393 (1998) 133-137
    • (1998) Nature (London) , vol.393 , pp. 133-137
    • Kane, B.E.1
  • 15
    • 11344283019 scopus 로고    scopus 로고
    • Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms
    • Khaneja N., Reiss T., Kehlet C., Schulte-Herbrüggen T., and Glaser S.J. Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. J. Magn. Reson. 172 (2005) 296-305
    • (2005) J. Magn. Reson. , vol.172 , pp. 296-305
    • Khaneja, N.1    Reiss, T.2    Kehlet, C.3    Schulte-Herbrüggen, T.4    Glaser, S.J.5
  • 17
    • 84976772007 scopus 로고
    • Parallel prefix computation
    • Ladner R.E., and Fischer M.J. Parallel prefix computation. J. ACM 27 4 (1980) 831-838
    • (1980) J. ACM , vol.27 , Issue.4 , pp. 831-838
    • Ladner, R.E.1    Fischer, M.J.2
  • 18
    • 0035535325 scopus 로고    scopus 로고
    • Quantum-state engineering with Josephson-junction devices
    • Makhlin Y., Schön G., and Shnirman A. Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys. 73 (2001) 357-400
    • (2001) Rev. Mod. Phys. , vol.73 , pp. 357-400
    • Makhlin, Y.1    Schön, G.2    Shnirman, A.3
  • 19
    • 0001143041 scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix
    • Moler C., and van Loan C. Nineteen dubious ways to compute the exponential of a matrix. SIAM Rev. 20 4 (1978) 801-836
    • (1978) SIAM Rev. , vol.20 , Issue.4 , pp. 801-836
    • Moler, C.1    van Loan, C.2
  • 20
    • 0037354371 scopus 로고    scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later
    • Moler C., and van Loan C. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Rev. 45 1 (2003) 3-49
    • (2003) SIAM Rev. , vol.45 , Issue.1 , pp. 3-49
    • Moler, C.1    van Loan, C.2
  • 23
    • 28844484702 scopus 로고    scopus 로고
    • Optimal control-based efficient synthesis of building blocks of quantum algorithms: a perspective from network complexity towards time complexity
    • Schulte-Herbrüggen T., Spörl A.K., Khaneja N., and Glaser S.J. Optimal control-based efficient synthesis of building blocks of quantum algorithms: a perspective from network complexity towards time complexity. Phys. Rev. A 72 (2005) 042331
    • (2005) Phys. Rev. A , vol.72 , pp. 042331
    • Schulte-Herbrüggen, T.1    Spörl, A.K.2    Khaneja, N.3    Glaser, S.J.4
  • 24
    • 0142051871 scopus 로고    scopus 로고
    • Polynomial-time algorithms for prime factorisation and discrete logarithm on a quantum computer
    • Shor P.W. Polynomial-time algorithms for prime factorisation and discrete logarithm on a quantum computer. SIAM J. Comput. 26 (1997) 1484-1509
    • (1997) SIAM J. Comput. , vol.26 , pp. 1484-1509
    • Shor, P.W.1
  • 25
    • 33846383668 scopus 로고    scopus 로고
    • A.K. Spörl, T. Schulte-Herbrüggen, S.J. Glaser, V. Bergholm, M.J. Storcz, J. Ferber, F.K. Wilhelm, Optimal control of coupled Josephson qubits, Phys. Rev. A 75 (2007) 012302, e-print: .
    • A.K. Spörl, T. Schulte-Herbrüggen, S.J. Glaser, V. Bergholm, M.J. Storcz, J. Ferber, F.K. Wilhelm, Optimal control of coupled Josephson qubits, Phys. Rev. A 75 (2007) 012302, e-print: .
  • 26
    • 0031123769 scopus 로고    scopus 로고
    • SUMMA: scalable universal matrix multiplication algorithm
    • van de Geijn R., and Watts J. SUMMA: scalable universal matrix multiplication algorithm. Concurrency: Pract. Exp. 9 4 (1997) 255-274
    • (1997) Concurrency: Pract. Exp. , vol.9 , Issue.4 , pp. 255-274
    • van de Geijn, R.1    Watts, J.2
  • 27
    • 77953135313 scopus 로고    scopus 로고
    • H. Yuan, R. Zeier, N. Khaneja, Elliptic functions and efficient control of ising spin chains with unequal couplings (2007), e-print: .
    • H. Yuan, R. Zeier, N. Khaneja, Elliptic functions and efficient control of ising spin chains with unequal couplings (2007), e-print: .


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.