Simulating arbitrary pair-interactions by a given Hamiltonian: Graph-theoretical bounds on the time complexity

Quantum Information and Computation

Volumn 2, Issue 2, 2002, Pages 117-132

  Wocjan, Pawel ^a   Janzing, Dominik ^a   Beth, Thomas ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Chromatic index; Graph spectra; Quantum complexity; Quantum control theory; Simulating pair interactions

Indexed keywords

CONTROL THEORY; CONVEX OPTIMIZATION; GRAPH THEORY; QUANTUM THEORY; QUBITS;

CHROMATIC INDEX; GRAPH SPECTRA; PAIR INTERACTIONS; QUANTUM COMPLEXITY; QUANTUM CONTROL THEORIES;

HAMILTONIANS;

EID: 0001686740     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge, 2000.
2. N. Duffield, and R. Werner, Local dynamics of mean-field quantum systems, Helv. Phys. Acta, Vol. 95, pp. 1016-1054, 1992.
3. 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, quant-ph/0106064v2.
4. D. Janzing, P. Wocjan, and Th. Beth, Complexity of inverting n-spin interactions: Arrow of time in quantum control, quant-ph/0106085, 2001.
5. N. Khaneja, R. Brockett, and S. J. Glaser, Time optimal control in spin systems, Phys. Rev. A, Vol. 63, pp. 032308 1-13, 2001.
6. R. R. Ernst, G. Bodenhausen, and Wokaun A., Principles of nuclear magnetic resonance in one and two dimension, Clarendon Press, Oxford, 1987.
7. M. A. Nielsen, Conditions for a class of entanglement transformations, Phys. Rev. Lett., Vol. 83, pp. 436-439, 1999.
8. M. A. Nielsen, Characterizing mixing and measurements in quantum mechanics, quant-ph/ 0008073, 2000.
9. R. Bhatia, Matrix Analysis, Graduate texts in mathematics; 169, Springer, 1996.
10. D. Janzing and Th. Beth, Complexity measure for continuous time quantum algorithms, Phys. Rev. A, Vol. 64, pp.022301 1-6, 2000, quant-ph/0009094.
11. D. W. Leung, I. L. Chuang, F. Yamaguchi, and Y. Yamamoto, Efficient implementation of coupled logic gates for quantum computing, Phys. Rev. A, Vol. 61, pp. 042310-0-7, 2000.
12. R. A. Horn, and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1985.
13. B. Bollobás, Modern Graph Theory, Springer Verlag, 1998.
14. D. M. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs: theory and applications, 3rd edition, Johann Ambrosius Barth Verlag, 1995.
15. W. D. Wallis, Guo-Hui Zhang, On the partition and coloring of a graph by cliques, Discrete Math. 120., No. 1-3, pp. 191-203, 1993.
16. J. A. Jones and E. Knill, E., Efficient Refocussing of One Spin and Two Spin Interactions for NMR Quantum Computation, J. Magn. Resonance, Vol. 141, pp.323-325, 1999.