Universal simulation of Hamiltonians using a finite set of control operations

Quantum Information and Computation

Volumn 2, Issue 2, 2002, Pages 133-150

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

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Adjoint representation; Average Hamiltonian approach; Decoupling; Simulation of Hamiltonians; Transformer groups

Indexed keywords

COMPUTATIONAL METHODS; INFORMATION SYSTEMS;

ADJOINT REPRESENTATION; CONTROL OPERATIONS; DECOUPLING; FINITE GROUPS; HAMILTONIAN APPROACH; LARGE GROUPS; QUANTUM SYSTEM; TRANSFORMER GROUPS;

HAMILTONIANS;

EID: 0000613820     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. R. P. Feynman. Simulating physics with computers. Int. J. Theor. Phys., 21:467, 1982.
2. S. Lloyd. Universal Quantum Simulators. Science, 273:1073-1078, 1996.
3. Khaneja, N. and Brockett, R. and Glaser, S. J. Time optimal control in spin systems. Phys. Rev. A, 63(3):032308-1-13, 2001.
4. 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. Technical report, Los Alamos National Laboratory, 2000. LANL preprint quant-ph/0106064.
5. P. Wocjan, D. Janzing, and Th. Beth. Simulating Arbitrary Pair-Interactions by a Given Hamiltonian: Graph-Theoretical Bounds on the Time Complexity. Technical report, Los Alamos National Laboratory, 2001. LANL preprint quant-ph/0106077.
6. C. H. Bennett, J. I. Cirac, M. S. Leifer, D. W. Leung, N. Linden, S. Popescu, and G. Vidal. Optimal simulation of two-qubit Hamiltonians using general local operations. Technical report, Los Alamos National Laboratory, 2001. LANL preprint quant-ph/0107035.
7. M. Stollsteimer and G. Mahler. Suppression of arbitrary internal couplings in a quantum register. Technical report, Los Alamos National Laboratory, 2001. LANL preprint quant-ph/0107059.
8. G. Vidal and J. I. Cirac. Optimal simulation of nonlocal Hamiltonians using local operations and classical communication. Technical report, Los Alamos National Laboratory, 2000. LANL preprint quant-ph/0108076.
9. P. Zanardi. Symmetrizing Evolutions. Phys. Lett. A, 258:77, 1999.
10. R. R. Ernst, G. Bodenhausen, and A. Wokaun. Principles of nuclear magnetic resonance in one and two dimension. Clarendon Press, Oxford, 1987.
11. n by a single measurement. Technical report, Los Alamos National Laboratory, 2001. LANL preprint quant-ph/0103021.
12. D. Janzing, R. Zeier, F. Armknecht, and T. Beth. Quantum control without access to the controlling interaction. Technical report, Los Alamos National Laboratory, 2001. LANL preprint quant-ph/0103022.
13. D. Janzing, P. Wocjan, and Th. Beth. Complexity of inverting n-spin interactions: Arrow of time in quantum control. Technical report, Los Alamos National Laboratory, 2001. LANL preprint quant-ph/0106085.
14. D. W. Leung. Simulation and reversal of n-qubit Hamiltonians using Hadamard matrices. Technical report, Los Alamos National Laboratory, 2001. LANL preprint quant-ph/0107041.
15. U. Haeberlen. High Resolution NMR in Solids: Selective Averaging. Academic Press, 1976.
16. C. P. Slichter. Principles of Magnetic Resonance. Springer, 3rd edition, 1990.
17. E. Knill. Non-binary Unitary Error Bases and Quantum Codes. Technical report, Los Alamos National Laboratory, 1996. LANL preprint quant-ph/9608048.
18. A. Klappenecker and M. Rötteler. A remark on unitary error bases. Technical report, Los Alamos National Laboratory, 2000. LANL preprint quant-ph/0010082, to appear in: IEEE Transactions on Information Theory.
19. L. Viola, S. Lloyd, and E. Knill. Universal control of decoupled quantum systems. Phys. Rev. Lett., 83(23):4888-4891, 1999.
20. K. Zyczkowski, P. Horodecki, M. Horodecki, and R. Horodecki. Dynamics of quantum entanglement. Technical report, Los Alamos National Laboratory, 2000. LANL preprint quant-ph/0008115v2.
21. M. Nielsen and I. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.
22. R. F. Werner. All teleportation and dense coding schemes. Technical report, Los Alamos National Laboratory, 2000. LANL preprint quant-ph/0003070.
23. L. Viola, E. Knill, and S. Lloyd. Dynamical decoupling of open quantum systems. Phys. Rev. Lett., 82:2417-2421, 1999.
24. A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane. Quantum Error Correction Via Codes Over GF(4). IEEE Trans. Inform. Theory, 44:1369-1387, 1998.
25. D. Gottesman. Class of quantum error-correcting codes saturating the quantum Hamming bound. Phys. Rev. A, 54:1862-1868, 1996.
26. E. Knill. Group representations, error bases and quantum codes. Technical report, Los Alamos National Laboratory, 1996. LANL preprint quant-ph/9608049.
27. A. Steane. Simple quantum error correcting codes. Phys. Rev. A, 54:4741, 1996.
28. E. Knill, R. Laflamme, and L. Viola. Theory of Quantum Error Correction for General Noise. Phys. Rev. Lett., 84(11):2525-2528, 2000.
29. P. Zanardi. Stabilizing quantum information. Phys. Rev. A, 63:012301, 2001.
30. H. Barnum. Quantum message authentication codes. Technical report, Los Alamos National Laboratory, 2001. LANL preprint quant-ph/0103123.
31. B. Huppert. Endliche Gruppen, volume I. Springer Verlag, 1983.
32. I. M. Isaacs. Character Theory of Finite Groups. Pure and Applied Mathematics. Academic Press, 1976.
33. J. P. Serre. Linear Representations of Finite Groups. Springer, 1977.
34. W.-K. Rhim, A. Pines, and J. S. Waugh. Violation of the spin-temperature hypothesis. Phys. Rev. Lett., 25:218, 1970.
35. L. Viola and S. Lloyd. Dynamical suppression of decoherence in two-state quantum systems. Phys. Rev. Lett., 58(4):2733, 1998.
36. R. Bhatia. Matrix Analysis, volume 169 of Graduate texts in mathematics. Springer, 1996.
37. J. H. Conway, R. T. Curtis, S. P. Norton, and R. A. Wilson. Atlas of Finite Groups. Clarendon Press, Oxford, 1985.
38. W. Bosma, J.J. Cannon, and C. Playoust. The Magma algebra system I: The user language. J. Symb. Comp., 24:235-266, 1997.
39. The GAP Team. GAP - Groups, Algorithms, and Programming. Lehrstuhl D für Mathematik, RWTH Aachen and School of Mathematical and Computational Sciences, Univ. St. Andrews, Scotland, 1997.
40. M. A. Nielsen and G. Vidal. Majorization and the interconversion of bipartite states. Quantum Information and Computation, 1(1):76-93, 2001.