Symmetry and subspace controllability for spin networks with a single-node control

IEEE Transactions on Automatic Control

Volumn 57, Issue 8, 2012, Pages 1945-1956

  Wang, Xiaoting ^a   Pemberton Ross, Peter ^b   Schirmer, Sophie G ^c  

^a UNIVERSITY OF MASSACHUSETTS BOSTON   (United States)

^b UNIVERSITY OF BASEL   (Switzerland)

^c SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Controllability; nonlinear control; quantum systems; spin networks; symmetries

Indexed keywords

BRANCHED NETWORK; CONTROL NODES; COUPLING STRENGTHS; EIGENSTATES; HEISENBERG; INTERNAL SYMMETRY; NON LINEAR CONTROL; QUANTUM SYSTEM; RANDOM PERTURBATIONS; SINGLE EXCITATION; SPIN NETWORKS; SYMMETRIES; XX CHAIN;

CONTROLLABILITY; QUANTUM ELECTRONICS; QUANTUM OPTICS;

HAMILTONIANS;

EID: 84864769869     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2012.2202057     Document Type: Article

References (44)

1. S. C. Benjamin and S. Bose, "Quantum computing with an always-on Heisenberg interaction," Phys. Rev. Lett, vol. 90, p. 247901, 2003.
2. S. Lloyd, A. J. Landahl, and J.-J. E. Slotine, "Universal quantum interfaces," Phys. Rev. A, vol. 69, p. 012305, 2004.
3. A. Kay and M. Ericsson, "Geometric effects and computation in spin networks," New J. Phys, vol. 7, p. 143, 2005.
4. K. G. H. Vollbrecht and J. I. Cirac, "Quantum Simulators, Continuous-Time Automata, and Translationally Invariant Systems," Phys. Rev. Lett, vol. 100, p. 010501, 2008.
5. L. M. K. Vandersypen and I. L. Chuang, "NMR techniques for quantum control and computation," Rev. Mod. Phys, vol. 76, p. 1037, 2005.
6. J. Garcia-Ripoll and J. Cirac, "Spin dynamics for bosons in an optical lattice," New J. Phys, vol. 5, p. 76, 2003.
7. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. Cambridge, U. K. : Cambridge Univ. Press, 2000.
8. D. P. DiVincenzo, "Two-bit gates are universal for quantum computation," Phys. Rev. A, vol. 51, p. 1015, 1995.
9. A. Berenco et al. , "Elementary gates for quantum computation," Phys. Rev. A, vol. 52, p. 3457, 1995.
10. V. Jurdjevic and H. Sussmann, "Control systems on Lie groups," J. Diff. Equations, vol. 12, p. 313, 1972.
11. D. D'Alessandro, Introduction to Quantum Control and Dynamics. Boca Raton, FL: Chapman & Hall/CRC, 2008.
12. C. Altafini, "Controllability of quantum mechanical systems by root space decomposition of su(N)," J. Math. Phys, vol. 43, pp. 2051-2062, 2002.
13. H. Fu, S. G. Schirmer, and A. I. Solomon, "Complete controllability of finite-level quantum systems," J. Phys. A, vol. 34, pp. 1679-1693, 2001.
14. F. Albertini and D. D'Alessandro, "The Lie algebra structure and controllability of spin systems," Linear Algebra Appl. , vol. 350, pp. 213-235, 2002.
15. F. Albertini and D. D'Alessandro, "Notions of controllability for multilevel bilinear quantum mechanical systems," IEEE Trans. Autom. Control, vol. 48, no. 8, pp. 1399-1403, Aug. 2003.
16. S. G. Schirmer, J. V. Leahy, and A. I. Solomon, "Degrees of controllability for quantum systems and application to atomic systems," J. Phys. A, vol. 35, pp. 4125-4141, 2002. (Pubitemid 37023869)
17. S. G. Schirmer, I. C. H. Pullen, and A. I. Solomon, Hamiltonian and Lagrangian Methods in Nonlinear Control. Oxford, U. K. : Pergamon, 2003, pp. 281-286.
18. S. G. Schirmer, I. C. H. Pullen, and A. I. Solomon, "Controllability of multi-partite quantum systems and selective excitation of quantum dots," J. Opt. B, vol. 7, pp. S293-S299, 2005. (Pubitemid 41383156)
19. F. Albertini and D. D'Alessandro, Controllability of Quantum Walks on Graphs. Ithaca, NY: Cornell Univ. Library, 2010.
20. N. Khaneja, "Cartan decomposition of SU(n) and Control of Spin Systems,," Chem. Phys, vol. 267, pp. 11-23, 2001. (Pubitemid 32428603)
21. D. Burgarth, S. Bose, C. Bruder, and V. Giovannetti, "Local controllability of quantum networks," Phys. Rev. A, vol. 79, p. 060305(R), 2009.
22. R. Heule, C. Bruder, D. Burgarth, and V. M. Stojanovic, "Local quantum control of Heisenberg spin chains," Phys. Rev. A, vol. 82, p. 052333, 2010.
23. S. G. Schirmer, I. C. H. Pullen, and P. J. Pemberton-Ross, "Global controllability with a single local actuator," Phys. Rev. A, vol. 78, p. 062339, 2008.
24. A. Kay and P. J. Pemberton-Ross, "Computation on spin chains with limited access," Phys. Rev. A, vol. 81, p. 010301(R), 2010.
25. S. G. Schirmer and P. J. Pemberton-Ross, "Fast high-fidelity information transmission through spin-chain quantum wires," Phys. Rev. A, vol. 80, p. 030201(R), 2009.
26. D. Burgarth, "Full Control by Locally Induced Relaxation," Phys. Rev. Lett, vol. 99, p. 100501, 2007.
27. D. Burgarth, "Quantum state transfer and time-dependent disorder in quantum chains," Eur. Phys. J. Special Topics, vol. 151, p. 147, 2007.
28. D. Burgarth et al. , "Scalable quantum computation via local control of only two qubi," Phys. Rev. A, vol. 81, p. 040303(R), 2010.
29. R. Heule, C. Bruder, D. Burgarth, and V. M. Stojanovic, "Controlling qubit arrays with anisotropic XXZ Heisenberg interaction by acting on a single qubit," Eur. Phys. J. D, vol. 63, p. 41, 2011.
30. X. Wang, A. Bayat, S. G. Schirmer, and S. Bose, "Robust entanglement in antiferromagnetic Heisenberg chains by single-spin optimal control," Phys. Rev. A, vol. 81, p. 032312, 2010.
31. W. Greiner and B. Muller, Quantum Mechanics: Symmetries. Berlin, Germany: Springer, 1989.
32. T. Polack, H. Suchowski, and D. J. Tannor, "Uncontrollable quantum systems: A classification scheme based on Lie subalgebras," Phys. Rev. A, vol. 79, p. 053403, 2009.
33. S. G. Schirmer, A. I. Solomon, and J. V. Leahy, "Criteria for reachability of quantum states," J. Phys. A, vol. 35, p. 8551, 2002.
34. U. Sander et al. , Controllability and Observability of Multi-Spin Systems: Constraints by Symmetry and by Relaxation. Ithaca, NY: Cornell Univ. Library, 2009.
35. P. J. Pemberton-Ross, A. Kay, and S. G. Schirmer, "Quantum control theory for state transformations: Dark states and their enlightenment," Phys. Rev. A, vol. 82, p. 042322, 2010.
36. R. Zeier and T. Schulte-Herbruggen, "Symmetry principles in quantum systems theory," J. Math. Phys. , vol. 52, pp. 1-48, 2011.
37. N. Jacobson, Lie Algebras. New York: Dover, 1979.
38. H. Bethe, "On the theory of metals. 1. Eigenvalues and eigenfunctions for the linear atomic chain," Zeitschrift für Physik A, vol. 71, p. 205, 1931.
39. G. S. Engel et al. , "Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems," Nature, vol. 446, p. 782, 2007.
40. F. Caruso et al. , "Highly efficient energy excitation transfer in lightharvesting complexes: The fundamental role of noise-assisted transport," J. Chem. Phys. arXiv:1103. 0929 (2011), vol. 131, p. 105106, 2009.
41. M. Mohseni, P. Rebentrost, S. Lloyd, and A. Aspuru-Guzik, "Environment-assisted quantum walks in photosynthetic energy transfer," J. Chem. Phys, vol. 129, p. 174106, 2008.
42. S. Bose, "Quantum Communication through an Unmodulated Spin Chain," Phys. Rev. Lett, vol. 91, p. 207901, 2003.
43. M. Karabach and G. Müller, "Introduction to the Bethe ansatz I," Comput. Phys, vol. 11, p. 36, 1997.
44. T. S. Chihara, An Introduction to Orthogonal Polynomials. London, U. K. : Routledge, 1978.