Abstract
Elementary logical operators (selective rotation, Fourier transform, controllable phase shift, and SUM gate) are considered for a quantum computer based on three-level systems (qutrits) represented by nuclear spins I = 1 under nuclear magnetic resonance conditions. The computer simulation of the realization of these operators by means of simple and composite selective radiofrequency (RF) pulses and optimized RF pulses is performed. The time dependence of the amplitude of last pulses is found by numerical optimization at different durations. Two variants are proposed for realization of a two-qutrit SUM gate by using one-qutrit or two-qutrit optimized RF pulses. The calculated time dependences of realization errors were used to study the time optimality of different methods for obtaining gates, proposed earlier and in this paper. The advantages and disadvantages of each of the methods are evaluated for different values of physical parameters.
Similar content being viewed by others
References
T. C. Ralph, K. J. Resch, and A. Gilchrist, Phys. Rev. A: At., Mol., Opt. Phys. 75, 022313 (2007).
B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, Nat. Phys. 5, 134 (2009).
D. Aharonov, W. van Dam, J. Kampe, Z. Landau, S. Lloyd, and O. Regev, SIAM J. Comput. 37(1), 166 (2007); arXiv:quant-ph/0405098.
B. A. Chase and A. J. Landahl, arXiv:quant-ph//0802.1207.
K. G. H. Vollbrecht and J. I. Cirac, Phys. Rev. Lett. 100, 010501 (2008).
D. Nagaj and P. Wocjan, Phys. Rev. A: At., Mol., Opt. Phys. 78, 032311 (2008).
D. Nagaj, arXiv:quant-ph/1002.0420.
J. Cai, A. Miyake, W. Dür, and H. J. Briegel, Phys. Rev. A: At., Mol., Opt. Phys. 82, 052309 (2010).
A. Muthukrishnan and C. R. Stroud, Jr., Phys. Rev. A: At., Mol., Opt. Phys. 62, 052309 (2000).
S. D. Bartlett, H. de Guise, and B. C. Sanders, Phys. Rev. A: At., Mol., Opt. Phys. 65, 052316 (2002).
V. E. Zobov, V. P. Shauro, and A. S. Ermilov, Pis’ma Zh. Eksp. Teor. Fiz. 87(6), 385 (2008) [JETP Lett. 87 (6), 334 (2008)].
B. Tamir, Phys. Rev. A: At., Mol., Opt. Phys. 77, 022326 (2008).
A. Kushnerov, Ternary Digital Techniques: Retrospective and Contemporaneity (Ben-Gurion University Press, Bersabee, Israel, 2005) [in Russian].
V. E. Zobov and D. I. Pekhterev, Pis’ma Zh. Eksp. Teor. Fiz. 89(5), 303 (2009) [JETP Lett. 89 (5), 260 (2009)].
D. Gottesman, Lect. Notes Comput. Sci. 1509, 302 (1999).
D. Gottesman, A. Kitaev, and J. Preskill, Phys. Rev. A: At., Mol., Opt. Phys. 64, 012310 (2001).
A. Yu. Vlasov, J. Math. Phys. 43, 2959 (2002).
J. Daboul, X. Wang, and B. C. Sanders, J. Phys. A: Math. Gen. 36, 2525 (2003).
A. B. Klimov, R. Guzman, J. C. Retamal, and C. Saavedra, Phys. Rev. A: At., Mol., Opt. Phys. 67, 062313 (2003).
Ch. Slichter, Principles of Magnetic Resonance (Springer, Heidelberg, 1978; Mir, Moscow, 1981).
R. Das, A. Mitra, V. Kumar, and A. Kumar, Int. J. Quantum Inf. 1, 387 (2003).
A. K. Khitrin and B. M. Fung, J. Chem. Phys. 112, 6963 (2000).
V. L. Ermakov and B. M. Fung, Phys. Rev. A: At., Mol., Opt. Phys. 66, 042310 (2002).
R. Das and A. Kumar, Phys. Rev. A: At., Mol., Opt. Phys. 68, 032304 (2003).
R. Das and A. Kumar, Appl. Phys. Lett. A 89, 024107 (2006).
T. Gopinath and A. Kumar, J. Magn. Reson. 193, 2 (2008); arXiv:quant-ph/0909.4034.
A. K. Khitrin, H. Sun, and B. M. Fung, Phys. Rev. A: At., Mol., Opt. Phys. 63, 020301 (2001).
A. K. Khitrin and B. M. Fung, Phys. Rev. A: At., Mol., Opt. Phys. 64, 032306 (2001).
V. E. Zobov and V. P. Shauro, Pis’ma Zh. Eksp. Teor. Fiz. 86(4), 260 (2007) [JETP Lett. 86 (4), 230 (2007)].
V. E. Zobov and V. P. Shauro, Zh. Eksp. Teor. Fiz. 135(1), 10 (2009) [JETP 108 (1), 5 (2009)].
T. Vosegaard, C. Kehlet, N. Khaneja, S. J. Glaser, and N. Chr. Nielsen, J. Am. Chem. Soc. 127, 13768 (2005).
N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S. J. Glaser, J. Magn. Reson. 172, 296 (2005).
J.-S. Lee, R. R. Regatte, and A. Jerschow, J. Chem. Phys. 129, 224510 (2008).
I. I. Maximov, J. Salomon, G. Turinici, and N. Chr. Nielsen, J. Chem. Phys. 132, 084107 (2010).
H. Kampermann and W. S. Veeman, J. Chem. Phys. 122, 214108 (2005).
D. O. Soares-Pinto, L. C. Celeri, R. Auccaise, F. F. Fanchini, E. R. deAzevedo, J. Maziero, T. J. Bonagamba, and R. M. Serra, Phys. Rev. A: At., Mol., Opt. Phys. 81, 062118 (2010).
E. M. Fortunato, M. A. Pravia, N. Boulant, G. Teklemariam, T. F. Havel, and D. G. Cory, J. Chem. Phys. 116, 7599 (2002).
V. P. Shauro, D. I. Pekhterev, and V. E. Zobov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 6, 41 (2007) [Russ. Phys. J. 50 (6), 566 (2007)].
C. A. Ryan, C. Negrevergne, M. Laforest, E. Knill, and R. Laflamme, Phys. Rev. A: At., Mol., Opt. Phys. 78, 012328 (2008).
P. Rebentrost and F. K. Wilhelm, Phys. Rev. B: Condens. Matter 79, 060507 (2009).
F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, Phys. Rev. Lett. 103, 110501 (2009).
A. S. Ermilov and V. E. Zobov, Opt. Spektrosk. 103(6), 994 (2007) [Opt. Spectrosc. 103 (6), 969 (2007)].
T. Gopinath and A. Kumar, Phys. Rev. A: At., Mol., Opt. Phys. 73, 022326 (2006).
G. P. Berman, G. D. Doolen, G. V. Lopez, and V. I. Tsifrinovich, Phys. Rev. A: At., Mol., Opt. Phys. 61, 042307 (2000).
N. Khaneja, R. Brockett, and S. J. Glaser, Phys. Rev. A: At., Mol., Opt. Phys. 63, 032308 (2001).
T. Schulte-Herbrüggen, A. Spörl, N. Khaneja, and S. J. Glaser, Phys. Rev. A: At., Mol., Opt. Phys. 72, 042331 (2005).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.E. Zobov, V.P. Shauro, 2011, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2011, Vol. 140, No. 2, pp. 211–223.
Rights and permissions
About this article
Cite this article
Zobov, V.E., Shauro, V.P. On time-optimal NMR control of states of qutrits represented by quadrupole nuclei with the spin I = 1. J. Exp. Theor. Phys. 113, 181–191 (2011). https://doi.org/10.1134/S1063776111060094
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776111060094