Diabatic quantum gates
P.J. Salas Peralta
Departamento de Tecnologías Especiales Aplicadas a la Telecomunicación, Universidad Politécnica de Madrid, Ciudad Universitaria s/n, 28040 Madrid (Spain). e-mail: psalas@etsit.upm.es
Recibido el 12 de enero de 2012; ]]> Aceptado el 30 de julio de 2012
Abstract
At present, several models for quantum computation have been proposed. Adiabatic quantum computation scheme particularly offers this possibility and is based on a slow enough time evolution of the system, where no transitions take place. In this work, a new strategy for quantum computation is provided from the opposite point of view. The objective is to control the non-adiabatic transitions between some states in order to produce the desired exit states after the evolution. The model is introduced by means of an analogy between the adiabatic quantum computation and an inelastic atomic collision. By means of a simple two-state model, several quantum gates are reproduced, concluding the possibility of diabatic universal fault-tolerant quantum computation. Going a step further, a new quantum diabatic computation model is glimpsed, where a carefully chosen Hamiltonian could carry out a non-adiabatic transition between the initial and the sought final state.
Keywords: Quantum gates; fault-tolerance; adiabatic quantum computation.
Resumen
En la actualidad se han propuesto varios modelos de computación cuántica. Concretamente, se ha introducido el esquema de computación cuántica adiabática, basado en una lenta evolución temporal del sistema empleado, lo que impide la aparición de transiciones entre estados. En este trabajo, se propone una nueva estrategia para la computación cuántica, basada en el punto de vista opuesto. El objetivo es controlar las transiciones no-adiabáticas entre estados que den lugar a la evolución deseada. Se introduce el modelo por medio de una analogía entre la computación adiabática y una colisión inelástica. Mediante un simple modelo con dos estados, es posible reproducir varias puertas cuánticas, concluyendo la posibilidad de una computación cuántica diabática universal tolerante a fallos. Dando un paso más, se vislumbra un nuevo modelo de computación cuántica diabático, en el que las transiciones entre el estado inicial y final deseado, se controlan mediante una adecuada elección del Hamiltoniano.
Descriptores: Puertas cuánticas; tolerancia a fallos; computación cuántica adiabática.
]]> PACS: 03.67.Lx; 03.67.Pp; 03.67.Hk
DESCARGAR ARTÍCULO EN FORMATO PDF
Acknowledgment
This work has been supported by the research project Quantum Information Technologies (QUITEMAD), P2009/ESP-1594 of Comunidad Autónoma de Madrid in Spain.
References
1. A. Messiah, Quantum Mechanics (John Wiley & Sons, New York, 1958). [ Links ]
]]>2. E. Farhi, J. Goldstone, S. Gutmann and M. Sipser, arXiv:quant-ph/0001106v1 (2000). [ Links ]
3. W. van Dam, M. Mosca, and U. Vazirani, in Proceedings of the 42nd Annual Symposium on Foundations of Computer Science (FOCS '01), Las Vegas, USA, 2001, IEEE Computer Society Press, New York 2001, p.279. [ Links ]
4. D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev, Siam Journal of Computing 37 (2007) 166. [ Links ]
5. A. M. Childs, E. Farhi, and J. Preskill, Phys. Rev. A65 (2002) 012322. [ Links ]
6. S. Lloyd, quant-ph/0805.2757, (2008) [ Links ]
7. S. P. Jordan, E. Farhi, and P. W. Shor, Phys. Rev. A74 (2006) 052322. [ Links ]
8. M. Steffen, W. van Dam, T. Hogg, G. Breyta, and I. Chuang, Phys. Rev. Lett. 90 (2003) 067903. [ Links ]
9. J. Roland, Adiabatic Quantum Computation, PhD. thesis, (Universite Libre de Bruxelles 2004). [ Links ] Sebastian D. Pinski, Adiabatic Quantum Computation, PhD thesis, (Loughborough University, U.K.) arXiv:1108.0560 (2011). [ Links ]
10. M. S. Sarandy, L.-A. Wu, and D. A. Lidar, Quantum Information Processing 3 (2004) 331. [ Links ]
11. S. Jansen, M.-B. Ruskai, and R. Seiler, J. Math. Phys. 48 (2007) 102111. [ Links ]
]]>12. M. J. O'Hara, and D. P. O'Leary, Phys. Rev. A77 (2008) 042319. [ Links ]
13. M. Born, and J. R. Oppenheimer, Ann. Physik 84 (1927) 457. [ Links ]
14. A. Macias, and A. Riera, Physics Reports 90 (1982) 299. [ Links ]
15. C. D. Lin, and F. Martin, in: Encyclopedia of Scattering (Academic Press, 2001). p1025. [ Links ]
16. H. S. W. Massey, Rep. Prog. Phys. 12 (1949) 248. [ Links ]
]]>17. The Riemann-Lebesgue theorem: Let f (x) : [a,b] → C be an integrable function on the interval [a,b], then ∫ba dx exp(inx) f (x) → 0 as n → [ Links ] ± ∞.
18. W. Lichten, Phys. Rev. 131 (1963) 229. [ Links ]
19. F. T. Smith, Phys. Rev. 179 (1969) 111. [ Links ]
20. Ch. Zhu, and H. Nakamura, J. Chem. Phys. 102 (1995) 7448. [ Links ]
21. P. W. Shor, Phys. Rev. A52 (1995) R2493. [ Links ]
]]>22. A. R. Calderbank, and P. W. Shor, Phys. Rev. A54 (1996) 1098. [ Links ]
23. A. M. Steane, Proc. Soc. Lond. A452 (1996) 2551. [ Links ]
24. P. Shor, in Proceedings of the 37th Symposium on Fundamentals of Computer Science, Los Alamitos, (IEEE Press, CA 1996). p56. [ Links ]
25. E. Knill, and R. Laflamme, quant-ph/9608012 (1996). [ Links ]
26. D. Aharonov and M. Ben-Or, in Proceedings of 29th Annual ACM Symposium on Theory of Computing (STOC), (ACM Press, New York 1997). p. 176. [ Links ]
]]>27. E. Knill, R. Laflamme, and W. Zurek, quant-ph/9610011 (1996). [ Links ]
28. B. W. Reichardt, quant-ph/0406025 (2004). [ Links ]
29. A. M. Steane, Phys. Rev. A 68 (2003) 042322. [ Links ]
30. P. J. Salas, and A. L. Sanz, Int. J. of Quant. Inf. 3 (2005) 371. [ Links ]
31. P. Aliferis, and J. Preskill, Phys. Rev. A79 (2009) 012332. [ Links ]
]]>32. R. Li, M. Hoover, and F. Gaitan, Quant. Inf. and Comp. 7 (2007) 594. [ Links ]
33. M. S. Child, Molecular Collision Theory, (Courier Dover Publications, London, 1996). [ Links ]
]]>