I. Foundations of Quantum Optics and Quantum InformationNo Access

EVALUATION OF DECOHERENCE FOR QUANTUM COMPUTING ARCHITECTURES: QUBIT SYSTEM SUBJECT TO TIME-DEPENDENT CONTROL

DMITRY SOLENOV

Department of Physics, Clarkson University, Potsdam, New York 13729-5721, USA

Search for more papers by this author

and

VLADIMIR PRIVMAN

Department of Physics, Clarkson University, Potsdam, New York 13729-5721, USA

Search for more papers by this author

https://doi.org/10.1142/S0217979206034066Cited by:8 (Source: Crossref)

Abstract

We present an approach that allows quantifying decoherence processes in an open quantum system subject to external time-dependent control. Interactions with the environment are modeled by a standard bosonic heat bath. We develop two unitarity-preserving approximation schemes to calculate the reduced density matrix. One of the approximations relies on a short-time factorization of the evolution operator, while the other utilizes expansion in terms of the system-bath coupling strength. Applications are reported for two illustrative systems: an exactly solvable adiabatic model, and a model of a rotating-wave quantum-computing gate function. The approximations are found to produce consistent results at short and intermediate times.

Keywords:

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

B. E. Kane, Nature 393, 133 (1998). Crossref, Web of Science, ADS, Google Scholar
D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998). Crossref, Web of Science, ADS, Google Scholar
V. Privman, I. D. Vagner and G. Kventsel, Phys. Lett. A 239, 141 (1998). Crossref, Web of Science, ADS, Google Scholar
L. Fedichkin, M. Yanchenko and K. A. Valiev, Nanotechnology 11, 392 (2000). Crossref, Web of Science, Google Scholar
Y. Makhlin, G. Schon and A. Shnirman, Rev. Mod. Phys. 73, 357 (2001). Crossref, Web of Science, ADS, Google Scholar
D. Vionet al., Science 296, 886 (2002). Crossref, Web of Science, ADS, Google Scholar
I. Chiorescuet al., Science 299, 1850 (2003). Web of Science, Google Scholar
R. Hansonet al., Phys. Rev. Lett. 91, 196802 (2003). Crossref, Web of Science, Google Scholar
Y. A. Pashkinet al., Nature 421, 823 (2003). Crossref, Web of Science, ADS, Google Scholar
I. Shlimak, HAIT J. Sci. Eng. 1, 196 (2004). Web of Science, Google Scholar
P. W. Shor, Phys. Rev. A 52, R2493 (1995). Crossref, Web of Science, ADS, Google Scholar
A. R. Calderbank and P. W. Shor, Phys. Rev. A 54, 1098 (1996). Crossref, Web of Science, Google Scholar
A. M. Steane, Phys. Rev. Lett. 77, 793 (1996). Crossref, Web of Science, ADS, Google Scholar
D. Aharonov, "Fault-Tolerant Quantum Computation With Constant Error Rate", quant-ph/9906129 . Google Scholar
E. Knill, Phys. Rev. A 71, 042322 (2005). Crossref, Web of Science, Google Scholar
P. Zanardi and M. Rasetti, Phys. Rev. Lett. 79, 3306 (1997). Crossref, Web of Science, ADS, Google Scholar
D. A. Lidar, I. L. Chuang and K. B. Whaley, Phys. Rev. Lett. 81, 2594 (1998). Crossref, Web of Science, ADS, Google Scholar
D. A. Lidaret al., Phys. Rev. A 63, 022306 (2001). Crossref, Web of Science, Google Scholar
L. Viola and S. Lloyd, Phys. Rev. A 58, 2733 (1998). Crossref, Web of Science, ADS, Google Scholar
L. Viola, E. Knill and S. Lloyd, Phys. Rev. Lett. 82, 2417 (1999). Crossref, Web of Science, ADS, Google Scholar
V. Gorini, M. Verri and A. Frigerio, Physica A 161, 357 (1989). Crossref, Web of Science, ADS, Google Scholar
A. Suarez, R. Silbey and I. Oppenheim, J. Chem. Phys. 97, 5101 (1992). Crossref, Web of Science, ADS, Google Scholar
N. G. van Kampen, J. Stat. Phys. 78, 299 (1995). Crossref, Web of Science, ADS, Google Scholar
J. I. Kimet al., Phys. Rev. Lett. 77, 207 (1996). Crossref, Web of Science, ADS, Google Scholar
H. Garbert, P. Schramm and G.-L. Ingold, Phys. Rep. 168, 115 (1998). Crossref, Web of Science, Google Scholar
D. Mozyrsky and V. Privman, J. Stat. Phys. 91, 787 (1998). Crossref, Web of Science, Google Scholar
V. Privman and D. Mozyrsky, Proc. SPIE 4047 (2000) p. 36. Google Scholar
D. Mozyrskyet al., Phys. Rev. B 65, 245213 (2002). Crossref, Web of Science, ADS, Google Scholar
V. Privman, Mod. Phys. Lett. B 16, 459 (2002). Link, Web of Science, ADS, Google Scholar
A. Shnirman and G. Schon, e-print: cond-mat/0210023 at www.arxiv.org . Google Scholar
B. J. Dalton, J. Mod. Opt. 50, 951 (2003). Crossref, Web of Science, ADS, Google Scholar
L. Fedichkin, A. Fedorov and V. Privman, Proc. SPIE 5105 (2003) p. 243. Google Scholar
N. G. van Kampen, J. Stat. Phys. 115, 1057 (2003). Crossref, Web of Science, Google Scholar
V. Privman, Proc. SPIE 5115 (2003) p. 345. Google Scholar
V. Privman, J. Stat. Phys. 110, 957 (2003). Crossref, Web of Science, Google Scholar
L. Fedichkin, A. Fedorov and V. Privman, Phys. Lett. A 328, 87 (2004). Crossref, Web of Science, ADS, Google Scholar
L. Fedichkin and A. Fedorov, Phys. Rev. A 69, 032311 (2004). Crossref, Web of Science, Google Scholar
A. Fedorov, L. Fedichkin and V. Privman, J. Theor. Comp. Nanosci. 1, 132 (2004). Crossref, Web of Science, Google Scholar
D. Solenov and V. Privman, Proc. SPIE 5436 (2004) p. 172. Google Scholar
D. Tolkunov and V. Privman, Phys. Rev. A 69, 062309 (2004). Crossref, Web of Science, Google Scholar
P. G. Averbuch, HAIT J. Sci. Eng. 1, 626 (2005). Google Scholar
D. P. DiVincenzo and D. Loss, Phys. Rev. B 71, 035318 (2005). Crossref, Web of Science, Google Scholar
L. Fedichkin and A. Fedorov, IEEE Trans. Nanotech. 4, 65 (2005). Crossref, Web of Science, ADS, Google Scholar
A. Fedorov and L. Fedichkin, e-print: quant-ph/0502178 at www.arxiv.org . Google Scholar
T. Hakioglu and K. Sarvan, Phys. Rev. B 71, 115115 (2005). Crossref, Web of Science, ADS, Google Scholar
M. A. Nielsen and I. L. Chuang , Quantum Computation and Quantum Information ( Cambridge University Press , 2002 ) . Google Scholar
D. P. DiVincenzo and D. Loss, J. Magnetism Magnetic Mater. 200, 202 (1999). Crossref, Web of Science, ADS, Google Scholar
R. Alickiet al., Phys. Rev. A 65, 062101 (2002). Crossref, Web of Science, Google Scholar
T. Brandes and T. Vorrath, Phys. Rev. B 66, 075341 (2002). Crossref, Web of Science, Google Scholar
T. Brandes, R. Aguado and G. Platero, Phys. Rev. B 69, 205326 (2004). Crossref, Web of Science, Google Scholar
W. H. Louisell , Quantum Statistical Properties of Radiation ( Wiley , New York , 1973 ) . Google Scholar
K. Blum , Density Matrix Theory and Applications ( Plenum Press , New York , 1996 ) . Crossref, Google Scholar
N. G. van Kampen , Stochastic Processes in Physics and Chemistry ( North-Holland , Amsterdam , 2001 ) . Google Scholar
R. P. Feynman and A. R. Hibbs , Quantum Mechanics and Path Integrals ( McGraw-Hill , New York , 1965 ) . Google Scholar
G. W. Ford, M. Kac and P. Mazur, J. Math. Phys. 6, 504 (1965). Crossref, Web of Science, ADS, Google Scholar
A. O. Caldeira and A. J. Leggett, Phys. Rev. Lett. 46, 211 (1981). Crossref, Web of Science, ADS, Google Scholar
A. O. Caldeira and A. J. Leggett, Ann. Phys. 149, 374 (1983). Crossref, Web of Science, ADS, Google Scholar
A. O. Caldeira and A. J. Leggett, Physica A 121, 587 (1983). Crossref, Web of Science, ADS, Google Scholar
S. Chakravarty and A. J. Leggett, Phys. Rev. Lett. 52, 5 (1984). Crossref, Web of Science, ADS, Google Scholar
A. J. Leggettet al., Rev. Mod. Phys. 59, 1 (1987). Crossref, Web of Science, ADS, Google Scholar
X.-T. Liang and Y.-J. Xiong, Phys. Lett. A 332, 8 (2004). Crossref, Web of Science, ADS, Google Scholar
X.-T. Liang and Y.-J. Xiong, Physica B 362, 243 (2005). Crossref, Web of Science, ADS, Google Scholar
X.-T. Liang, "Initial Decoherence and Disentanglement of Open Two-Qubit Systems", quant-ph/0507226 . Google Scholar
W. Magnus, Commun. Pure Appl. Math. 7, 649 (1954). Crossref, Web of Science, Google Scholar
J. A. Oteo and J. Ros, J. Math. Phys. 41, 3268 (2000). Crossref, Web of Science, ADS, Google Scholar
L. Mandel and E. Wolf , Optical coherence and quantum optics ( Cambridge University Press , 1995 ) . Crossref, Google Scholar
A. Abragam , Principles of Nuclear Magnetism ( Oxford University Press , 1999 ) . Google Scholar
J. H. Shirley, Phys. Rev. 138, B979 (1965). Crossref, Web of Science, ADS, Google Scholar
V. I. Ritus, Sov. Phys. JETP 24, 1041 (1967). Google Scholar
Ya. B. Zel'dovich, Sov. Phys. JETP 24, 1006 (1967). Google Scholar
S. Blanes and P. C. Moan, Phys. Lett. A 265, 35 (2000). Crossref, Web of Science, ADS, Google Scholar
V. A. Burdov and D. S. Solenov, Physica E 24, 217 (2004). Crossref, ADS, Google Scholar
G. M. Palma, K. A. Suominen and A. K. Ekert, Proc. Royal Soc. London A 452, 567 (1996). Crossref, Web of Science, ADS, Google Scholar