Characterization of decoherence processes in quantum computation
Optics Express, Vol. 2, Issue 9, pp. 372377 (1998)
http://dx.doi.org/10.1364/OE.2.000372
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Abstract
We show how the dynamics of open quantum systems can be fully characterized by using quantum tomography methods. We apply these methods to the case of an ion trap quantum computer, which does not operate under ideal conditions due to coupling to several environments. We study the performance of a fundamental two–bit quantum gate as a function of various parameters related to the interaction of the ions with external laser fields.
© Optical Society of America
1. Introduction
1. A. Ekert, “From quantumcodemakingto quantum codebreaking,” Report No. quantph/9703035, (Los Alamos Nat. Laboratory, Albuquerky, NM, 1997), and references therein. http://xxx.lanl.gov/abs/quantph/9703035
2. D. P. Divincenzo, “Topics in Quantum Computers,” Report No. condmat/9612126 (Los Alamos Nat. Laboratory, Albuquerky, NM, 1996), and references therein. http://xxx.lanl.gov/abs/condmat/9612126
2. D. P. Divincenzo, “Topics in Quantum Computers,” Report No. condmat/9612126 (Los Alamos Nat. Laboratory, Albuquerky, NM, 1996), and references therein. http://xxx.lanl.gov/abs/condmat/9612126
3. J. F. Poyatos, J. I. Cirac, and P. Zoller, “Complete Characterization of a Quantum Process: The twobit Quantum Gate,” Phys. Rev. Lett. 78 , 390, (1997). http://info.uibk.ac.at/c/c7/c705/qo/pub/pub96.html [CrossRef]
4. J. I. Cirac and P. Zoller, “Quantum Computations with Cold Trapped Ions,” Phys. Rev. Lett. 74, 4091, (1995). [CrossRef] [PubMed]
3. J. F. Poyatos, J. I. Cirac, and P. Zoller, “Complete Characterization of a Quantum Process: The twobit Quantum Gate,” Phys. Rev. Lett. 78 , 390, (1997). http://info.uibk.ac.at/c/c7/c705/qo/pub/pub96.html [CrossRef]
5. I. Chuang and M. A. Nielsen, “Prescription for experimental determination of the dynamics of a quantum black box,” Report No. quantph/9610001 (Los Alamos Nat. Laboratory, Albuquerky, NM, 1997).http://xxx.lanl.gov/abs/quantph/9610001
2. Characterizing open quantum systems
3. J. F. Poyatos, J. I. Cirac, and P. Zoller, “Complete Characterization of a Quantum Process: The twobit Quantum Gate,” Phys. Rev. Lett. 78 , 390, (1997). http://info.uibk.ac.at/c/c7/c705/qo/pub/pub96.html [CrossRef]
3. The trapped ion quantum gate
6. William K. Wootters, “A Wignerfunction formulation of finitestate quantum mechanics,” Ann. Phys. 176, 121, (1987) [CrossRef]
3. J. F. Poyatos, J. I. Cirac, and P. Zoller, “Complete Characterization of a Quantum Process: The twobit Quantum Gate,” Phys. Rev. Lett. 78 , 390, (1997). http://info.uibk.ac.at/c/c7/c705/qo/pub/pub96.html [CrossRef]
8. C. H Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. Wooters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722, (1996) [CrossRef] [PubMed]
9. A. Peres, “Separability Criterion for Density Matrices,” Phys. Rev. Lett. 77, 1413 (1996). http://xxx.lanl.gov/abs/quantph/9604005 [CrossRef] [PubMed]
10. M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of Mixed States: Necessary and Sufficient Conditions,” Report No. quantph/9605038 (Los Alamos Nat. Laboratory,Albuquerky, NM, 1996). http://xxx.lanl.gov/abs/quantph/9605038
6. William K. Wootters, “A Wignerfunction formulation of finitestate quantum mechanics,” Ann. Phys. 176, 121, (1987) [CrossRef]
4. Conclusions
Footnotes
†  also with Departamento de Física Aplicada, Universidad de CastillaLa Mancha, 13071 Ciudad Real, Spain 
References and links
1.  A. Ekert, “From quantumcodemakingto quantum codebreaking,” Report No. quantph/9703035, (Los Alamos Nat. Laboratory, Albuquerky, NM, 1997), and references therein. http://xxx.lanl.gov/abs/quantph/9703035 
2.  D. P. Divincenzo, “Topics in Quantum Computers,” Report No. condmat/9612126 (Los Alamos Nat. Laboratory, Albuquerky, NM, 1996), and references therein. http://xxx.lanl.gov/abs/condmat/9612126 
3.  J. F. Poyatos, J. I. Cirac, and P. Zoller, “Complete Characterization of a Quantum Process: The twobit Quantum Gate,” Phys. Rev. Lett. 78 , 390, (1997). http://info.uibk.ac.at/c/c7/c705/qo/pub/pub96.html [CrossRef] 
4.  J. I. Cirac and P. Zoller, “Quantum Computations with Cold Trapped Ions,” Phys. Rev. Lett. 74, 4091, (1995). [CrossRef] [PubMed] 
5.  I. Chuang and M. A. Nielsen, “Prescription for experimental determination of the dynamics of a quantum black box,” Report No. quantph/9610001 (Los Alamos Nat. Laboratory, Albuquerky, NM, 1997).http://xxx.lanl.gov/abs/quantph/9610001 
6.  William K. Wootters, “A Wignerfunction formulation of finitestate quantum mechanics,” Ann. Phys. 176, 121, (1987) [CrossRef] 
7.  J. F. Poyatos, J. I. Cirac, and P. Zoller, “Quantum Computations with Trapped Ions at nonzero Temperature,” (unpublished). 
8.  C. H Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. Wooters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722, (1996) [CrossRef] [PubMed] 
9.  A. Peres, “Separability Criterion for Density Matrices,” Phys. Rev. Lett. 77, 1413 (1996). http://xxx.lanl.gov/abs/quantph/9604005 [CrossRef] [PubMed] 
10.  M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of Mixed States: Necessary and Sufficient Conditions,” Report No. quantph/9605038 (Los Alamos Nat. Laboratory,Albuquerky, NM, 1996). http://xxx.lanl.gov/abs/quantph/9605038 
OCIS Codes
(000.6800) General : Theoretical physics
(270.0270) Quantum optics : Quantum optics
ToC Category:
Focus Issue: Control of loss and decoherence in quantum systems
History
Original Manuscript: November 14, 1997
Published: April 27, 1998
Citation
Juan Poyatos, Ignacio Cirac, and Peter Zoller, "Characterization of decoherence processes in
quantum computation," Opt. Express 2, 372377 (1998)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe29372
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References

A. Ekert, "From quantumcodemaking to quantum codebreaking," Report No. quantph/9703035, (Los Alamos Nat. Laboratory, Albuquerky, NM, 1997), and references therein. http://xxx.lanl.gov/abs/quantph/9703035

D. P. Divincenzo, "Topics in Quantum Computers," Report No. condmat/9612126 (Los Alamos Nat. Laboratory, Albuquerky, NM, 1996), and references therein. http://xxx.lanl.gov/abs/condmat/9612126

J.F. Poyatos, J.I. Cirac and P. Zoller, "Complete Characterization of a Quantum Process: The twobit Quantum Gate," Phys. Rev. Lett. 78 , 390, (1997). http://info.uibk.ac.at/c/c7/c705/qo/pub/pub96.html
[CrossRef] 
J. I. Cirac and P. Zoller, "Quantum Computations with Cold Trapped Ions," Phys. Rev. Lett. 74, 4091, (1995).
[CrossRef] [PubMed] 
I. Chuang and M. A. Nielsen, "Prescription for experimental determination of the dynamics of a quantum black box," Report No. quantph/9610001 (Los Alamos Nat. Laboratory, Albuquerky, NM, 1997). http://xxx.lanl.gov/abs/quantph/9610001

William K. Wootters, "A Wignerfunction formulation of finitestate quantummechanics," Ann. Phys. 176, 121, (1987)
[CrossRef] 
J. F. Poyatos, J. I. Cirac and P. Zoller, "Quantum Computations with Trapped Ions at nonzero Temperature," (unpublished).

C. H Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin and W. Wooters, "Purification of noisy entanglement and faithful teleportation via noisy channels," Phys. Rev. Lett. 76, 722, (1996)
[CrossRef] [PubMed] 
A. Peres, "Separability Criterion for Density Matrices," Phys. Rev. Lett. 77, 1413 (1996). http://xxx.lanl.gov/abs/quantph/9604005
[CrossRef] [PubMed] 
M. Horodecki, P. Horodecki, and R. Horodecki, "Separability of Mixed States: Necessary and Sufficient Conditions," Report No. quantph/9605038 (Los Alamos Nat. Laboratory, Albuquerky, NM, 1996). http://xxx.lanl.gov/abs/quantph/9605038
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