Quantum computation in triangular decoherence-free subdynamic space

Qiao Bi

PDF(195 KB)
PDF(195 KB)
Front. Phys. ›› 2015, Vol. 10 ›› Issue (2) : 100304. DOI: 10.1007/s11467-015-0461-5
RESEARCH ARTICLE
RESEARCH ARTICLE

Quantum computation in triangular decoherence-free subdynamic space

Author information +
History +

Abstract

A formalism of quantum computing with 2000 qubits or more in decoherence-free subspaces is presented. The subspace is triangular with respect to the index related to the environment. The quantum states in the subspaces are projected states ruled by a subdynamic kinetic equation. These projected states can be used to perform general, large-scale decoherence-free quantum computing.

Keywords

quantum information / subdynamics / decoherence-free

Cite this article

Download citation ▾
Qiao Bi. Quantum computation in triangular decoherence-free subdynamic space. Front. Phys., 2015, 10(2): 100304 https://doi.org/10.1007/s11467-015-0461-5

References

[1]
D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I. O. Stamatescu, and H. D. Zeh, Decoherence and The Appearance of A Classical World in Quantum Theory, Heidelberg: Springer-Verlag, 1996
CrossRef ADS Google scholar
[2]
P. Zanardi and M. Rasetti, Error avoiding quantum codes, Mod. Phys. Lett. B11(25), 1085 (1997)
CrossRef ADS Google scholar
[3]
P. Zanardi and M. Rasetti, Noiseless quantum codes, Phys. Rev. Lett.79(17), 3306 (1997)
CrossRef ADS Google scholar
[4]
P. Zanardi, Virtual quantum subsystems, Phys. Rev. Lett87(7), 077901 (2001)
CrossRef ADS Google scholar
[5]
A. Barenco, A. Berthiaume, D. Deutsch, A. Ekert, R. Jozsa, and C. Macchiavello, Stabilization of quantum computations by symmetrization, SIAM J. Comput.26(5), 1541 (1997)
CrossRef ADS Google scholar
[6]
L. M. Duan and G. C. Guo, Preserving coherence in quantum computation by pairing quantum bits, Phys. Rev. Lett.79(10), 1953 (1997)
CrossRef ADS Google scholar
[7]
D. A. Lidar, I. L. Chuang, and K. B. Whaley, Decoherence Free Subspaces for Quantum Computation, Phys. Rev. Lett.81(12), 2594 (1998)
CrossRef ADS Google scholar
[8]
A. Shabani and D. A. Lidar, Maps for general open quantum systems and a theory of linear quantum error correction, Phys. Rev. A80(1), 012309 (2009)
CrossRef ADS Google scholar
[9]
O. Oreshkov, T. A. Brun, D. A. Lidar, and H. Q. C. Fault-Tolerant, Fault-Tolerant Holonomic Quantum Computation, Phys. Rev. Lett.102(7), 070502 (2009)
CrossRef ADS Google scholar
[10]
T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, Quantum computer, Nature464, 45 (2010)
CrossRef ADS Google scholar
[11]
P. Huang, X. Kong, N. Zhao, F. Shi, P. Wang, X. Rong, R. B. Liu, and J. Du, Observation of an anomalous decoherence effect in a quantum bath at room temperature, Nat. Commun.2, 570 (2011)
CrossRef ADS Google scholar
[12]
S. D. Filippo, Quantum computation using decoherence-free states of the physical operator algebra, Phys. Rev. A62(5), 052307 (2000)
CrossRef ADS Google scholar
[13]
C. Schön and A. Beige, Analysis of a two-atom double-slit experiment based on environment-induced measurements, Phys. Rev. A64(2), 023806 (2001)
CrossRef ADS Google scholar
[14]
L. Viola, Quantum control via encoded dynamical decoupling, Phys. Rev. A66(1), 012307 (2002)
CrossRef ADS Google scholar
[15]
S. Gheorghiu-Svirschevski, From Davydov solitons to decoherence-free subspaces: Self-consistent propagation of coherent-product states, Phys. Rev. E64(5), 051907 (2001)
CrossRef ADS Google scholar
[16]
Q. Bi, H. E. Ruda, and M. S. Zhan, Two-qubit quantum computing in a projected subspace, Phys. Rev. A65(4), 042325 (2002)
CrossRef ADS Google scholar
[17]
M. S. Tame, M. Paternostro, and M. S. Kim, One-way quantum computing in a decoherence-free subspace, New J. Phys.9(6), 201 (2007)
CrossRef ADS Google scholar
[18]
C. Bény, A. Kempf, and D. W. Kribs, Generalization of quantum error correction via the heisenberg picture, Phys. Rev. Lett.98(10), 100502 (2007)
CrossRef ADS Google scholar
[19]
D. A. Lidar and K. B. Whaley, in: Irreversible Quantum Dynamics, edited by F. Benatti and R. Floreanini, Leture Notes in Physics 622, 83, Berlin: Springer, 2003
[20]
H. K. Ng, D. A. Lidar, and J. Preskill, Combining dynamical decoupling with fault-tolerant quantum computation, Phys. Rev. A84, 012305 (2001)
CrossRef ADS Google scholar
[21]
L. Viola, S. Lloyd, and E. Knill, Universal control of decoupled quantum systems, Phys. Rev. Lett.83(23), 4888 (1999)
CrossRef ADS Google scholar
[22]
M. S. Byrd and D. A. Lidar, Comprehensive encoding and decoupling solution to problems of decoherence and design in solid-state quantum computing, Phys. Rev. Lett.89(4), 047901 (2002)
CrossRef ADS Google scholar
[23]
K. Khodjasteh and D. A. Lidar, Erratum: Quantum computing in the presence of spontaneous emission by a combined dynamical decoupling and quantum-error-correction strategy [Phys. Rev. A 68, 022322 (2003)], Phys. Rev. A72(2), 029905 (2005)
CrossRef ADS Google scholar
[24]
A. Sinatra, J. C. Dornstetter, and Y. Castin, Spin squeezing in Bose–Einstein condensates: Limits imposed by decoherence and non-zero temperature, Front. Phys.7, 86 (2012)
CrossRef ADS Google scholar
[25]
H. Wei, Z. J. Deng, W. L. Yang, and F. Zhou, Cavity quantum networks for quantum information processing in decoherence-free subspace, Front. Phys. China4(1), 21 (2009)
CrossRef ADS Google scholar
[26]
N. Boulant, M. A. Pravia, E. M. Fortunato, T. F. Havel, and D. G. Cory, Experimental con-catenation of quantum error correction with decoupling, Quantum Inf. Proc.1, 135 (2002)
CrossRef ADS Google scholar
[27]
J. Jing and L. A. Wu, Control of decoherence with no control, Scientific Reports3, 2746 (2013)
CrossRef ADS Google scholar
[28]
F. Dolde, V. Bergholm, , High-fidelity spin entanglement using optimal control, Nat. Commun.3, 4371 (2014)
[29]
N. Y. Yao, C. R. Laumann, A. V. Gorshkov, H. Weimer, L. Jiang, J. I. Cirac, P. Zoller, and M. D. Lukin, Topologically protected quantum state transfer in a chiral spin liquid, Nat. Commun.4, 1585 (2013)
CrossRef ADS Google scholar
[30]
I. Antoniou and S. Tasaki, Generalized spectral decompositions of mixing dynamical systems, Int. J. Quantum Chem.46(3), 425 (1993)
CrossRef ADS Google scholar
[31]
T. Petrosky and I. Prigogine, Alternative formulation of classical and quantum dynamics for non-integrable systems, Physica A175(1), 146 (1991)
CrossRef ADS Google scholar
[32]
Qiao Bi, Subdynamics Theory and Application in Complex Dynamical System, Wuhan: Wuhan University of Technology Press, 1998 (in Chinese)
[33]
A. Bohm, H. D. Doebner, and P. Kielanowski, Irreversibility and Causality, Semigroups and Rigged Hilbert Spaces, Heidelberg: Springer-Verlag, 1998
CrossRef ADS Google scholar
[34]
A. Bohm and M. Gadella, Dirac Kets, Gamow Vector and Gel’fand Triplets, Heidelberg: Springer-Verlag, 1989
[35]
Q. Bi and H. E. Ruda, Quantum computing using entanglement states in a photonic band gap, J. Appl. Phys.86(9), 5237 (1999)
CrossRef ADS Google scholar
[36]
R. Balescu, Equilibrium and Non-Equilibrium Statistical Mechanics, New York: John Wiley & Sons, 1975.
[37]
Q. Bi, Some charicteristics and applications for quantum information, Journal of Modern Physics03(09), 1070 (2012)
CrossRef ADS Google scholar
[38]
B. E. Kane, A silicon-based nuclear spin quantum computer, Nature393(6681), 133 (1998)
CrossRef ADS Google scholar
[39]
R. Vrijen, E. Yablonovitch, K. Wang, H. W. Jiang, A. Balandin, V. Roychowduhory, T. Mor, and D. DiVincenzo, Electron-spin-resonance transistors for quantum computing in silicon-germanium heterostructures, Phys. Rev. A62(1), 012306 (2000)
CrossRef ADS Google scholar
[40]
D. Loss and D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A57(1), 120 (1998)
CrossRef ADS Google scholar
[41]
W. A. Coish and D. Loss, Quantum computing with spins in solids, arXiv: cond-mat/0606550 (2006)
[42]
D. Kribs, R. La.amme, and D. Poulin, Unified and generalized approach to quantum error correction, Phys. Rev. Lett.94(18), 180501 (2005)
CrossRef ADS Google scholar
[43]
D. W. Kribs, R. La.amme, D. Poulin, and M. Lesosky, Operator quantum error correction, Quantum Inf. Compu.6, 382 (2006)
[44]
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. Wootters, Mixed-state entanglement and quantum error correction, Phys. Rev. A54(5), 3824 (1996)
CrossRef ADS Google scholar

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
AI Summary AI Mindmap
PDF(195 KB)

Accesses

Citations

Detail

Sections
Recommended

/