Abstract
Evolution of quantum states of array of quantum dots is analyzed by means of numerical solution of the von Neumann equation. For two qubit system with dipole–dipole interaction and common phonon bath the evolution of the symmetric state \(\frac{{ \uparrow \downarrow + \downarrow \uparrow }}{{\sqrt 2 }}\) leads to the mixture of the triplet states, leaving the singlet decoupled. For three qubit system \(\left( {D_{1/2}^{ \otimes 3} = D_{3/2} + 2D_{1/2} } \right)\) with common phonon bath we observed similar effects within the quartet state D3/2 if all qubits were symmetrically connected.
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References
R. Feynman, Int. J. Theor. Phys. 21, 467 (1982).
D. Deutsch and R. Jozsa, Proc. Roy. Soc. Lond. A 439, 553 (1992).
M. W. Johnson, M. H. S. Amin, S. Gildert, T. Lanting, F. Hamze, N. Dickson, R. Harris, A. J. Berkley, J. Johansson, P. Bunyk, et al., Nature 473, 194 (2011).
S. Haykin, Neural Networks (Pearson Education, 1999).
N. G. Berloff, M. Silva, K. Kalinin, A. Askitopoulos, J. D. Töpfer, P. Cilibrizzi, W. Langbein, and P. G. Lagoudakis, Nat. Mater. 16, 1120 (2017).
E. Cohen and B. Tamir, Int. J. Quant. Inf. 12, 1430002 (2014).
M. Schuld, I. Sinayskiy, and F. Petruccione, Quantum Information Processing 13, 2567 (2014).
V. Chavchanidze, Soobshch. ANGruzinskoi SSR 59, 37 (1970).
F. Beck and J. Eccles, PNAS 89, 11357 (1992).
E. Behrman, L. Nash, J. Steck, V. Chandrashekar, and S. Skinner, Inf. Sci. 128, 257 (2000).
M. Altaisky, N. Kaputkina, and V. Krylov, Phys. Part. Nucl. 45, 1013 (2014).
M. Altaisky, N. Zolnikova, N. Kaputkina, V. Krylov, Y. E. Lozovik, and N. Dattani, App. Phys. Lett. 108, 103108 (2016).
Y. E. Lozovik and N. Kaputkina, Phys. Stat. Sol. B 207, 147 (1998).
N. E. Kaputkina and Y. E. Lozovik, Phys. Solid State 40, 1594 (1998).
F. J. Rodríguez, L. Quiroga, and N. F. Johnson, Phys. Rev. B 66, 161302 (2002).
M. Altaisky, N. Zolnikova, N. Kaputkina, V. Krylov, Y. E. Lozovik, and N. Dattani, Photonics and Nanostructures—Fundamentals and Applications 24, 24 (2017).
P. Zanardi and M. Rasetti, Phys. Rev. Lett. 79, 3306 (1997).
R. P. Feynman and F. L. Vernon Jr., Ann. Phys. 24, 118 (1963).
N. Makri and D. E. Makarov, J. Chem. Phys. 102, 4611 (1995).
C. Bennet, D. Di Vincenzo, J. Smolin, and W. Wooters, Phys. Rev. A 54, 3824 (1996).
M. Altaisky, N. Zolnikova, N. Kaputkina, A. Krylov, Y. E. Lozovik, and N. Dattani, Eur. Phys. J. WebConf. 108, 02006 (2016).
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Altaisky, M.V., Kaputkina, N.E. & Krylov, V.A. Symmetry and Decoherence-Free Subspaces in Quantum Neural Networks. Phys. Atom. Nuclei 81, 792–798 (2018). https://doi.org/10.1134/S1063778818060030
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DOI: https://doi.org/10.1134/S1063778818060030