Abstract
The development of high-capacity memory devices plays an increasingly important role in modern society. High capacities in information storage constitutes a key resource for dealing with the everyday generation of information, as well as for handling the so called Big Data generated in different scientific and technological scenarios. By combining precision metrology and quantum devices such as quantum dots and quantum wires, we propose a quantum memory whose capacity depends on the particular architecture chosen, namely, linear or planar. We show that the geometric disposition of minimal quantum cells or chips is critical in having similar or dramatically outperformed information capacities as compared to current devices. This information is stored in the form of classical bits, though. Realization of such a quantum memory may solve a two-fold problem at the same time: unprecedented higher information capacity with undefined longevity.
We shall obtain as well, by rigorously applying the definition of the exponentiation of a Hermitian matrix, the set of Hamiltonians whose evolution corresponds to the set of universal gates.
Also, Landauer’s principle is a fundamental link between thermodynamics and information theory, which implies that the erasure of information comes at an energetic price, either in classical or quantum computation. In the present contribution we analyze to what extend the usual molecular dynamics (MD) simulation formalism can handle the Landauer’s bound \(k_BT\ln 2\) in the simplest case of one particle treated classically. The erasure of one bit of information is performed by adiabatically varying the shape of a bistable potential in a full cycle. We will highlight the inadequacy of either the microcanonical or canonical ensemble treatments currently employed in MD simulations and propose potential solutions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Voyager NASA mission web site: http://voyager.jpl.nasa.gov/
Hammerer, K., Sorensen, A.S., Polzik, E.S.: 2010 Quantum interface between light and atomic ensembles. Rev. Mod. Phys. 82, 1041–93 (2010)
Choi, K.S., Deng, H., Laurat, J., Kimble, H.J.: Mapping photonic entanglement into and out of a quantum memory. Nature 452, 67–71 (2008)
Zhao, B., Chen, Y-A, Bao, X-H, Strassel, T., Chuu, C-S, Jin, X-M, Schmiedmayer, J., Yuan, Z-S, Chen, S. & Pan, J.W. A millisecond quantum memory for scalable quantum networks. Nature Phys. 5, 95–9 (2008)
Reim, K.F., Nunn, J., Lorenz, V.O., Sussman, B.J., Lee, K.C., Langford, N.K., Jaksch, D., Walmsley, I.A.: Towards high-speed optical quantum memories. Nature Photon. 4, 218–21 (2010)
Schnorrberger, U., Thompson, J.D., Trotzky, S., Pugatch, R., Davidson, N., Kuhr, S., Bloch, I.: Electromagnetically induced transparency and light storage in an atomic Mott insulator. Phys. Rev. Lett. 103, 033003 (2009)
Liu, C., Dutton, Z., Behroozi, C. H. & Hau, L. V. Observation of coherent optical information storage in an atomic medium using halted light pulses. Nature 409, 490–3 (2001)
Julsgaard, B., Sherson, J., Ignacio Cirac, J., Fiurasek, J., Polzik, E.S.: Experimental demonstration of quantum memory for light. Nature 432, 482–6 (2004)
Eisaman, M.D., André, A., Massou, F., Fleischhauer, M., Zibrov, A.S., Lukin, M.D.: Electromagnetically induced transparency with tunable single-photon pulses. Nature 438, 837–41 (2005)
Ran, Y., Xue, L., Hu, S., Su, R.-K.: On the Coulomb-type potential of the one-dimensional Schrödinger equation. J. Phys. A: Math. Gen. 33, 9265–9272 (2000)
Ginzburg, V.L.: Once again about high-temperature superconductivity. Contemp. Phys. 33, 15 (1992)
Brown, J.W., Spector, H.N.: Exciton binding energy in a quantum-well wire. Phys. Rev. B 35, 3009 (1987)
Reyes, J.A., del Castillo-Mussot, M.: Wannier-Mott exciton formed by electron and hole separated in parallel quantum wires. Phys. Rev. B 57, 1690 (1998)
Heeger, A.J., Kivelson, S., Schrieffer, J.R., Su, W.P.: Solitons in conducting polymers. Rev. Mod. Phys. 60, 731 (1988)
Abe, S., Su, W.P.: Excitons and Charge Transfer States in One-Dimensional Semiconductors. Mol. Cryst. Liq. Cryst. 194, 357–362 (1991)
Wigner, E.P.: Effects of the electron interaction on the energy levels of electrons in metals. Trans. Faraday Soc. 34, 678 (1938)
Carr Jr., W.J.: Energy, specific heat, and magnetic properties of the low-density electron gas. Phys. Rev. 122, 1437 (1961)
Andrews, G.E., Askey, R., Roy, R.: Special Functions. Cambridge University Press (1999)
Fowler, R.H., Nordheim, L.W.: Electron emission in intense electric fields. Proc. Roy. Soc. (London) A 119, 173–181 (1928)
Melmed, A.J.: The art of science and other aspects of making sharps tips. J. Vac. Sci. Technol. B 9, 601–608 (1991)
Library of Congress web site: http://www.loc.gov/
Barreiro, A., van der Zant, Herre S.J., Vandersypen, L.M.K.: Quantum Dots at Room Temperature carved out from Few-Layer Graphene. Nano Lett. 12 6096 (2012)
Tsutsui, M., Morikawa, T., Arima, A., Taniguchi, M.: Thermoelectricity in atom-sized junctions at room temperatures. Sci Rep. 3, 3326 (2013)
Deutsch, D.: Proc. Royal Soc. London A 425, 73 (1989)
Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Phys. Rev. A 52, 3457 (1995)
Deutsch, D., Barenco, A., Ekert, A.: Proc. Royal Soc. London 449, 669 (1995)
DiVincenzo, D.P.: Phys, Rev. A 51, 1015 (1995)
Lloyd, S.: Phys. Rev. Lett. 75, 346 (1995)
DiVincenzo, D.P.: Fortschr. Phys. 48, 771 (2000)
Barenco, A.: Proc. R. Soc. Lond. A 449, 679 (1995)
Leff, H.S., Rex, A.F. (eds.): Maxwell’s demon 2: Entropy, Classical and Quantum Information, Computing. Princeton University Press, New Jersey (2003)
Szilard, L.: Z. Phys. 53, 840 (1929)
Brillouin, L.: J. Appl. Phys. 22, 334 (1951)
Landauer, R.: IBM J. Res. Dev. 5(183) (1961); Landauer, R.: Nature 335, 779 (1988); Landauer, R.: Science 272, 1914 (1996)
Bennett, C.H.: Int. J. Theor. Phys. 21, 905 (1982)
Piechocinska, B.: Phys. Rev. A 61, 062314 (2000)
Barkeshli, M.M. (2005). arXiv:cond-mat/0504323
Maroney, O.J.E.: Phys. Rev. E 79, 031105 (2009)
Metawa, N., Elhoseny, M., Kabir Hassan, M., Hassanien, A.: Loan portfolio optimization using genetic algorithm: a case of credit constraints. In: 12th International Computer Engineering Conference (ICENCO), IEEE, 59–64 (2016). doi:10.1109/ICENCO.2016.7856446
Metawa, N., Hassan, M.K., Elhoseny, M.: Genetic algorithm based model for optimizing bank lending decisions, Expert Systems with Applications, vol. 80, 1 September 2017, pp. 75–82, ISSN 0957-4174. doi:10.1016/j.eswa.2017.03.021
Elhoseny, M., Elminir, H., Riad, A., Yuan, X.: Recent advances of secure clustering protocols in wireless sensor networks. Int. J. Comput. Netw. Commun. Secur. 2(11), 400–413 (2014)
Elhoseny, M., Yuan, X., El-Minir, H.K., Riad, A.M.: Riad, an energy efficient encryption method for secure dynamic WSN. Secur. Commun. Netw. 9, 2024–2031 (2016)
Sagawa, T., Ueda, M.: Phys. Rev. Lett. 100, 80403 (2008)
Bremermann, B.: Int. J. Theor. Phys. 21(203) (1982); Lloyd, S., Zurek, W.H.: J. Stat. Phys. 62(819) (1991); Caves, C.M., Drummond, P.M.: Rev. Mod. Phys. 66(481) (1994); Magnasco, M.O.: Europhys. Lett. 33(583) (1996); Zurek, W.H.: arXiv:quant-ph/0301076 (2003); Scully, M.O. et al. Science 299(862) (2003); Kieu, T.D.: Phys. Rev. Lett. 93, 140–403 (2004); Allahverdyan, A.E., et al.: J. Mod. Optics 51(2703) (2004); Maruyama, K., et al.: J. Phys. A 38(7175) (2005); Quan, H.T. et al.: Phys. Rev. Lett. 97(180402) (2006); Maruyama, K. et al.: Rev. Mod. Phys. 81(1) (2009)
Elhoseny, M., Yuan, X., Yu, Z., Mao, C., El-Minir, H.K., Riad, A.M.: Balancing energy consumption in heterogeneous wireless sensor networks using genetic algorithm. IEEE Commun. Lett. (99), 1–4 (2014)
Riad, A.M., El-minir, H.K., Elhoseny, M.: Secure routing in wireless sensor network: a state of the art. Int. J. Comput. Appl. 67(7) (2013)
Jarzynski, C.: Phys. Rev. Lett. 78(2690) (1997); Crooks, G.E.: Phys. Rev. E 60(2721) (1999); Mukamel, S.: Phys. Rev. Lett. 90(170604) (2003); Kawai, R.: et al. Phys. Rev. Lett. 98(80602) (2007); J. Liphardt et al. Science 296(1832) (2002); Collin, M. et al.: Nature 437(231) (2005)
Bérut, A., et al.: Nature 483, 187 (2012)
Vedral, V.: Proc. Roy. Soc. Lond. 456, 969 (1996)
Plenio, M.B.: Phys. Lett. A 263, 281 (1999)
Holevo, A.S.: Probl. Inf. Transm. 9, 3 (1973)
Pati, A.K., Braunstein, S.L.: Nature 404, 164 (2000)
Hilt, S., Shabbir, S., Anders, J., Lutz, E.: Phys. Rev. E 83, 030102 (2011)
Alder, B.J., Wainwright, T.E.: J. Chem. Phys. 27(1208) (1957); Alder, B.J., Wainwright, T.E.: J. Chem. Phys. 31(459) (1959)
Rahman, A.: Phys. Rev. 136, 405 (1964)
Elhoseny, M., Farouk, A., Zhou, N., Wang, M.-M., Abdalla, S., Batle, J.: Dynamic multi-hop clustering in a wireless sensor network: Performance improvement. Wirel. Pers. Commun., 121 (2017)
Elhoseny, M., Yuan, X., Yu, Z., Mao, C., El-Minir, H.K., Riad, A.M.: Balancing energy consumption in heterogeneous wireless sensor networks using genetic algorithm. IEEE Commun. Lett. (99), 1–4 (2014)
Yuan, X., Elhoseny, M., Minir, H., Riad, A.: A genetic algorithm-based, dynamic clustering method towards improved WSN longevity. J. Netw. Syst. Manage., 1–26, Springer US (2016). doi:10.1007/s10922-016-9379-7
Elhoseny, M., Yuan, X., El-Minir, H.K., Riad, A.M.: An energy efficient encryption method for secure dynamic WSN. Secur. Commun. Netw. (9), 2024–2031 (2016)
Verlet, L.: Phys. Rev. 159(98) (1964); Verlet, L.: Phys. Rev. 165(201) (1968)
Frenkel, D., Smit, B.: Understanding Molecular Simulation (Academic Press, San Diego, 1996). Computer Simulation of Liquids (Claredon Press, Oxford, M. P. Allen and D. J. Tildesley (1986)
Zurek, W.H.: Maxwell’s Demon, Szilard’s Engine and Quantum Measurements, Frontiers of Nonequilibrium Statistical Physics 135, 151. Plenum Press, New York (1986)
Nosé, S.: J. Chem. Phys. 81(511) (1984); Hoover, W.G.: Phys. Rev. A 31(1695) (1985)
Kumar Patra, P., Bhattacharya, B.: Phys. Rev. E 90, 43304 (2014)
Tsallis, C.: J. Stat. Phys. 52(479) (1988); Gell-Mann, M.: C. Tsallis (Eds.), Nonextensive Entropy: Interdisciplinary Applications. Oxford University Press, New York (2004); C. Tsallis, Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World. Springer, New York (2009)
Pekola, J.P., Suomela, S., Galperin, Y.M.: J. Low Temp. Phys. 184, 1015 (2016)
Acknowledgements
J. Batle acknowledges fruitful discussions with J. Rosselló, Maria del Mar Batle and Regina Batle.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Batle, J., Elhoseny, M., Farouk, A. (2018). Proposal for a Quantum-Based Memory for Storing Classical Information and the Connection Between Molecular Dynamics Simulations and the Landauer’s Principle. In: Hassanien, A., Elhoseny, M., Kacprzyk, J. (eds) Quantum Computing:An Environment for Intelligent Large Scale Real Application . Studies in Big Data, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-319-63639-9_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-63639-9_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-63638-2
Online ISBN: 978-3-319-63639-9
eBook Packages: EngineeringEngineering (R0)