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Algorithmic Cooling

1999; Schulman, Vazirani 2002; Boykin, Mor, Roychowdhury, Vatan, Vrijen

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Encyclopedia of Algorithms

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Keywords and Synonyms

Algorithmic cooling of spins;  Heat-bath algorithmic cooling          

Problem Definition

The fusion of concepts taken from the fields of quantum computation, data compression, and thermodynamics, has recently yielded novel algorithms that resolve problems in nuclear magnetic resonance and potentially in other areas as well; algorithms that “cool down” physical systems.

  • A leading candidate technology for the construction of quantum computers is Nuclear Magnetic Resonance (NMR). This technology has the advantage of being well-established for other purposes, such as chemistry and medicine. Hence, it does not require new and exotic equipment, in contrast to ion traps and optical lattices, to name a few. However, when using standard NMR techniques (not only for quantum computing purposes) one has to live with the fact that the state can only be initialized in a very noisy manner: The particles' spins point in mostly random directions, with only a tiny bias towards the...

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Notes

  1. 1.

    Quantum Computing entries in this encyclopedia, e.g. Quantum Dense Coding

  2. 2.

    This constant, γ, is thus responsible for the difference in equilibrium polarization bias [e. g., a hydrogen nucleus is 4 times more polarized than a carbon isotope \( {^{13} } \)C nucleus, but about 103 less polarized than an electron spin].

  3. 3.

    Furthermore, individual addressing of each spin during the algorithm requires a slightly different bias for each.

  4. 4.

    When the entire process is RPC, namely, any of the processes that follow SV ideas, one can refer to it as reversible AC or closed-system AC, rather than as RPC.

Recommended Reading

  1. Baugh, J., Moussa, O., Ryan, C.A., Nayak, A., Laflamme, R.: Experimental implementation of heat-bath algorithmic cooling using solid-state nuclear magnetic resonance. Nature 438, 470–473 (2005)

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  2. Boykin, P.O., Mor, T., Roychowdhury, V., Vatan, F., Vrijen, R.: Algorithmic cooling and scalable NMR quantum computers. Proc. Natl. Acad. Sci. 99, 3388–3393 (2002)

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  3. Brassard, G., Elias, Y., Fernandez, J.M., Gilboa, H., Jones, J.A., Mor, T., Weinstein, Y., Xiao, L.: Experimental heat-bath cooling of spins. Submitted to Proc. Natl. Acad. Sci. USA. See also quant-ph/0511156 (2005)

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  4. Chang, D.E., Vandersypen, L.M.K., Steffen, M.: NMR implementation of a building block for scalable quantum computation. Chem. Phys. Lett. 338, 337–344 (2001)

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  5. Cory, D.G., Fahmy, A.F., Havel, T.F.: Ensemble quantum computing by NMR spectroscopy. Proc. Natl. Acad. Sci. 94, 1634–1639 (1997)

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  6. Elias, Y., Fernandez, J.M., Mor, T., Weinstein, Y.: Optimal algorithmic cooling of spins. Isr. J. Chem. 46, 371–391 (2006), also in: Ekl, S. et al. (eds.) Lecture Notes in Computer Science, Volume 4618, pp. 2–26. Springer, Berlin (2007), Unconventional Computation. Proceedings of the Sixth International Conference UC2007 Kingston, August 2007

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  7. Fernandez, J.M.: De computatione quantica. Dissertation, University of Montreal (2004)

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  8. Fernandez, J.M., Lloyd, S., Mor, T., Roychowdhury V.: Practicable algorithmic cooling of spins. Int. J. Quant. Inf. 2, 461–477 (2004)

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  9. Gershenfeld, N.A., Chuang, I.L.: Bulk spin-resonance quantum computation. Science 275, 350–356 (1997)

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  10. Mor, T., Roychowdhury, V., Lloyd, S., Fernandez, J.M., Weinstein, Y.: Algorithmic cooling. US Patent 6,873,154 (2005)

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  11. Schulman, L.J., Mor, T., Weinstein, Y.: Physical limits of heat-bath algorithmic cooling. Phys. Rev. Lett. 94, 120501, pp. 1–4 (2005)

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  12. Schulman, L.J., Mor, T., Weinstein, Y.: Physical limits of heat-bath algorithmic cooling. SIAM J. Comput. 36, 1729–1747 (2007)

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  13. Schulman, L.J., Vazirani, U.: Molecular scale heat engines and scalable quantum computation. Proc. 31st ACM STOC, Symp. Theory of Computing,pp. 322–329 Atlanta, 01–04 May 1999

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  14. Sørensen, O.W.: Polarization transfer experiments in high-resolution NMR spectroscopy. Prog. Nuc. Mag. Res. Spect. 21, 503–569 (1989)

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Author information

Authors and Affiliations

  1. Department of Computer Science, Technion, Haifa, Israel

    Tal Mor

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  1. Tal Mor
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Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Mor, T. (2008). Algorithmic Cooling. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_8

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