Abstract
Algorithmic Cooling (AC) of Spins is potentially the first near-future application of quantum computing devices. Straightforward quantum algorithms combined with novel entropy manipulations can result in a method to improve the identification of molecules.
We introduce here several new exhaustive cooling algorithms, such as the Tribonacci and k-bonacci algorithms. In particular, we present the “all-bonacci” algorithm, which appears to reach the maximal degree of cooling obtainable by the optimal AC approach.
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Boykin, P.O., Mor, T., Roychowdhury, V., Vatan, F., Vrijen, R.: Algorithmic cooling and scalable NMR quantum computers. Proc. Natl. Acad. Sci. 99(6), 3388–3393 (2002)
Fernandez, J.M., Lloyd, S., Mor, T., Rowchoudury, V.: Algorithmic cooling of spins: A practicable method for increasing polarisation. Int. J. Quant. Inf. 2(4), 461–467 (2004)
Mor, T., Roychowdhury, V., Lloyd, S., Fernandez, J.M., Weinstein, Y.: US patent No. 6,873,154 (2005)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, New York (1991)
Brassard, G., Elias, Y., Fernandez, J.M., Gilboa, H., Jones, J.A., Mor, T., Weinstein, Y., Xiao, L.: Experimental heat-bath cooling of spins. Proc. Natl. Acad. Sci. USA (submitted) (also in arXiv:quant-ph/0511156)
Morris, G.A., Freeman, R.: Enhancement of nuclear magnetic resonance signals by polarization transfer. J. Am. Chem. Soc. 101, 760–762 (1979)
Sørensen, O.W.: Polarization transfer experiments in high-resolution NMR spectroscopy. Prog. Nucl. Mag. Res. Spec. 21, 503–569 (1989)
Schulman, L.J., Vazirani, U.V.: Scalable NMR quantum computation. In: Proceedings of ACM Symposium on the Theory of Computing (STOC), pp. 322–329. ACM Press, New York (1999)
Farrar, C.T., Hall, D.A., Gerfen, G.J., Inati, S.J., Griffin, R.G.: Mechanism of dynamic nuclear polarization in high magnetic fields. J. Chem. Phys. 114, 4922–4933 (2001)
Slichter, C.P.: Principles of Magnetic Resonance, 3rd edn. Springer, Heidelberg (1990)
Ardenkjær-Larsen, J.H., Fridlund, B., Gram, A., Hansson, G., Hansson, L., Lerche, M.H., Servin, R., Thaning, M., Golman, K.: Increase in signal-to-noise ratio of > 10,000 times in liquid-state NMR. Proc. Natl. Acad. Sci. 100, 10158–10163 (2003)
Anwar, M., Blazina, D., Carteret, H., Duckett, S.B., Halstead, T., Jones, J.A., Kozak, C., Taylor, R.: Preparing high purity initial states for nuclear magnetic resonance quantum computing. Phys. Rev. Lett. 93 (2004) (also in arXiv:quant-ph/0312014)
Oros, A.M., Shah, N.J.: Hyperpolarized xenon in NMR and MRI. Phys. Med. Biol. 49, R105–R153 (2004)
Emsley, L., Pines, A.: Lectures on pulsed NMR. In: Nuclear Magnetic Double Resonance, Proceedings of the CXXIII School of Physics “Enrico Fermi”, 2nd edn., p. 216. World Scientific, Amsterdam (1993)
Elias, Y., Fernandez, J.M., Mor, T., Weinstein, Y.: Algorithmic cooling of spins. Isr. J. Chem. (to be published on 2007)
Fernandez, J.M.: De computatione quantica. PhD thesis, University of Montreal, Canada (2003)
Weinstein, Y.: Quantum computation and algorithmic cooling by nuclear magnetic resonance. Master’s thesis, Physics Department, Technion - Israel Institute of Technology (August 2003)
Schulman, L.J., Mor, T., Weinstein, Y.: Physical limits of heat-bath algorithmic cooling. SIAM J. Comp. 36, 1729–1747 (2007)
Schulman, L.J., Mor, T., Weinstein, Y.: Physical limits of heat-bath algorithmic cooling. Phys. Rev. Lett. 94, 120501 (2005)
Cory, D.G., Fahmy, A.F., Havel, T.F.: Nuclear magnetic resonance spectroscopy: an experimentally accessible paradigm for quantum computing. In: Proceedings of PhysComp96, pp. 87–91 (1996)
Cory, D.G., Fahmy, A.F., Havel, T.F.: Ensemble quantum computing by nuclear magnetic resonance spectroscopy. Proc. Natl. Acad. Sci. 1634–1639 (1997)
Gershenfeld, N.A., Chuang, I.L.: Bulk spin-resonance quantum computation. Science 275, 350–356 (1997)
Price, M.D., Havel, T.F., Cory, D.G.: Multiqubit logic gates in NMR quantum computing. New Journal of Physics 2, 10.1–10.9 (2000)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comp. 26(5), 1484–1509 (1997)
Vandersypen, L.M.K., Steffen, M., Breyta, G., Yannoni, C.S., Sherwood, M.H., Chuang, I.L.: Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883–887 (2001)
Warren, W.S.: The usefulness of NMR quantum computing. Science 277, 1688–1690 (1997)
DiVincenzo, D.P.: Real and realistic quantum computers. Nature 393, 113–114 (1998)
Twamley, J.: Quantum-cellular-automaton quantum computing with endohedal fullerenes. Phys. Rev. A 67, 052318 (2003)
Freegarde, T., Segal, D.: Algorithmic cooling in a momentum state quantum computer. Phys. Rev. Lett. 91, 037904 (2003)
Ladd, T.D., Goldman, J.R., Yamaguchi, F., Yamamoto, Y., Abe, E., Itoh, K.M.: All-silicon quantum computer. Phys. Rev. Lett. 89, 017901 (2002)
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Elias, Y., Fernandez, J.M., Mor, T., Weinstein, Y. (2007). Optimal Algorithmic Cooling of Spins. In: Akl, S.G., Calude, C.S., Dinneen, M.J., Rozenberg, G., Wareham, H.T. (eds) Unconventional Computation. UC 2007. Lecture Notes in Computer Science, vol 4618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73554-0_2
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