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Experimental implementation of heat-bath algorithmic cooling using solid-state nuclear magnetic resonance

Nature volume 438, pages 470–473 (2005)Cite this article

Abstract

The counter-intuitive properties of quantum mechanics have the potential to revolutionize information processing by enabling the development of efficient algorithms with no known classical counterparts1,2. Harnessing this power requires the development of a set of building blocks3, one of which is a method to initialize the set of quantum bits (qubits) to a known state. Additionally, fresh ancillary qubits must be available during the course of computation to achieve fault tolerance4,5,6,7. In any physical system used to implement quantum computation, one must therefore be able to selectively and dynamically remove entropy from the part of the system that is to be mapped to qubits. One such method is an ‘open-system’ cooling protocol in which a subset of qubits can be brought into contact with an external system of large heat capacity. Theoretical efforts8,9,10 have led to an implementation-independent cooling procedure, namely heat-bath algorithmic cooling. These efforts have culminated with the proposal of an optimal algorithm, the partner-pairing algorithm, which was used to compute the physical limits of heat-bath algorithmic cooling11. Here we report the experimental realization of multi-step cooling of a quantum system via heat-bath algorithmic cooling. The experiment was carried out using nuclear magnetic resonance of a solid-state ensemble three-qubit system. We demonstrate the repeated repolarization of a particular qubit to an effective spin-bath temperature, and alternating logical operations within the three-qubit subspace to ultimately cool a second qubit below this temperature. Demonstration of the control necessary for these operations represents an important step forward in the manipulation of solid-state nuclear magnetic resonance qubits.

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Figure 1: Characteristics of the dilute 3- 13C malonic acid spin system.
Figure 2: Schematic quantum circuit diagram of the implemented protocol.
Figure 3: Experimental results in terms of 13C spectra and their integrated intensities.

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References

  1. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000)

    MATH  Google Scholar 

  2. Everitt, H., Havel, T. F. & Cory, D. G. (eds) Experimental aspects of quantum computing. Quant. Inform. Process. 3(1–5; special issue), 1–308 (2004).

  3. DiVincenzo, D. P. The physical implementation of quantum computation. Fortschr. Phys. 48, 771–793 (2000)

    Article  Google Scholar 

  4. Knill, E., Laflamme, R. & Zurek, W. H. Resilient quantum computation. Science 279, 342–345 (1998)

    Article  ADS  CAS  Google Scholar 

  5. Kitaev, A. Y. in Quantum Communication and Computing and Measurement (eds Holevo, A. S., Hirota, O. & Caves, C. M.) 181–188 (Plenum, New York, 1997)

    Book  Google Scholar 

  6. Aharonov, D. & Ben-Or, M. in Proc. 29th Annual ACM Symp. on Theory of Computing (eds Leighton, F. T. & Shor, P.) 176–188 (ACM Press, New York, 1997)

    Google Scholar 

  7. Preskill, J. Reliable quantum computers. Proc. R. Soc. Lond. A 454, 385–410 (1998)

    Article  ADS  Google Scholar 

  8. Schulman, L. J. & Vazirani, U. V. in Proc. 31st Annual ACM Symp. on Theory of Computing (eds Vitter, J. S., Larmore, L. & Leighton, T.) 322–329 (ACM Press, New York, 1999)

    Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  10. Fernandez, J. M., Lloyd, S., Mor, T. & Roychowdhury, V. Algorithmic cooling of spins: a practicable method for increasing polarization. Int. J. Quant. Inform. 2, 461–467 (2004)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. Knill, E., Laflamme, R., Martinez, R. & Tseng, C.-H. An algorithmic benchmark for quantum information processing. Nature 404, 368–370 (2000)

    Article  ADS  CAS  Google Scholar 

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

    Article  MathSciNet  CAS  Google Scholar 

  14. Cory, D. G., Price, M. D. & Havel, T. F. Nuclear magnetic resonance spectroscopy: An experimentally accessible paradigm for quantum computing. Physica D 120, 82–101 (1998)

    Article  ADS  CAS  Google Scholar 

  15. Cory, D. G. et al. NMR based quantum information processing: achievements and prospects. Fortschr. Phys. 48, 875–907 (2000)

    Article  CAS  Google Scholar 

  16. Leskowitz, G. M., Ghaderi, N., Olsen, R. A. & Mueller, L. J. Three-qubit nuclear magnetic resonance quantum information processing with a single-crystal solid. J. Chem. Phys. 119, 1643–1649 (2003)

    Article  ADS  CAS  Google Scholar 

  17. Abragam, A. & Goldman, M. Nuclear Magnetism: Order and Disorder 339–393 (Clarendon, Oxford, 1982)

    Google Scholar 

  18. Fortunato, E. M. et al. Design of strongly modulating pulses to implement precise effective Hamiltonians for quantum information processing. J. Chem. Phys. 116, 7599–7606 (2002)

    Article  ADS  CAS  Google Scholar 

  19. Jagannathan, N. R., Rajan, S. S. & Subramanian, E. Refinement of the crystal structure of malonic acid, C3H4O4 . J. Chem. Crystallogr. 24, 75–78 (1994)

    Article  CAS  Google Scholar 

  20. Cory, D. G., Miller, J. B. & Garroway, A. N. Time-suspension multiple-pulse sequences: applications to solid-state imaging. J. Magn. Res. 90, 205–213 (1990)

    ADS  CAS  Google Scholar 

  21. Haeberlen, U. High Resolution NMR in Solids: Selective Averaging Suppl. 1, Advances in Magnetic Resonance 64–69 (Academic, New York, 1976)

    Google Scholar 

  22. Moussa, O. On Heat-bath Algorithmic Cooling and its Implementation in Solid-state NMR. Page 20, M.Sc. thesis, Univ. Waterloo (2005); available at http://www.iqc.ca/~omoussa/work/thesis/

    Google Scholar 

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Acknowledgements

We thank D. G. Cory, T. F. Havel and C. Ramanathan for discussions and use of NMR simulation code; W. P. Power, M. J. Ditty and N. J. Taylor for facility use and experimental assistance; CIAR, ARDA and NSERC for support. O.M. acknowledges the Ontario Ministry of Training, Colleges and Universities for support.

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Authors and Affiliations

  1. Institute for Quantum Computing,

    J. Baugh, O. Moussa, C. A. Ryan, A. Nayak & R. Laflamme

  2. Department of Combinatorics and Optimization, University of Waterloo, Ontario, N2L 3G1, Waterloo, Canada

    A. Nayak

  3. Perimeter Institute for Theoretical Physics, Ontario, N2L 2Y5, Waterloo, Canada

    A. Nayak & R. Laflamme

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  1. J. Baugh
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Correspondence to J. Baugh.

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Baugh, J., Moussa, O., Ryan, C. et al. Experimental implementation of heat-bath algorithmic cooling using solid-state nuclear magnetic resonance. Nature 438, 470–473 (2005). https://doi.org/10.1038/nature04272

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