Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Quantum annealing with manufactured spins

Abstract

Many interesting but practically intractable problems can be reduced to that of finding the ground state of a system of interacting spins; however, finding such a ground state remains computationally difficult1. It is believed that the ground state of some naturally occurring spin systems can be effectively attained through a process called quantum annealing2,3. If it could be harnessed, quantum annealing might improve on known methods for solving certain types of problem4,5. However, physical investigation of quantum annealing has been largely confined to microscopic spins in condensed-matter systems6,7,8,9,10,11,12. Here we use quantum annealing to find the ground state of an artificial Ising spin system comprising an array of eight superconducting flux quantum bits with programmable spin–spin couplings. We observe a clear signature of quantum annealing, distinguishable from classical thermal annealing through the temperature dependence of the time at which the system dynamics freezes. Our implementation can be configured in situ to realize a wide variety of different spin networks, each of which can be monitored as it moves towards a low-energy configuration13,14. This programmable artificial spin network bridges the gap between the theoretical study of ideal isolated spin networks and the experimental investigation of bulk magnetic samples. Moreover, with an increased number of spins, such a system may provide a practical physical means to implement a quantum algorithm, possibly allowing more-effective approaches to solving certain classes of hard combinatorial optimization problems.

This is a preview of subscription content

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Superconducting flux qubit.
Figure 2: Quantum annealing.
Figure 3: Single-qubit results.
Figure 4: Eight-qubit ferromagnetic chain.
Figure 5: Results for the eight-qubit ferromagnetic chain.

References

  1. 1

    Barahona, F. On the computational complexity of Ising spin glass models. J. Phys. Math. Gen. 15, 3241–3253 (1982)

    ADS  MathSciNet  Article  Google Scholar 

  2. 2

    Kadowaki, T. & Nishimori, H. Quantum annealing in the transverse Ising model. Phys. Rev. E 58, 5355–5363 (1998)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Finnila, A. B., Gomez, M. A., Sebenik, C., Stenson, C. & Doll, J. D. Quantum annealing: a new method for minimizing multidimensional functions. Chem. Phys. Lett. 219, 343–348 (1994)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Farhi, E. et al. A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292, 472–475 (2001)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  5. 5

    Hogg, T. Quantum search heuristics. Phys. Rev. A 61, 052311 (2000)

    ADS  Article  Google Scholar 

  6. 6

    Wernsdorfer, W. Molecular nanomagnets: towards molecular spintronics. Int. J. Nanotechnol. 7, 497–522 (2010)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Carretta, S., Liviotti, E., Magnani, N., Santini, P. & Amoretti, G. S mixing and quantum tunneling of the magnetization in molecular nanomagnets. Phys. Rev. Lett. 92, 207205 (2004)

    ADS  CAS  Article  Google Scholar 

  8. 8

    Caciuffo, R. et al. Spin dynamics of heterometallic Cr7M wheels (M = Mn, Zn, Ni) probed by inelastic neutron scattering. Phys. Rev. B 71, 174407 (2005)

    ADS  Article  Google Scholar 

  9. 9

    Guidi, T. et al. Inelastic neutron scattering study of the molecular grid nanomagnet Mn-[3 × 3]. Phys. Rev. B 69, 104432 (2004)

    ADS  Article  Google Scholar 

  10. 10

    Waldmann, O., Guidi, T., Carretta, S., Mondelli, C. & Dearden, A. L. Elementary excitations in the cyclic molecular nanomagnet Cr8 . Phys. Rev. Lett. 91, 237202 (2003)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Brooke, J., Bitko, D., Rosenbaum, T. F. & Aeppli, G. Quantum annealing of a disordered magnet. Science 284, 779–781 (1999)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Ghosh, S. & Rosenbaum, T. F. Aeppli, G. & Coppersmith, S. N. Entangled quantum state of magnetic dipoles. Nature 425, 48–51 (2003)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Harris, R. et al. Experimental demonstration of a robust and scalable flux qubit. Phys. Rev. B 81, 134510 (2010)

    ADS  Article  Google Scholar 

  14. 14

    Harris, R. et al. Experimental investigation of an eight-qubit unit cell in a superconducting optimization processor. Phys. Rev. B 82, 024511 (2010)

    ADS  Article  Google Scholar 

  15. 15

    Aharonov, D. et al. Adiabatic quantum computation is equivalent to standard quantum computation. SIAM J. Comput. 37, 166–194 (2007)

    MathSciNet  Article  Google Scholar 

  16. 16

    Hinton, G. E. & Salakhutdinov, R. R. Reducing the dimensionality of data with neural networks. Science 313, 504–507 (2006)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  17. 17

    Chen, X. & Tompa, M. Comparative assessment of methods for aligning multiple genome sequences. Nature Biotechnol. 28, 567–572 (2010)

    CAS  Article  Google Scholar 

  18. 18

    Steffen, M., van Dam, W., Hogg, T., Breyta, G. & Chuang, I. Experimental implementation of an adiabatic quantum optimization algorithm. Phys. Rev. Lett. 90, 067903 (2003)

    ADS  Article  Google Scholar 

  19. 19

    Kim, K. et al. Quantum simulation of frustrated Ising spins with trapped ions. Nature 465, 590–593 (2010)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Lupas¸cu, A. et al. Quantum non-demolition measurement of a superconducting two-level system. Nature Phys. 3, 119–125 (2007)

    ADS  Article  Google Scholar 

  21. 21

    Berns, D. M. et al. Amplitude spectroscopy of a solid-state artificial atom. Nature 455, 51–58 (2008)

    ADS  CAS  Article  Google Scholar 

  22. 22

    Poletto, S. et al. Coherent oscillations in a superconducting tunable flux qubit manipulated without microwaves. N. J. Phys. 11, 013009 (2009)

    Article  Google Scholar 

  23. 23

    DiCarlo, L. et al. Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature 460, 240–244 (2009)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Bennett, D. A. et al. Decoherence in rf SQUID qubits. Quantum Inf. Process. 8, 217–243 (2009)

    CAS  Article  Google Scholar 

  25. 25

    Yoshihara, F., Nakamura, Y. & Tsai, J. S. Correlated flux noise and decoherence in two inductively coupled flux qubits. Phys. Rev. B 81, 132502 (2010)

    ADS  Article  Google Scholar 

  26. 26

    Il’ichev, E. et al. Multiphoton excitations and inverse population in a system of two flux qubits. Phys. Rev. B 81, 012506 (2010)

    ADS  Article  Google Scholar 

  27. 27

    Vion, D. et al. Manipulating the quantum state of an electrical circuit. Science 296, 886–889 (2002)

    ADS  CAS  Article  Google Scholar 

  28. 28

    Burkard, G., Koch, R. H. & DiVincenzo, D. P. Multilevel quantum description of decoherence in superconducting qubits. Phys. Rev. B 69, 064503 (2004)

    ADS  Article  Google Scholar 

  29. 29

    Harris, R. et al. Compound Josephson-junction coupler for flux qubits with minimal crosstalk. Phys. Rev. B 80, 052506 (2009)

    ADS  Article  Google Scholar 

  30. 30

    Voss, R. F. & Webb, R. A. Macroscopic quantum tunneling in 1-μm Nb Josephson junctions. Phys. Rev. Lett. 47, 265–268 (1981)

    ADS  CAS  Article  Google Scholar 

  31. 31

    Devoret, M. H., Martinis, J. M. & Clarke, J. Measurements of macroscopic quantum tunneling out of the zero-voltage state of a current-biased josephson junction. Phys. Rev. Lett. 55, 1908–1911 (1985)

    ADS  CAS  Article  Google Scholar 

  32. 32

    Biamonte, J. D. & Love, P. J. Realizable Hamiltonians for universal adiabatic quantum computers. Phys. Rev. A 78, 012352 (2008)

    ADS  MathSciNet  Article  Google Scholar 

  33. 33

    Harris, R. et al. Probing noise in flux qubits via macroscopic resonant tunneling. Phys. Rev. Lett. 101, 117003 (2008)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

We would like to thank J. Preskill, A. Kitaev, D. A. Lidar, F. Wilhelm, A. Lupas¸cu, A. Blais, T. A. Brun, P. Smith, F. Altomare, E. Hoskinson, T. Przybysz, T. Mahon and R. Neufeld for discussions. We are grateful to the volunteers of the AQUA@home BOINC project for their help in running the classical simulations.

Author information

Affiliations

Authors

Contributions

M.H.S.A. and M.W.J. developed the idea for the experiment; M.W.J. conducted the experiment; T.L., R.H., M.W.J. and J.W. conducted supporting experiments; M.H.S.A. developed the theory; N.D., F.H. and M.H.S.A. developed simulation code; N.D., M.H.S.A., M.W.J., F.H. and C.J.S.T. performed simulations and analysed results; M.W.J., M.H.S.A., S.G. and R.H. wrote the article; M.W.J., S.G., M.H.S.A. and N.D. generated the figures; A.J.B., R.H., J.J., M.W.J., T.L., I.P., E.M.C. and B.W. developed measurement algorithms and testing software; C.R., S.U. and M.C.T. achieved the low-magnetic-field environment for the device; C.E. and C.R. mounted the sample, P.B., E.T., A.J.B., R.H., J.J., M.W.J. and T.L. designed the devices; E.L., N.L. and T.O. fabricated the devices; M.C.T. and S.U. developed the testing apparatus; K.K. allowed use of BOINC for classical simulations; J.P.H. and G.R. provided logistical support; and J.P.H. selected the chip.

Corresponding author

Correspondence to M. W. Johnson.

Ethics declarations

Competing interests

Some of the authors are employees of D-Wave Systems Inc., a company seeking to develop a processor that uses a computational model known as quantum annealing. This work describes progress in that effort.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data comprising I Overview; II Experiment and III Simulations (see contents list for full details), Supplementary Figures 1. (PDF 1421 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Johnson, M., Amin, M., Gildert, S. et al. Quantum annealing with manufactured spins. Nature 473, 194–198 (2011). https://doi.org/10.1038/nature10012

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing