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Quantum annealing with manufactured spins


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.

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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.


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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




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.

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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)

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Johnson, M., Amin, M., Gildert, S. et al. Quantum annealing with manufactured spins. Nature 473, 194–198 (2011).

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