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.

Digitized adiabatic quantum computing with a superconducting circuit

Nature volume 534, pages 222–226 (2016)Cite this article

Subjects

Abstract

Quantum mechanics can help to solve complex problems in physics1 and chemistry2, provided they can be programmed in a physical device. In adiabatic quantum computing3,4,5, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing6, which enables the construction of arbitrary interactions and is compatible with error correction7,8, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation9,10,11,12 of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Spin-chain problem and device.
Figure 2: Quantum state tomography of the digital evolution into a Greenberger–Horne–Zeilinger state.
Figure 3: Kink errors, residual energy and scaling with system size.
Figure 4: Digital evolutions of random stoquastic and non-stoquastic problems.

References

  1. Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982)

    Article  MathSciNet  Google Scholar 

  2. Aspuru-Guzik, A., Dutoi, A. D., Love, P. J. & Head-Gordon, M. Simulated quantum computation of molecular energies. Science 309, 1704–1707 (2005)

    Article  CAS  ADS  Google Scholar 

  3. Farhi, E., Goldstone, J., Gutmann, S. & Sipser, M. Quantum computation by adiabatic evolution. Preprint at http://arxiv.org/abs/quant-ph/0001106 (2000)

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

    Article  MathSciNet  CAS  ADS  Google Scholar 

  5. Nishimori, H. Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford Univ. Press, 2001)

  6. Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  7. Bravyi, S. B. & Kitaev, A. Yu. Quantum codes on a lattice with boundary. Preprint at http://arxiv.org/abs/quant-ph/9811052 (1998)

  8. Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012)

    Article  ADS  Google Scholar 

  9. Steffen, M. et al. Experimental implementation of an adiabatic quantum optimization algorithm. Phys. Rev. Lett. 90, 067903 (2003)

    Article  ADS  Google Scholar 

  10. Lanyon, B. P. et al. Universal digital quantum simulation with trapped ions. Science 334, 57–61 (2011)

    Article  CAS  ADS  Google Scholar 

  11. Barends, R. et al. Digital quantum simulation of fermionic models with a superconducting circuit. Nat. Commun. 6, 7654 (2015)

    Article  CAS  ADS  Google Scholar 

  12. Salathé, Y. et al. Digital quantum simulation of spin models with circuit quantum electrodynamics. Phys. Rev. X 5, 021027 (2015)

    Google Scholar 

  13. Bravyi, S., DiVincenzo, D. P., Oliveira, R. I. & Terhal, B. M. The complexity of stoquastic local Hamiltonian problems. Quantum Inf. Comput. 8, 361–385 (2008)

    MathSciNet  MATH  Google Scholar 

  14. Aharonov, D. et al. Adiabatic quantum computation is equivalent to standard quantum computation. SIAM Rev. 50, 755–787 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  15. Lloyd, S. & Terhal, B. M. Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions. New J. Phys. 18, 023042 (2016)

    Article  ADS  Google Scholar 

  16. Crosson, E., Farhi, E., Lin, C. Y.-Y., Lin, H.-H. & Shor, P. Different strategies for optimization using the quantum adiabatic algorithm. Preprint at http://arxiv.org/abs/1401.7320 (2014)

  17. Babbush, R., Love, P. J. & Aspuru-Guzik, A. Adiabatic quantum simulation of quantum chemistry. Sci. Rep. 4, 6603 (2014)

    Article  CAS  ADS  Google Scholar 

  18. Troyer, M. & Wiese, U.-J. Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations. Phys. Rev. Lett. 94, 170201 (2005)

    Article  ADS  Google Scholar 

  19. Boixo, S. et al. Computational multiqubit tunnelling in programmable quantum annealers. Nat. Commun. 7, 10327 (2016)

    Article  CAS  ADS  Google Scholar 

  20. Bravyi, S. B. & Kitaev, A. Yu. Fermionic quantum computation. Ann. Phys. 298, 210–226 (2002)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  21. Seeley, J. T., Richard, M. J. & Love, P. J. The Bravyi–Kitaev transformation for quantum computation of electronic structure. J. Chem. Phys. 137, 224109 (2012)

    Article  ADS  Google Scholar 

  22. Barends, R. et al. Coherent Josephson qubit suitable for scalable quantum integrated circuits. Phys. Rev. Lett. 111, 080502 (2013)

    Article  CAS  ADS  Google Scholar 

  23. Kelly, J. et al. State preservation by repetitive error detection in a superconducting quantum circuit. Nature 519, 66–69 (2015)

    Article  CAS  ADS  Google Scholar 

  24. Suzuki, M. Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations. Phys. Lett. A 146, 319–323 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  25. Barends, R. et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014)

    Article  CAS  ADS  Google Scholar 

  26. Kibble, T. W. B. Some implications of a cosmological phase transition. Phys. Rep. 67, 183–199 (1980)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  27. Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985)

    Article  CAS  ADS  Google Scholar 

  28. Wiebe, N., Berry, D., Hoyer, P. & Sanders, B. C. Higher order decompositions of ordered operator exponentials. J. Phys. A 43, 065203 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  29. Berry, D., Childs, A. M., Cleve, R., Kothari, R. & Somma, R. D. Simulating Hamiltonian dynamics with a truncated Taylor series. Phys. Rev. Lett. 114, 090502 (2015)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge support from Spanish MINECO FIS2012-36673-C03-02; Ramón y Cajal grant RYC-2012-11391; UPV/EHU UFI 11/55 and EHUA14/04; Basque Government IT472-10; a UPV/EHU PhD grant; and PROMISCE and SCALEQIT EU projects. Devices were made at the UC Santa Barbara Nanofabrication Facility, a part of the NSF-funded National Nanotechnology Infrastructure Network, and at the NanoStructures Cleanroom Facility.

Author information

Author notes

  1. A. Mezzacapo

    Present address: †Present address: IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA.,

Authors and Affiliations

  1. Google Inc., Santa Barbara, 93117, California, USA

    R. Barends, J. Kelly, A. G. Fowler, Yu Chen, E. Jeffrey, E. Lucero, J. Y. Mutus, M. Neeley, P. Roushan, D. Sank & John M. Martinis

  2. Google Inc., Venice, 90291, California, USA

    A. Shabani, R. Babbush & H. Neven

  3. Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, Bilbao, E-48080, Spain

    L. Lamata, A. Mezzacapo, U. Las Heras & E. Solano

  4. Department of Physics, University of California, Santa Barbara, 93106, California, USA

    B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, A. Megrant, C. Neill, P. J. J. O’Malley, C. Quintana, A. Vainsencher, J. Wenner, T. C. White & John M. Martinis

  5. IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, Bilbao, 48013, Spain

    E. Solano

Authors
  1. R. Barends
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Shabani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. Lamata
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. Kelly
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Mezzacapo
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. U. Las Heras
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. R. Babbush
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. A. G. Fowler
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. B. Campbell
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Yu Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Z. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. B. Chiaro
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. A. Dunsworth
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. E. Jeffrey
    View author publications

    You can also search for this author in PubMed Google Scholar

  15. E. Lucero
    View author publications

    You can also search for this author in PubMed Google Scholar

  16. A. Megrant
    View author publications

    You can also search for this author in PubMed Google Scholar

  17. J. Y. Mutus
    View author publications

    You can also search for this author in PubMed Google Scholar

  18. M. Neeley
    View author publications

    You can also search for this author in PubMed Google Scholar

  19. C. Neill
    View author publications

    You can also search for this author in PubMed Google Scholar

  20. P. J. J. O’Malley
    View author publications

    You can also search for this author in PubMed Google Scholar

  21. C. Quintana
    View author publications

    You can also search for this author in PubMed Google Scholar

  22. P. Roushan
    View author publications

    You can also search for this author in PubMed Google Scholar

  23. D. Sank
    View author publications

    You can also search for this author in PubMed Google Scholar

  24. A. Vainsencher
    View author publications

    You can also search for this author in PubMed Google Scholar

  25. J. Wenner
    View author publications

    You can also search for this author in PubMed Google Scholar

  26. T. C. White
    View author publications

    You can also search for this author in PubMed Google Scholar

  27. E. Solano
    View author publications

    You can also search for this author in PubMed Google Scholar

  28. H. Neven
    View author publications

    You can also search for this author in PubMed Google Scholar

  29. John M. Martinis
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

R. Barends, A.S. and L.L. designed the experiment, with E.S., H.N. and J.M.M. providing supervision and A. Mezzacapo, U.L.H. and R. Babbush providing additional theoretical support. R. Barends, A.S., L.L. and R. Babbush co-wrote the manuscript with E.S., H.N. and J.M.M. R. Barends, A.S. and L.L. performed the experiment and analysed the data. The device was designed by R. Barends and J.K. All authors contributed to the fabrication process, experimental set-up and manuscript preparation.

Corresponding authors

Correspondence to R. Barends or A. Shabani.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Related audio

Supplementary information

Supplementary Information

This fie contains Supplementary Text and Data, Supplementary Figures 1-10, Supplementary Tables 1-10 and additional references. (PDF 2956 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barends, R., Shabani, A., Lamata, L. et al. Digitized adiabatic quantum computing with a superconducting circuit. Nature 534, 222–226 (2016). https://doi.org/10.1038/nature17658

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature17658

This article is cited by

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

Advanced 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