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Superconducting quantum circuits at the surface code threshold for fault tolerance

Abstract

A quantum computer can solve hard problems, such as prime factoring1,2, database searching3,4 and quantum simulation5, at the cost of needing to protect fragile quantum states from error. Quantum error correction6 provides this protection by distributing a logical state among many physical quantum bits (qubits) by means of quantum entanglement. Superconductivity is a useful phenomenon in this regard, because it allows the construction of large quantum circuits and is compatible with microfabrication. For superconducting qubits, the surface code approach to quantum computing7 is a natural choice for error correction, because it uses only nearest-neighbour coupling and rapidly cycled entangling gates. The gate fidelity requirements are modest: the per-step fidelity threshold is only about 99 per cent. Here we demonstrate a universal set of logic gates in a superconducting multi-qubit processor, achieving an average single-qubit gate fidelity of 99.92 per cent and a two-qubit gate fidelity of up to 99.4 per cent. This places Josephson quantum computing at the fault-tolerance threshold for surface code error correction. Our quantum processor is a first step towards the surface code, using five qubits arranged in a linear array with nearest-neighbour coupling. As a further demonstration, we construct a five-qubit Greenberger–Horne–Zeilinger state8,9 using the complete circuit and full set of gates. The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.

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Figure 1: Architecture.
Figure 2: Single-qubit randomized benchmarking.
Figure 3: Controlled-phase gate physics and randomized benchmarking results.
Figure 4: Quantum state tomography and generation of the GHZ states.

References

  1. 1

    Vandersypen, L. M. K. et al. Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883–887 (2001)

    CAS  ADS  Article  Google Scholar 

  2. 2

    Lucero, E. et al. Computing prime factors with a Josephson phase qubit quantum processor. Nature Phys. 8, 719–723 (2012)

    CAS  ADS  Article  Google Scholar 

  3. 3

    Jones, J., Mosca, M. & Hansen, R. Implementation of a quantum search algorithm on a quantum computer. Nature 393, 334–346 (1998)

    ADS  Google Scholar 

  4. 4

    Chuang, I. L., Gershenfeld, N. & Kubinec, M. Experimental implementation of fast quantum searching. Phys. Rev. Lett. 80, 3408 (1998)

    CAS  ADS  Article  Google Scholar 

  5. 5

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

    MathSciNet  Article  Google Scholar 

  6. 6

    Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information Ch. 10 (Cambridge Univ. Press, 2010)

    Book  Google Scholar 

  7. 7

    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)

    ADS  Article  Google Scholar 

  8. 8

    DiCarlo, L. et al. Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature 467, 574–578 (2010)

    CAS  ADS  Article  Google Scholar 

  9. 9

    Neeley, M. et al. Generation of three-qubit entangled states using superconducting phase qubits. Nature 467, 570–573 (2010)

    CAS  ADS  Article  Google Scholar 

  10. 10

    Martinis, J. & Geller, M. R. Fast adiabatic control of qubits using optimal windowing theory. Preprint at http://arxiv.org/abs/1402.5467

  11. 11

    Ryan, C. A., Laforest, M. & Laflamme, R. Randomized benchmarking of single- and multi-qubit control in liquid-state NMR quantum information processing. New J. Phys. 11, 013034 (2009)

    ADS  Article  Google Scholar 

  12. 12

    Benhelm, J., Kirchmair, G., Roos, C. F. & Blatt, R. Towards fault-tolerant quantum computing with trapped ions. Nature Phys. 4, 463–466 (2008)

    CAS  ADS  Article  Google Scholar 

  13. 13

    Choi, T. et al. Optimal quantum control of multi-mode couplings between trapped ion qubits for scalable entanglement. Preprint at http://arxiv.org/abs/1401.1575 (2014)

  14. 14

    Chow, J. M. et al. Implementing a strand of a scalable fault-tolerant quantum computing fabric. Preprint at http://arxiv.org/abs/1311.6330 (2013)

  15. 15

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

    CAS  ADS  Article  Google Scholar 

  16. 16

    Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004)

    CAS  ADS  Article  Google Scholar 

  17. 17

    Jeffrey, E. et al. Fast scalable state measurement with superconducting qubits. Preprint at http://arxiv.org/abs/1401.0257 (2014)

  18. 18

    Brown, K. R. et al. Single-qubit-gate error below 10−4 in a trapped ion. Phys. Rev. A 84, 030303 (2011)

    ADS  Article  Google Scholar 

  19. 19

    Córcoles, A. D. et al. Process verification of two-qubit quantum gates by randomized benchmarking. Phys. Rev. A 87, 030301 (2013)

    ADS  Article  Google Scholar 

  20. 20

    Magesan, E., Gambetta, J. M. & Emerson, J. Scalable and robust randomized benchmarking of quantum processes. Phys. Rev. Lett. 106, 180504 (2011)

    ADS  Article  Google Scholar 

  21. 21

    Lucero, E. et al. Reduced phase error through optimized control of a superconducting qubit. Phys. Rev. A 82, 042339 (2010)

    ADS  Article  Google Scholar 

  22. 22

    Gambetta, J. M. et al. Characterization of addressability by simultaneous randomized benchmarking. Phys. Rev. Lett. 109, 240504 (2012)

    ADS  Article  Google Scholar 

  23. 23

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

    CAS  ADS  Article  Google Scholar 

  24. 24

    Mariantoni, M. et al. Implementing the quantum von Neumann architecture with superconducting circuits. Science 334, 61–65 (2011)

    CAS  ADS  Article  Google Scholar 

  25. 25

    Strauch, F. W. et al. Quantum logic gates for coupled superconducting phase qubits. Phys. Rev. Lett. 91, 167005 (2003)

    ADS  Article  Google Scholar 

  26. 26

    Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Appl. Phys. Lett. 100, 113510 (2012)

    ADS  Article  Google Scholar 

  27. 27

    Sendelbach, S., Hover, D., Mück, M. & McDermott, R. Complex inductance, excess noise, and surface magnetism in dc SQUIDs. Phys. Rev. Lett. 103, 117001 (2009)

    CAS  ADS  Article  Google Scholar 

  28. 28

    Gühne, O. & Seevinck, M. Separability criteria for genuine multiparticle entanglement. New J. Phys. 12, 053002 (2010)

    ADS  Article  Google Scholar 

  29. 29

    Monz, T. et al. 14-qubit entanglement: creation and coherence. Phys. Rev. Lett. 106, 130506 (2011)

    ADS  Article  Google Scholar 

  30. 30

    Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007)

    ADS  Article  Google Scholar 

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Acknowledgements

We thank F. Wilhelm, D. Egger, and J. Baselmans for discussions. We are indebted to E. Lucero for photography of the device. This work was supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), through the Army Research Office grants W911NF-09-1-0375 and W911NF-10-1-0334. All statements of fact, opinion or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of IARPA, the ODNI or the US Government. Devices were made at the UC Santa Barbara Nanofabrication Facility, a part of the US NSF-funded National Nanotechnology Infrastructure Network, and at the NanoStructures Cleanroom Facility.

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Contributions

R.B. and J.K. designed the sample, performed the experiment and analysed the data. J.K., A.M. and R.B. fabricated the sample. R.B., J.K., J.M.M. and A.N.C. co-wrote the manuscript. A.V. and A.N.K. provided assistance with randomized benchmarking. A.G.F. verified the experimental gate fidelities to be at the surface code threshold. All authors contributed to the fabrication process, experimental set-up and manuscript preparation.

Corresponding authors

Correspondence to R. Barends or John M. Martinis.

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The authors declare no competing financial interests.

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Barends, R., Kelly, J., Megrant, A. et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014). https://doi.org/10.1038/nature13171

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