Error-transparent operations on a logical qubit protected by quantum error correction

Abstract

Universal quantum computation1 is striking for its unprecedented capability in processing information, but its scalability is challenging in practice because of the inevitable environment noise. Although quantum error correction (QEC) techniques2,3,4,5,6,7,8 have been developed to protect stored quantum information from leading orders of error, the noise-resilient processing of the QEC-protected quantum information is highly demanded but remains elusive9. Here, we demonstrate phase gate operations on a logical qubit encoded in a bosonic oscillator in an error-transparent (ET) manner. Inspired by refs. 10,11, the ET gates are extended to the bosonic code and are able to tolerate errors on the logical qubit during gate operations, regardless of the random occurrence time of the error. With precisely designed gate Hamiltonians through photon-number-resolved a.c. Stark shifts, the ET condition is fulfilled experimentally. We verify that the ET gates outperform the non-ET gates with a substantial improvement of gate fidelity after an occurrence of the single-photon-loss error. Our ET gates in superconducting quantum circuits can be readily extended to multiple encoded qubits and a universal gate set is within reach, holding the potential for reliable quantum information processing.

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Fig. 1: Concept of the ET gate.
Fig. 2: PASS and ET phase gates.
Fig. 3: ET gates on a logical qubit with AQEC.
Fig. 4: ET gates protected by repetitive AQEC.

Data availability

Source data for Figs. 24 are available with the paper. All other data relevant to this study are available from the corresponding author upon reasonable request.

Code availability

The code used for simulations is available from the corresponding authors upon reasonable request.

References

  1. 1.

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

  2. 2.

    Chiaverini, J. et al. Realization of quantum error correction. Nature 432, 602–605 (2004).

    ADS  Article  Google Scholar 

  3. 3.

    Schindler, P. et al. Experimental repetitive quantum error correction. Science 332, 1059–1061 (2011).

    ADS  Article  Google Scholar 

  4. 4.

    Reed, M. D. et al. Realization of three-qubit quantum error correction with superconducting circuits. Nature 482, 382–385 (2012).

    ADS  Article  Google Scholar 

  5. 5.

    Yao, X.-C. et al. Experimental demonstration of topological error correction. Nature 482, 489–494 (2012).

    ADS  Article  Google Scholar 

  6. 6.

    Waldherr, G. et al. Quantum error correction in a solid-state hybrid spin register. Nature 506, 204–207 (2014).

    ADS  Article  Google Scholar 

  7. 7.

    Nigg, D. et al. Quantum computations on a topologically encoded qubit. Science 345, 302–305 (2014).

    ADS  MathSciNet  Article  Google Scholar 

  8. 8.

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

    ADS  Article  Google Scholar 

  9. 9.

    Campbell, E. T., Terhal, B. M. & Vuillot, C. Roads towards fault-tolerant universal quantum computation. Nature 549, 172–179 (2017).

    ADS  Article  Google Scholar 

  10. 10.

    Vy, O., Wang, X. & Jacobs, K. Error-transparent evolution: the ability of multi-body interactions to bypass decoherence. New J. Phys. 15, 053002 (2013).

    ADS  MathSciNet  Article  Google Scholar 

  11. 11.

    Kapit, E. Error-transparent quantum gates for small logical qubit architectures. Phys. Rev. Lett. 120, 050503 (2018).

    ADS  Article  Google Scholar 

  12. 12.

    Shor, P. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, 2493–2496 (1995).

    ADS  Article  Google Scholar 

  13. 13.

    Ofek, N. et al. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 536, 441–445 (2016).

    ADS  Article  Google Scholar 

  14. 14.

    Bravyi, S. & Kitaev, A. Universal quantum computation with ideal Clifford gates and noisy ancillas. Phys. Rev. A 71, 022316 (2005).

    ADS  MathSciNet  Article  Google Scholar 

  15. 15.

    Gottesman, D. Quantum fault tolerance in small experiments. Preprint at https://arxiv.org/pdf/1610.03507.pdf (2016).

  16. 16.

    Chao, R. & Reichardt, B. W. Fault-tolerant quantum computation with few qubits. npj Quantum Inf. 4, 42 (2018).

    ADS  Article  Google Scholar 

  17. 17.

    Chamberland, C. & Beverland, M. E. Flag fault-tolerant error correction with arbitrary distance codes. Quantum 2, 53 (2018).

    Article  Google Scholar 

  18. 18.

    Takita, M., Cross, A. W., Córcoles, A. D., Chow, J. M. & Gambetta, J. M. Experimental demonstration of fault-tolerant state preparation with superconducting qubits. Phys. Rev. Lett. 119, 180501 (2017).

    ADS  Article  Google Scholar 

  19. 19.

    Linke, N. M. et al. Fault-tolerant quantum error detection. Sci. Adv. 3, e1701074 (2017).

    ADS  Article  Google Scholar 

  20. 20.

    Rosenblum, S. et al. Fault-tolerant detection of a quantum error. Science 361, 266–270 (2018).

    ADS  MathSciNet  Article  Google Scholar 

  21. 21.

    Gao, Y. Y. et al. Entanglement of bosonic modes through an engineered exchange interaction. Nature 566, 509–512 (2019).

    ADS  Article  Google Scholar 

  22. 22.

    Flühmann, C. et al. Encoding a qubit in a trapped-ion mechanical oscillator. Nature 566, 513–517 (2019).

    ADS  Article  Google Scholar 

  23. 23.

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

    ADS  Article  Google Scholar 

  24. 24.

    Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Phys. Rev. Lett. 107, 240501 (2011).

    ADS  Article  Google Scholar 

  25. 25.

    Michael, M. H. et al. New class of quantum error-correcting codes for a bosonic mode. Phys. Rev. X 6, 031006 (2016).

    Google Scholar 

  26. 26.

    Hu, L. et al. Quantum error correction and universal gate set operation on a binomial bosonic logical qubit. Nat. Phys. 15, 503–508 (2019).

    Article  Google Scholar 

  27. 27.

    Schuster, D. I. et al. ac Stark shift and dephasing of a superconducting qubit strongly coupled to a cavity field. Phys. Rev. Lett. 94, 123602 (2005).

    ADS  Article  Google Scholar 

  28. 28.

    Gamel, O. & James, D. F. V. Time-averaged quantum dynamics and the validity of the effective Hamiltonian model. Phys. Rev. A 82, 052106 (2010).

    ADS  Article  Google Scholar 

  29. 29.

    Sun, L. et al. Tracking photon jumps with repeated quantum non-demolition parity measurements. Nature 511, 444–448 (2014).

    ADS  Article  Google Scholar 

  30. 30.

    Lihm, J.-M., Noh, K. & Fischer, U. R. Implementation-independent sufficient condition of the Knill–Laflamme type for the autonomous protection of logical qudits by strong engineered dissipation. Phys. Rev. A 98, 012317 (2018).

    ADS  Article  Google Scholar 

  31. 31.

    P. Reinhold et al. Error-corrected gates on an encoded qubit. Preprint at https://arxiv.org/pdf/1907.12327.pdf (2019).

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Acknowledgements

This work was supported by the National Key Research and Development Program of China (grant 2017YFA0304303) and the National Natural Science Foundation of China (grants 11925404 and 11874235). C.-L.Z. was supported by the National Natural Science Foundation of China (grants 11874342 and 11922411) and the Anhui Initiative in Quantum Information Technologies (AHY130200).

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Authors

Contributions

Y.M. performed the experiment and analysed the data with the assistance of Y.X. L.S. directed the experiment. Y.M. and C.-L.Z. proposed the experiment. C.-L.Z. provided theoretical support. L.H. developed the field-programmable gate array logic. W.C. fabricated the Josephson parametric amplifier. X.Y., X.M. and W.W. fabricated the devices with the assistance of X.P., H.W. and Y.P.S. Y.M., C.-L.Z. and L.S. wrote the manuscript with feedback from all authors.

Corresponding authors

Correspondence to C.-L. Zou or L. Sun.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Tanay Roy and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary information

Supplementary Figs. 1–8, Tables 1–4 and Discussion.

Source data

Source Data Fig. 2

Data of Fig. 2c, including standard deviation as the error bars.

Source Data Fig. 3

Data of Fig. 3b–d, including standard deviation as the error bars.

Source Data Fig. 4

Data of Fig. 4b, including standard deviation as the error bars.

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Ma, Y., Xu, Y., Mu, X. et al. Error-transparent operations on a logical qubit protected by quantum error correction. Nat. Phys. 16, 827–831 (2020). https://doi.org/10.1038/s41567-020-0893-x

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