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Quantum control of a cat qubit with bit-flip times exceeding ten seconds

An Author Correction to this article was published on 17 May 2024

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Quantum bits (qubits) are prone to several types of error as the result of uncontrolled interactions with their environment. Common strategies to correct these errors are based on architectures of qubits involving daunting hardware overheads1. One possible solution is to build qubits that are inherently protected against certain types of error, so the overhead required to correct the remaining errors is greatly reduced2,3,4,5,6,7. However, this strategy relies on one condition: any quantum manipulations of the qubit must not break the protection that has been so carefully engineered5,8. A type of qubit known as a cat qubit is encoded in the manifold of metastable states of a quantum dynamical system, and thereby acquires continuous and autonomous protection against bit-flips. Here, in a superconducting-circuit experiment, we implemented a cat qubit with bit-flip times exceeding 10 s. This is an improvement of four orders of magnitude over previously published cat-qubit implementations. We prepared and imaged quantum superposition states, and measured phase-flip times greater than 490 ns. Most importantly, we controlled the phase of these quantum superpositions without breaking the bit-flip protection. This experiment demonstrates the compatibility of quantum control and inherent bit-flip protection at an unprecedented level, showing the viability of these dynamical qubits for future quantum technologies.

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Fig. 1: Encoding quantum information in a bistable dynamical system.
Fig. 2: Quantum tomography protocol based on the holonomic gate24.
Fig. 3: Cat-qubit phase-flip and bit-flip time measurements.
Fig. 4: Quantum control that preserves bit-flip protection.

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Data availability

The data that support the findings of this work are available from the corresponding author upon reasonable request.

Code availability

The code used for data acquisition, analysis and visualization is available from the corresponding author upon reasonable request.

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  1. Google Quantum AI Suppressing quantum errors by scaling a surface code logical qubit. Nature 614, 676–681 (2023).

    Article  ADS  CAS  Google Scholar 

  2. Aliferis, P. & Preskill, J. Fault-tolerant quantum computation against biased noise. Phys. Rev. A 78, 052331 (2008).

    Article  ADS  Google Scholar 

  3. Webster, P., Bartlett, S. D. & Poulin, D. Reducing the overhead for quantum computation when noise is biased. Phys. Rev. A 92, 062309 (2015).

    Article  ADS  Google Scholar 

  4. Tuckett, D. K., Bartlett, S. D. & Flammia, S. T. Ultrahigh error threshold for surface codes with biased noise. Phys. Rev. Lett. 120, 050505 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  5. Guillaud, J. & Mirrahimi, M. Repetition cat qubits for fault-tolerant quantum computation. Phys. Rev. X 9, 041053 (2019).

    CAS  Google Scholar 

  6. Darmawan, A. S., Brown, B. J., Grimsmo, A. L., Tuckett, D. K. & Puri, S. Practical quantum error correction with the XZZX code and Kerr-cat qubits. PRX Quantum 2, 030345 (2021).

    Article  ADS  Google Scholar 

  7. Ruiz, D., Guillaud, J., Leverrier, A., Mirrahimi, M. & Vuillot, C. LDPC-cat codes for low-overhead quantum computing in 2D. Preprint at (2024).

  8. Puri, S. et al. Bias-preserving gates with stabilized cat qubits. Sci. Adv. 6, eaay5901 (2020).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  9. Guckenheimer, J. & Holmes, P. in Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields 1–65 (Springer, 1983).

  10. Muppalla, P. R. et al. Bistability in a mesoscopic Josephson junction array resonator. Phys. Rev. B 97, 024518 (2018).

    Article  ADS  CAS  Google Scholar 

  11. Mabuchi, H. Nonlinear interferometry approach to photonic sequential logic. Appl. Phys. Lett. 99, 153103 (2011).

    Article  ADS  Google Scholar 

  12. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge Univ. Press, 2010).

  13. Chamberland, C. et al. Building a fault-tolerant quantum computer using concatenated cat codes. PRX Quantum 3, 010329 (2022).

    Article  ADS  Google Scholar 

  14. 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 

  15. Zurek, W. H. Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715–775 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  16. Wolinsky, M. & Carmichael, H. J. Quantum noise in the parametric oscillator: from squeezed states to coherent-state superpositions. Phys. Rev. Lett. 60, 1836–1839 (1988).

    Article  ADS  CAS  PubMed  Google Scholar 

  17. Leghtas, Z. et al. Confining the state of light to a quantum manifold by engineered two-photon loss. Science 347, 853–857 (2015).

    Article  ADS  CAS  PubMed  Google Scholar 

  18. Mirrahimi, M. et al. Dynamically protected cat-qubits: a new paradigm for universal quantum computation. New J. Phys. 16, 045014 (2014).

    Article  ADS  Google Scholar 

  19. Lescanne, R. et al. Exponential suppression of bit-flips in a qubit encoded in an oscillator. Nat. Phys. 16, 509–513 (2020).

    Article  CAS  Google Scholar 

  20. Grimm, A. et al. Stabilization and operation of a Kerr-cat qubit. Nature 584, 205–209 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  21. Frattini, N. E. et al. The squeezed Kerr oscillator: spectral kissing and phase-flip robustness. Preprint at (2022).

  22. Berdou, C. et al. One hundred second bit-flip time in a two-photon dissipative oscillator. PRX Quantum 4, 020350 (2023).

    Article  ADS  Google Scholar 

  23. Touzard, S. et al. Coherent oscillations inside a quantum manifold stabilized by dissipation. Phys. Rev. X 8, 021005 (2018).

    CAS  Google Scholar 

  24. Albert, V. V. et al. Holonomic quantum control with continuous variable systems. Phys. Rev. Lett. 116, 140502 (2016).

    Article  ADS  PubMed  Google Scholar 

  25. Haroche, S. & Raimond, J.-M. Exploring the Quantum: Atoms, Cavities, and Photons (Oxford Univ. Press, 2006).

  26. Gottesman, D., Kitaev, A. & Preskill, J. Encoding a qubit in an oscillator. Phys. Rev. A 64, 012310 (2001).

    Article  ADS  Google Scholar 

  27. Girvin, S. M. in Quantum Machines: Measurement and Control of Engineered Quantum Systems (eds Devoret, M. et al.) 113–256 (Oxford Univ. Press, 2014).

  28. Place, A. P. M. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nat. Commun. 12, 1779 (2021).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  29. Flurin, E. The Josephson mixer: a Swiss army knife for microwave quantum optics. Phd thesis, ENS Paris (2014).

  30. Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).

  31. Touzard, S. et al. Gated conditional displacement readout of superconducting qubits. Phys. Rev. Lett. 122, 080502 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  32. Yurke, B. & Stoler, D. The dynamic generation of Schrödinger cats and their detection. Physica B+C 151, 298–301 (1988).

    Article  ADS  Google Scholar 

  33. Kirchmair, G. et al. Observation of quantum state collapse and revival due to the single-photon Kerr effect. Nature 495, 205–209 (2013).

    Article  ADS  CAS  PubMed  Google Scholar 

  34. Gautier, R,., Mirrahimi, M. & Sarlette, A. Designing high-fidelity Zeno gates for dissipative cat qubits. PRX Quantum 4, 040316 (2023).

    Article  ADS  Google Scholar 

  35. Gautier, R., Sarlette, A. & Mirrahimi, M. Combined dissipative and Hamiltonian confinement of cat qubits. PRX Quantum 3, 020339 (2022).

    Article  ADS  Google Scholar 

  36. Aiello, G. et al. Quantum bath engineering of a high impedance microwave mode through quasiparticle tunneling. Nat. Commun. 13, 7146 (2022).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  37. Marquet, A. et al. Autoparametric resonance extending the bit-flip time of a cat qubit up to 0.3 s. Preprint at (2024).

  38. Eickbusch, A. et al. Fast universal control of an oscillator with weak dispersive coupling to a qubit. Nat. Phys. 18, 1464–1469 (2022).

    Article  CAS  Google Scholar 

  39. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Inf. 8, 3 (2022).

    Article  ADS  Google Scholar 

  40. Kono, S. et al. Mechanically induced correlated errors on superconducting qubits with relaxation times exceeding 0.4 milliseconds. Preprint at (2023).

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We thank N. Frattini for his help applying a previously published protocol24 to Wigner tomography, and the SPEC at CEA Saclay for providing nanofabrication facilities. This work was supported by the QuantERA grant QuCOS and ANR 19-QUAN-0006-04. This project has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreements 851740 and 884762); grants ANR-22-PETQ-0003 and ANR-22-PETQ-0006 under the France 2030 plan; and is partly funded by the CATQUBIT Horizon Europe project (grant agreement 190110172).

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Authors and Affiliations



P.C.-I., R.L., S.J. and Z.L. conceived the experiment. U.R. and A.B. designed the chip with support from M.H. and F.R. U.R. and A.B. measured the device and analysed the data. E.A. and N.P. fabricated the chip. R.G., J.C., A.M., L.-A.S., P.R., A.S. and M.M. provided theory support. U.R., A.B. and Z.L. wrote the paper with input from all authors.

Corresponding author

Correspondence to Z. Leghtas.

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Competing interests

Authors affiliated with Alice & Bob have financial interests in the company. Z.L., M.M. and P.C.-I. are shareholders of Alice & Bob. P.C.-I. is a part-time employee of Alice & Bob.

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Nature thanks Yvonne Gao and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Supplementary information sections 1–8. 

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Réglade, U., Bocquet, A., Gautier, R. et al. Quantum control of a cat qubit with bit-flip times exceeding ten seconds. Nature 629, 778–783 (2024).

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