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Stabilization and operation of a Kerr-cat qubit

Nature volume 584, pages 205–209 (2020)Cite this article

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Abstract

Quantum superpositions of macroscopically distinct classical states—so-called Schrödinger cat states—are a resource for quantum metrology, quantum communication and quantum computation. In particular, the superpositions of two opposite-phase coherent states in an oscillator encode a qubit protected against phase-flip errors1,2. However, several challenges have to be overcome for this concept to become a practical way to encode and manipulate error-protected quantum information. The protection must be maintained by stabilizing these highly excited states and, at the same time, the system has to be compatible with fast gates on the encoded qubit and a quantum non-demolition readout of the encoded information. Here we experimentally demonstrate a method for the generation and stabilization of Schrödinger cat states based on the interplay between Kerr nonlinearity and single-mode squeezing1,3 in a superconducting microwave resonator4. We show an increase in the transverse relaxation time of the stabilized, error-protected qubit of more than one order of magnitude compared with the single-photon Fock-state encoding. We perform all single-qubit gate operations on timescales more than sixty times faster than the shortest coherence time and demonstrate single-shot readout of the protected qubit under stabilization. Our results showcase the combination of fast quantum control and robustness against errors, which is intrinsic to stabilized macroscopic states, as well as the potential of these states as resources in quantum information processing5,6,7,8.

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Fig. 1: Qubit encoding, stabilization and implementation.
Fig. 2: Rabi oscillations of the protected KCQ.
Fig. 3: KCQ gate process tomography.
Fig. 4: Cat-quadrature readout (CR) and coherence times.

Data availability

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

Code availability

Numerical simulations were performed using a Python-based open source software (QuTiP). Custom Python code was used to obtain and analyse the experimental data following standard practices as outlined in Methods and the Supplementary Information. The code used in this study is available from the corresponding authors upon reasonable request.

Change history

  • 27 August 2020

    This article was amended to remove a duplicated word in the summary paragraph.

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Acknowledgements

We acknowledge the contributions of L. Burkhart, P. Campagne-Ibarcq, A. Eickbusch, L. Frunzio, P. Reinhold, K. Serniak and Y. Zhang. Facilities use was supported by YINQE and the Yale SEAS cleanroom. This work was supported by ARO under grant number W911NF-18-1-0212 and grant number W911NF-16-1-0349, and NSF under grant number DMR-1609326. We also acknowledge support of the Yale Quantum Institute.

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Author notes

  1. A. Grimm

    Present address: Photon Science Division, Paul Scherrer Institut, Villigen, Switzerland

  2. S. Shankar

    Present address: Electrical and Computer Engineering, University of Texas, Austin, TX, USA

  3. These authors contributed equally: A. Grimm, N. E. Frattini

Authors and Affiliations

  1. Department of Applied Physics, Yale University, New Haven, CT, USA

    A. Grimm, N. E. Frattini, S. O. Mundhada, S. Touzard, S. Shankar & M. H. Devoret

  2. Department of Physics, Yale University, New Haven, CT, USA

    S. Puri & S. M. Girvin

  3. QUANTIC team, Inria Paris, Paris, France

    M. Mirrahimi

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Contributions

A.G. designed and carried out initial experiments with help from S.T. and S.O.M., and designed the final experiment with input from N.E.F., M.H.D. and S.P. A.G. and N.E.F. fabricated the sample, performed measurements and analysed the data used in the manuscript. A.G., N.E.F. and M.H.D. wrote the manuscript with input from all authors.

Corresponding authors

Correspondence to A. Grimm or M. H. Devoret.

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Competing interests

M.H.D. is a co-founder of Quantum Circuits, Incorporated. A.G., S.P., S.M.G. and M.H.D. are inventors on US Provisional Patent Application Number 62/692,243 submitted by Yale University, which covers quantum information processing with an asymmetric error channel.

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Supplementary information

Supplementary Information

Detailed description of experimental methods (sample design, measurement setup, calibration), more in-depth theory descriptions (full system Hamiltonian, numerical simulations), and results of additional characterization and control experiments.

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Grimm, A., Frattini, N.E., Puri, S. et al. Stabilization and operation of a Kerr-cat qubit. Nature 584, 205–209 (2020). https://doi.org/10.1038/s41586-020-2587-z

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