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Phase transition in magic with random quantum circuits

Nature Physics (2024)Cite this article

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Abstract

Magic is a property of quantum states that enables universal fault-tolerant quantum computing using simple sets of gate operations. Understanding the mechanisms by which magic is created or destroyed is, therefore, a crucial step towards efficient and practical fault-tolerant computation. Many proposals for error correction in quantum computing make use of so-called stabilizer codes, which use multiqubit measurements to detect deviations from logical qubit states. Here we observe that a random stabilizer code subject to coherent errors exhibits a phase transition in magic, which we characterize through analytical, numerical and experimental probes. Below a critical error rate, stabilizer measurements remove the accumulated magic in the circuit, effectively protecting against coherent errors; above the critical error rate measurements concentrate magic. A better understanding of this behaviour in the resource theory of magic could help to identify the origins of quantum speedup and lead to methods for more efficient magic state generation.

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Fig. 1: Model and phase diagram.
Fig. 2: Results for vanishing-rate codes.
Fig. 3: Results for constant-rate codes.

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Data availability

All the data used in this work can be found via Zenodo at https://doi.org/10.5281/zenodo.7847794 (ref. 35). Source data are provided with this paper.

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Acknowledgements

We thank K. Wright, M. Hiles and J. Nguyen from IonQ for their assistance, and L. Zhukas, N. Yunger Halpern, W. Braasch and B. Ware for comments on the manuscript. We are also grateful to an anonymous reviewer for a thorough, careful and thoughtful review. This work is supported by the NSF STAQ program; the NSF QLCI RQS Program OMA-2120757; the DOE QSA program DE-FOA-0002253; and the AFOSR MURIs on Dissipation Engineering in Open Quantum Systems, Quantum Measurement/Verification, and Quantum Interactive Protocols. C.D.W. thanks DOE-ASCR Quantum Computing Application Teams program for support under fieldwork proposal number ERKJ347. The experiments were performed on the IonQ Aria system through the UMD/IonQ Q-Lab consortium. Certain commercial equipment, instruments or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.

Author information

Authors and Affiliations

  1. Joint Center for Quantum Information and Computer Science, University of Maryland and NIST, College Park, MD, USA

    Pradeep Niroula, Christopher David White, Christopher Monroe & Michael J. Gullans

  2. Joint Quantum Institute, University of Maryland and NIST, College Park, MD, USA

    Pradeep Niroula, Qingfeng Wang & Christopher Monroe

  3. Chemical Physics Program and Institute for Physical Science and Technology, University of Maryland, College Park, MD, USA

    Qingfeng Wang

  4. IonQ, Inc., College Park, MD, USA

    Sonika Johri, Daiwei Zhu & Christopher Monroe

  5. Duke Quantum Center, Department of Electrical & Computer Engineering and Department of Physics, Duke University, Durham, NC, USA

    Christopher Monroe & Crystal Noel

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  1. Pradeep Niroula
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Contributions

P.N., C.D.W. and M.J.G. developed the theory. P.N. collected and analysed the data. Q.W., S.J., D.Z. and C.N. provided support and guidance on experiments. C.M., C.N. and M.J.G. supervised the project. All authors discussed results and contributed to the manuscript.

Corresponding authors

Correspondence to Pradeep Niroula or Michael J. Gullans.

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The authors declare no competing interests.

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Nature Physics thanks Alioscia Hamma, Xhek Turkeshi and Guo-Yi Zhu for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–8 and Discussion.

Source data

Source Data Fig. 1

Statistical source data for the plots.

Source Data Fig. 2

Statistical source data for the plots.

Source Data Fig. 3

Statistical source data for the plots.

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Niroula, P., White, C.D., Wang, Q. et al. Phase transition in magic with random quantum circuits. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02637-3

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