Abstract
High-dimensional quantum systems are a valuable resource for quantum information processing. They can be used to encode error-correctable logical qubits, which has been demonstrated using continuous-variable states in microwave cavities or the motional modes of trapped ions. For example, high-dimensional systems can be used to realize ‘Schrödinger cat’ states, which are superpositions of widely displaced coherent states that can be used to illustrate quantum effects at large scales. Recent proposals have suggested encoding qubits in high-spin atomic nuclei, which are finite-dimensional systems that can host hardware-efficient versions of continuous-variable codes. Here we demonstrate the creation and manipulation of Schrödinger cat states using the spin-7/2 nucleus of an antimony atom embedded in a silicon nanoelectronic device. We use a multi-frequency control scheme to produce spin rotations that preserve the symmetry of the qudit, and we constitute logical Pauli operations for qubits encoded in the Schrödinger cat states. Our work demonstrates the ability to prepare and control non-classical resource states, which is a prerequisite for applications in quantum information processing and quantum error correction, using our scalable, manufacturable semiconductor platform.
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Data availability
Source data are available via Dryad at https://doi.org/10.5061/dryad.931zcrjtf (ref. 49).
Code availability
Scripts to analyse the source data are available via Dryad at https://doi.org/10.5061/dryad.931zcrjtf (ref. 49).
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Acknowledgements
We thank J. A. Gross, V. Scarani, J. Marshall and J. Saied for insightful discussions. The research was funded by an Australian Research Council Discovery Project (Grant No. DP210103769), the US Army Research Office (Contract No. W911NF-23-1-0113) and the Australian Department of Industry, Innovation and Science (Grant No. AUSMURI000002). We acknowledge the facilities and the scientific and technical assistance provided by the UNSW node of the Australian National Fabrication Facility (ANFF) and by the Heavy Ion Accelerators (HIA) nodes at the University of Melbourne and the Australian National University. ANFF and HIA are supported by the Australian Government through the National Collaborative Research Infrastructure Strategy programme. Ion beam facilities employed by D.N.J. and A.M.J. were co-funded by the Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology (Grant No. CE170100012). X.Y., B.W., M.R.v.B. and A.V. acknowledge support from the Sydney Quantum Academy. D.N.J. acknowledges the support of a Royal Society (UK) Wolfson Visiting Fellowship (RSWVF/211016). P.G. and B.C.S. acknowledge funding from the Natural Sciences and Engineering Research Council of Canada, Alberta Innovates and the Government of Alberta. N.A. is a KBR employee working under Prime Contract No. 80ARC020D0010 with the NASA Ames Research Center and is grateful for the collaborative agreement between NASA and CQC2T. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the US Government. The US Government is authorized to reproduce and distribute reprints for government purposes notwithstanding any copyright notation herein. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the US Department of Energy or the United States Government.
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X.Y., B.W., A.V., D.S., M.N., D.H., A.K., M.R.v.B. and A.M. conceived and designed the experiments, with theoretical input from P.G., B.C.S. and N.A. X.Y., B.W., A.V., M.N., D.H., D.S., A.K. and M.R.v.B. performed and analysed the measurements. D.H. and F.E.H. fabricated the device under A.S.D.’s supervision using materials supplied by K.M.I. A.M.J., D.H. and D.N.J. designed and performed the ion implantation. R.J.M., R.B.-K. and T.D.L. contributed to the data analysis. A.M., X.Y., B.W., D.H., A.V., R.B.-K., P.G., T.D.L. and N.A. wrote the manuscript with input from all co-authors. A.M. supervised the project.
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A.M. is an inventor on a patent related to this work. The patent describes the use of high-spin donor nuclei as quantum information processing elements (Application Nos. AU2019227083A1, US16/975,669 and WO2019165494A1). A.S.D. is the chief executive officer and a director of Diraq Pty Ltd. F.E.H. and A.S.D. declare an equity interest in Diraq Pty Ltd. The other authors declare no competing interests.
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Yu, X., Wilhelm, B., Holmes, D. et al. Schrödinger cat states of a nuclear spin qudit in silicon. Nat. Phys. (2025). https://doi.org/10.1038/s41567-024-02745-0
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DOI: https://doi.org/10.1038/s41567-024-02745-0
