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A universal qudit quantum processor with trapped ions


Most quantum computers use binary encoding to store information in qubits—the quantum analogue of classical bits. Yet, the underlying physical hardware consists of information carriers that are not necessarily binary, but typically exhibit a rich multilevel structure. Operating them as qubits artificially restricts their degrees of freedom to two energy levels1. Meanwhile, a wide range of applications—from quantum chemistry2 to quantum simulation3—would benefit from access to higher-dimensional Hilbert spaces, which qubit-based quantum computers can only emulate4. Here we demonstrate a universal quantum processor using trapped ions that act as qudits with a local Hilbert-space dimension of up to seven. With a performance similar to qubit quantum processors5, this approach enables the native simulation of high-dimensional quantum systems3, as well as more efficient implementation of qubit-based algorithms6,7.

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Fig. 1: Level scheme of the 40Ca+ ion.
Fig. 2: Single-qudit randomized benchmarking in an eight-ion register.
Fig. 3: Qutrit entangling gates in an eight-ion register.
Fig. 4: Full qudit readout.

Data availability

Source data are provided with this paper. The data underlying this work are available via Zenodo at

Code availability

All the codes used for data analysis are available from the corresponding author upon reasonable request.


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We thank M. Huber and J. Wallman for discussions. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 840450. It reflects only the author’s view; the EU Agency is not responsible for any use that may be made of the information it contains. We also acknowledge support by the Austrian Science Fund (FWF), through the SFB BeyondC (FWF project no. F7109); by the Institut für Quanteninformation GmbH; by the US Army Research Office (ARO) through grant no. W911NF-21-1-0007; by the US Air Force Office of Scientific Research (AFOSR) via IOE grant no. FA9550-19-1-7044 LASCEM; and by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via the US ARO grant no. W911NF-16-1-0070. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 801110 and the Austrian Federal Ministry of Education, Science and Research (BMBWF).

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Authors and Affiliations



M.R. developed the concepts. M.R., M.M., L.P., R.S., P.S. and T.M. performed the experiments. M.R. analyzed the data. T.M. and R.B. supervised the project. All the authors contributed to writing the manuscript.

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Correspondence to Martin Ringbauer.

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Nature Physics thanks Winfried Hensinger and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Discussion 1–8, Figs. 1–11, Tables 1 and 2, and Algorithm 1.

Source data

Source Data Fig. 2

Statistical source data.

Source Data Fig. 3a

Statistical source data.

Source Data Fig. 3b

Statistical source data.

Source Data Fig. 4

Statistical source data.

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Ringbauer, M., Meth, M., Postler, L. et al. A universal qudit quantum processor with trapped ions. Nat. Phys. 18, 1053–1057 (2022).

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