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arXiv:2306.03340 · npj Quantum Information

Control and readout of a 13-level trapped ion qudit

Pei Jiang Low, Brendan White, Crystal Senko

Published May 24, 2025• 24 citations
arXivHTMLPDF

Abstract

Abstract Scaling up the computational space of a quantum system is necessary to demonstrate quantum algorithmic advantage. Currently, including more information carriers is still a physical challenge in general. A less explored avenue for scaling up the computational space involves utilizing the rich energy level structure of a trapped ion to encode multi-level qudits rather than two-level qubits. Here we show control and single-shot readout of qudits with 13 computational states in our chosen information host, 137 Ba + . Utilizing the additional energy states found in 137 Ba + comes with non-trivial complexities which obscure the practical choices of energy states for qudit encoding. We report on tools we have developed for predicting energy states that are practical for qudit encoding, validated with good agreement with our experimental data. We also identify the major error sources for qudit control with 137 Ba + as avenues for improvement to achieve high fidelity operations.

DOI
10.1038/s41534-025-01031-y

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Abstract Scaling up the computational space of a quantum system is necessary to demonstrate quantum algorithmic advantage. Currently, including more information carriers is still a physical challenge in general. A less explored avenue for scaling up the computational space involves utilizing the rich energy level structure of a trapped ion to encode multi-level qudits rather than two-level qubits. Here we show control and single-shot readout of qudits with 13 computational states in our chosen information host, 137 Ba + . Utilizing the additional energy states found in 137 Ba + comes with non-trivial complexities which obscure the practical choices of energy states for qudit encoding. We report on tools we have developed for predicting energy states that are practical for qudit encoding, validated with good agreement with our experimental data. We also identify the major error sources for qudit control with 137 Ba + as avenues for improvement to achieve high fidelity operations.
Scaling quantum computers remains a substantial scientific and technological challenge. Leveraging the full range of intrinsic degrees of freedom in quantum systems offers a promising route towards enhanced algorithmic performance and hardware efficiency. We experimentally study the use of 137Ba+ ions for quantum information processing, achieving high-fidelity state preparation and readout of up to 25 internal levels, thus forming a 25-dimensional trapped-ion qudit. By probing superpositions of up to 24 states, we investigate how errors scale with qudit dimension d and identify the primary error sources affecting quantum coherence. Additionally, we demonstrate high-dimensional qudit operations by implementing a 3-qubit Bernstein-Vazirani algorithm and a 4-qubit Toffoli gate with a single trapped-ion. Our findings suggest that quantum computing architectures based on large-dimensional qudits hold significant promise. A single trapped barium ion is operated as a 25-level quantum system or ‘qudit’. The authors examine how errors scale with dimensionality and demonstrate multi-level quantum logic, suggesting a promising route to efficient quantum computing.
Qudits, or multi-level quantum information carriers, present a promising path for scaling quantum computers. However, their use introduces increased complexity in quantum logic, necessitating careful control of relative phases between different qudit levels. In trapped-ion systems, entangling operations accumulate phases on specific levels that are no longer global, unlike in qubit architectures. Furthermore, the structure of multi-level gates becomes increasingly intricate with higher-dimensional Hilbert spaces. This work explores the theory of these additional local and nonlocal phases, accumulated in Mølmer--Sørensen and Light-shift gates. We propose methods to actively compensate for these phases, enhance gate robustness against parameter fluctuations, and simplify native gates for more efficient circuit decomposition. Our results pave the way toward the practical and scalable implementation of qudit-based quantum processors.
Demonstration of quantum advantage remains challenging due to the increased overhead of controlling large quantum systems. While significant effort has been devoted to qubit-based devices, qudits (d-level systems) offer potential advantages in both hardware efficiency and algorithmic performance. In this paper, we demonstrate multi-tone control of a single trapped ion qudit of up to eight levels, as well as the implementation of Grover’s search algorithm on a qudit with dimensions five and eight, achieving operation fidelity of 96.8(3)% and 69(6)%, respectively, which correspond to 99.9(1)% and 97.1(3) % squared statistical overlap, respectively, with the expected result for a single iteration of the Grover search algorithm. The performance is competitive when compared to qubit-based systems; moreover, the sequence requires only O(d){{{\mathcal{O}}}}(d)O(d) single-qudit gates and no entangling gates. This work highlights the potential of using qudits for efficient implementations of quantum algorithms. The authors demonstrate high-fidelity multi-tone electronic control of trapped-ion qudits up to d=8 levels, enabling efficient SU(d) operations and showcasing advantage by implementing Grover’s search algorithm using encoding in a single qudit, rather than in multiple qubits.
Quantum information has typically focused on using 2-level qubits to perform simulation and computation. We propose to expand the number of levels for computation using qudits, where \\(d>2\\). Doing so could be a viable option for making trapped ion systems scalable for quantum computation. Our group in particular will use Barium ions because of some energy features and convenient laser wavelengths. This thesis presents much of the necessary background needed to work with Barium as a qudit for quantum computation. Energy structure, branching ratios, and saturation intensities are derived and presented. In addition, a method for selecting different isotopes of Barium for trapping is discussed. A method for measuring out the state of a Barium qudit is presented, with error rates estimated to be under \11\\%\1 for up to 5-level qudits. Finally, various optics projects which were necessary for building up our first ion trap are outlined.
We demonstrate a quantum processor based on a 3D linear Paul trap that uses Yb+171 ions with eight individually controllable four-level qudits (ququarts), which is computationally equivalent to a sixteen-qubit quantum processor. The design of the developed ion trap provides high secular frequencies and a low heating rate, which, together with individual addressing and readout optical systems, allows executing quantum algorithms. In each of the eight ions, we use four electronic levels coupled by E2 optical transition at 435 nm for qudit encoding. We present the results of single- and two-qubit operations benchmarking and realizing basic quantum algorithms, including the Bernstein–Vazirani and Grover’s search algorithms as well as H2 and LiH molecular simulations. Our results pave the way to scalable qudit-based quantum processors using trapped ions.
Recent developments in qudit-based quantum computing, in particular with trapped ions, open interesting possibilities for scaling quantum processors without increasing the number of physical information carriers. Here, we propose a method for compiling quantum circuits in the case, where qubits are embedded into qudits of experimentally relevant dimensionalities, d=3,...,8d=3,...,8d=3,...,8, for the trapped-ion platform. In particular, we demonstrate how single-qubit, two-qubit, and multiqubit gates can be realized using single-qudit operations and the $\text{M}\o{}\text{lmer-S}\o{}\text{rensen}$ (MS) gate as a basic two-particle operation. We expect that our findings are directly applicable to the current generation of trapped-ion-based qudit processors.