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<p>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 (<i>d</i>-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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({{{\mathcal{O}}}}(d)\)</EquationSource> <EquationSource Format="MATHML"><math> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> <mrow> <mo>(</mo> <mrow> <mi>d</mi> </mrow> <mo>)</mo> </mrow> </math></EquationSource> </InlineEquation> single-qudit gates and no entangling gates. This work highlights the potential of using qudits for efficient implementations of quantum algorithms.</p>

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Efficient implementation of a quantum algorithm with a trapped ion qudit

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月21日

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  • Xiaoyang Shi,
  • Jasmine Sinanan-Singh,
  • Timothy J. Burke,
  • John Chiaverini,
  • Isaac L. Chuang

摘要

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 \({{{\mathcal{O}}}}(d)\) O ( d ) single-qudit gates and no entangling gates. This work highlights the potential of using qudits for efficient implementations of quantum algorithms.