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.

DOI: 10.1038/s41467-026-68746-0

Related papers

Efficient Implementation of a Quantum Algorithm with a Trapped Ion Qudit

Xiaoyang Shi, Jasmine Sinanan-Singh, Timothy Burke +2 more

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 first implementation of Grover's search algorithm on a qudit with dimension 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 (SSO), 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 $\mathcal{O}(d)$ single qudit gates and no entangling gates. This work highlights the potential of using qudits for efficient implementations of quantum algorithms.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 first implementation of Grover's search algorithm on a qudit with dimension 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 (SSO), 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 $\mathcal{O}(d)$ single qudit gates and no entangling gates. This work highlights the potential of using qudits for efficient implementations of quantum algorithms.

arXiv:2506.09371Jun 11, 20250 citations

Quantum logic operations and algorithms in a single 25-level atomic qudit

Pei Jiang Low, Nicholas Zutt, Gaurav A. Tathed +1 more

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.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.

arXiv:2507.15799Nature CommunicationsJun 2, 20261 citation

Efficient realization of quantum algorithms with qudits

Anastasiia S. Nikolaeva, Evgeniy O. Kiktenko, Aleksey K. Fedorov

Abstract The development of a universal fault-tolerant quantum computer that can solve efficiently various difficult computational problems is an outstanding challenge for science and technology. In this work, we propose a technique for an efficient implementation of quantum algorithms with multilevel quantum systems (qudits). Our method uses a transpilation of a circuit in the standard qubit form, which depends on the characteristics of a qudit-based processor, such as the number of available qudits and the number of accessible levels. This approach provides a qubit-to-qudit mapping and comparison to a standard realization of quantum algorithms highlighting potential advantages of qudits. We provide an explicit scheme of transpiling qubit circuits into sequences of single-qudit and two-qudit gates taken from a particular universal set. We then illustrate our method by considering an example of an efficient implementation of a 6-qubit quantum algorithm with qudits. In this particular example, we demonstrate how using qudits allows a decreasing amount of two-body interactions in the qubit circuit implementation. We expect that our findings are of relevance for ongoing experiments with noisy intermediate-scale quantum devices that operate with information carriers allowing qudit encodings, such as trapped ions and neutral atoms, as well as optical and solid-state systems.Abstract The development of a universal fault-tolerant quantum computer that can solve efficiently various difficult computational problems is an outstanding challenge for science and technology. In this work, we propose a technique for an efficient implementation of quantum algorithms with multilevel quantum systems (qudits). Our method uses a transpilation of a circuit in the standard qubit form, which depends on the characteristics of a qudit-based processor, such as the number of available qudits and the number of accessible levels. This approach provides a qubit-to-qudit mapping and comparison to a standard realization of quantum algorithms highlighting potential advantages of qudits. We provide an explicit scheme of transpiling qubit circuits into sequences of single-qudit and two-qudit gates taken from a particular universal set. We then illustrate our method by considering an example of an efficient implementation of a 6-qubit quantum algorithm with qudits. In this particular example, we demonstrate how using qudits allows a decreasing amount of two-body interactions in the qubit circuit implementation. We expect that our findings are of relevance for ongoing experiments with noisy intermediate-scale quantum devices that operate with information carriers allowing qudit encodings, such as trapped ions and neutral atoms, as well as optical and solid-state systems.

arXiv:2111.04384EPJ Quantum TechnologyJun 26, 202445 citations

Towards a Multiqudit Quantum Processor Based on a 171Yb+ Ion String: Realizing Basic Quantum Algorithms

Ilia V. Zalivako, Anastasiia S. Nikolaeva, Alexander S. Borisenko +12 more

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.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.

arXiv:2402.03121Quantum ReportsApr 12, 202520 citations

Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover’s Algorithm with Qudits

Anastasiia S. Nikolaeva, Evgeniy O. Kiktenko, Aleksey K. Fedorov

Qubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states—qudits. Recently, significant attention has been paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on five-level quantum systems—so-called ququints—that use ququints’ space as the space of two qubits with a joint ancillary state. The basic two-qubit operation we use is a version of the controlled-phase gate. The proposed N-qubit Toffoli gate decomposition has O(N) asymptotic depth and does not use ancillary qubits. We then apply our results for Grover’s algorithm, where we indicate on the sizable advantage of using the qudit-based approach with the proposed decomposition in comparison to the standard qubit case. We expect that our results are applicable for quantum processors based on various physical platforms, such as trapped ions, neutral atoms, protonic systems, superconducting circuits, and others.Qubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states—qudits. Recently, significant attention has been paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on five-level quantum systems—so-called ququints—that use ququints’ space as the space of two qubits with a joint ancillary state. The basic two-qubit operation we use is a version of the controlled-phase gate. The proposed N-qubit Toffoli gate decomposition has O(N) asymptotic depth and does not use ancillary qubits. We then apply our results for Grover’s algorithm, where we indicate on the sizable advantage of using the qudit-based approach with the proposed decomposition in comparison to the standard qubit case. We expect that our results are applicable for quantum processors based on various physical platforms, such as trapped ions, neutral atoms, protonic systems, superconducting circuits, and others.

arXiv:2212.12505EntropyFeb 20, 202316 citations

Scalable, High-Fidelity All-Electronic Control of Trapped-Ion Qubits

Clemens Löschnauer, Jacopo Mosca Toba, A. C. Hughes +10 more

The central challenge of quantum computing is implementing high-fidelity quantum gates at scale. However, many existing approaches to qubit control suffer from a scale-performance trade-off, impeding progress towards the creation of useful devices. Here, we present a vision for an electronically controlled trapped-ion quantum computer that alleviates this bottleneck. Our architecture utilizes shared current-carrying traces and local tuning electrodes in a microfabricated chip to perform quantum gates with low noise and crosstalk regardless of device size. To verify our approach, we experimentally demonstrate low-noise site-selective single- and two-qubit gates in a seven-zone ion trap. We implement electronic single-qubit gates with fidelities ≥ 99.99912 ( 8 ) % and demonstrate consistent performance with low crosstalk across the device. We also electronically generate two-qubit maximally entangled states with 99.97 ( 1 ) % fidelity and long-term stable performance over continuous system operation. These state-of-the-art results highlight the potential of our all-electronic approach for coherent control of trapped-ion qubits in large-scale quantum computers.The central challenge of quantum computing is implementing high-fidelity quantum gates at scale. However, many existing approaches to qubit control suffer from a scale-performance trade-off, impeding progress towards the creation of useful devices. Here, we present a vision for an electronically controlled trapped-ion quantum computer that alleviates this bottleneck. Our architecture utilizes shared current-carrying traces and local tuning electrodes in a microfabricated chip to perform quantum gates with low noise and crosstalk regardless of device size. To verify our approach, we experimentally demonstrate low-noise site-selective single- and two-qubit gates in a seven-zone ion trap. We implement electronic single-qubit gates with fidelities ≥ 99.99912 ( 8 ) % and demonstrate consistent performance with low crosstalk across the device. We also electronically generate two-qubit maximally entangled states with 99.97 ( 1 ) % fidelity and long-term stable performance over continuous system operation. These state-of-the-art results highlight the potential of our all-electronic approach for coherent control of trapped-ion qubits in large-scale quantum computers.

arXiv:2407.07694PRX QuantumSep 18, 202537 citations

{{{\mathcal{O}}}}(d)

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 first implementation of Grover's search algorithm on a qudit with dimension 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 (SSO), 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)

single qudit gates and no entangling gates. This work highlights the potential of using qudits for efficient implementations of quantum algorithms.