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arXiv:2602.21886 · Physical Review A

Analysis of the action of conventional trapped-ion entangling gates in qudit space

Pavel Kamenskikh, Nikita Semenin, Ilia Zalivako, Vasiliy Smirnov, Ilya Semerikov, Ksenia Khabarova, Nikolay Kolachevsky

quant-phphysics.atom-phSubmitted Feb 25, 2026• Announced Feb 26, 2026• 0 citations• Revised Sep 3, 2026 (v2)
v1 · Feb 25, 2026v2 · Sep 3, 2026
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Abstract

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.

Journal reference
Phys. Rev. A 114, 012458 (2026)
DOI
10.1103/sxrf-1h7v
Comments
20 pages, 9 figures

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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.
Quantum information carriers, just like most physical systems, naturally occupy high-dimensional Hilbert spaces. Instead of restricting them to a two-level subspace, these high-dimensional (qudit) quantum systems are emerging as a powerful resource for the next generation of quantum processors. Yet harnessing the potential of these systems requires efficient ways of generating the desired interaction between them. Here, we experimentally demonstrate an implementation of a native two-qudit entangling gate up to dimension 5 in a trapped-ion system. This is achieved by generalizing a recently proposed light-shift gate mechanism to generate genuine qudit entanglement in a single application of the gate. The gate seamlessly adapts to the local dimension of the system with a calibration overhead that is independent of the dimension.
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.
High-fidelity and parallel realization in scalable platforms of the two-qubit entangling gates fundamental to universal quantum computing constitutes one of the largest challenges in implementing fault-tolerant quantum computation. Integrated optical addressing of trapped-ion qubits offers routes to scaling the high-fidelity optical control demonstrated to date in small systems. Here we show that in addition to scaling, capabilities practically enabled by integrated optics can substantially alleviate laser powers required for both light-shift (LS) and Molmer-Sorensen (MS) geometric phase gates acting on long-lived ground-state qubit encodings in a broad range of ion species. In the proposed gate schemes utilizing carrier nulling via ion positioning at phase-stable standing-wave (SW) nodes, our calculations suggest that suppressed spontaneous photon scattering at the SW node allows for gate drives operating at smaller Raman detunings, resulting in approximately an order-of-magnitude reduction in power requirement (and significantly larger in certain parameter regimes) for gates of a given duration and scattering-limited fidelity as compared to conventional running wave (RW)-based approaches. The SW schemes have the additional benefit of simultaneously eliminating undesired coherent couplings that typically limit gate speeds. Our work quantifies power requirements for multiple ion species and enhancements to be expected from carrier-nulled configurations practically enabled by integrated delivery, and informs experiments and systems for realization of fast and power-efficient laser-based entangling gates in scalable platforms.
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The use of multilevel information carriers, also known as qudits, is a promising path for exploring scalability of quantum computing devices. Here we present a proof-of-principle realization of a quantum processor register that uses optically addressed 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ ion qudits in a linear trap. The rich level structure of 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ ions allows using the Zeeman sublevels of the quadrupole clock transition at 435.5 nm for efficient and robust qudit encoding. We demonstrate the realization of the universal set of gates consisting of single-qudit rotations and a two-qudit M\o{}lmer-S\o{}rensen operation with a two-ququart system, which is formally equivalent to a universal gate-based four-qubit processor. Our results paves a way toward further studies of more efficient implementations of quantum algorithms with trapped-ion-based processors and, specifically, exploring properties of 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ ion qudits.
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.