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arXiv · 2510.25561

Transition-aware decomposition of single-qudit gates

Denis A. Drozhzhin·Evgeniy O. Kiktenko·Aleksey K. Fedorov·Anastasiia S. Nikolaeva
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Abstract

Quantum computation with $d$-level quantum systems, also known as qudits, benefits from the possibility to use a richer computational space compared to qubits. However, for an arbitrary qudit-based hardware platform, the issue is that a generic qudit operation has to be decomposed into the sequence of native operations $-$ pulses that are adjusted to the transitions between two levels in a qudit. Typically, not all levels in a qudit are simply connected to each other due to specific selection rules. Moreover, the number of pulses plays a significant role, since each pulse takes a certain execution time and may introduce error. In this paper, we propose a resource-efficient algorithm to decompose single-qudit operations into the sequence of pulses that are allowed by qudit selection rules. Using the developed algorithm, the number of pulses is at most $d(d{-}1)/2$ for an arbitrary single-qudit operation. For specific operations, the algorithm could produce even fewer pulses. We provide a comparison of qudit decompositions for several types of trapped ions, specifically $^{171}\text{Yb}^+$, $^{137}\text{Ba}^+$ and $^{40}\text{Ca}^+$ with different selection rules, and also decomposition for superconducting qudits. Although our approach deals with single-qudit operations, the proposed approach is important for realizing two-qudit operations since they can be implemented as a standard two-qubit gate that is surrounded by efficiently implemented single-qudit gates.

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Denis A. Drozhzhin, Evgeniy O. Kiktenko, Aleksey K. Fedorov, Anastasiia S. Nikolaeva. 2025-10-29. Transition-aware decomposition of single-qudit gates. https://doi.org/10.3390/e28010056

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