In this paper, we introduce the workflow for converting qubit circuits represented by Open Quantum Assembly format (OpenQASM, also known as QASM) into the qudit form for execution on qudit hardware and provide a method for translating qudit experiment results back into qubit results. We present the comparison of several qudit transpilation regimes, which differ in decomposition of multicontrolled gates: qubit as ordinary qubit transpilation and execution, qutrit with $d=3$ levels and single qubit in qudit, and ququart with $d=4$ levels and 2 qubits per ququart. We provide several examples of transpiling circuits for trapped ion qudit processors, which demonstrate potential advantages of qudits.

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 ${}^{171}\mathrm{Yb}^{+}$, ${}^{137}\mathrm{Ba}^{+}$ and ${}^{40}\mathrm{Ca}^{+}$ 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.

We propose a scalable qudit-based quantum processor using rotational states of polar molecules. Previously, molecular internal states were used to enlarge Hilbert space, whereas our approach uses optical tweezer arrays to achieve scalable architectures with exponential state-space growth without increasing qudit dimensionality d . Entangling gates are implemented by adiabatically bringing traps together to activate dipole-dipole interactions. We develop encoding schemes mapping single qubits into qudits with 2 ≤ d ≤ 5 and pairs of qubits into d = 4 , 5 qudits, enabling universal set of quantum gates. Additional levels in d = 3 and d = 5 qudits simplify multiqubit gate decompositions. We analyze experimental parameters for SrF and NaCs molecules. This approach provides a promising route to scalable quantum information processing with multilevel systems using existing experimental platforms.