Quantum computers have the potential to solve important problems which are fundamentally intractable on a classical computer. The underlying physics of quantum computing platforms supports using multi-valued logic, which promises a boost in performance over the prevailing two-level logic. One key element to exploiting this potential is the capability to efficiently prepare quantum states for multi-valued, or qudit, systems. Due to the time sensitivity of quantum computers, the circuits to prepare the required states have to be as short as possible. In this paper, we investigate quantum state preparation with a focus on mixed-dimensional systems, where the individual qudits may have different dimensionalities. The proposed approach automatically realizes quantum circuits constructing a corresponding mixed-dimensional quantum state. To this end, decision diagrams are used as a compact representation of the quantum state to be realized. We further incorporate the ability to approximate the quantum state to enable a finely controlled trade-off between accuracy, memory complexity, and number of operations in the circuit. Empirical evaluations demonstrate the effectiveness of the proposed approach in facilitating fast and scalable quantum state preparation, with performance directly linked to the size of the decision diagram. The implementation is freely available as part of Munich Quantum Toolkit (MQT) at github.com/cda-tum/mqt-qudits.

Most quantum computing architectures to date natively support multi-valued logic, albeit being typically operated in a binary fashion. Multi-valued, or qudit, quantum processors have access to much richer forms of quantum entanglement, which promise to significantly boost the performance and usefulness of quantum devices. However, much of the theory as well as corresponding design methods required for exploiting such hardware remain insufficient and generalizations from qubits are not straightforward. A particular challenge is the compilation of quantum circuits into sets of native qudit gates supported by state-of-the-art quantum hardware. In this work, we address this challenge by introducing a complete workflow for compiling any two-qudit unitary into an arbitrary native gate set. Case studies demonstrate the feasibility of both, the proposed approach as well as the corresponding implementation (which is freely available at github.com/cda-tum/qudit-entanglement-compilation).