Qudit-based quantum computation offers unique advantages over qubit-based systems in terms of noise mitigation capabilities as well as algorithmic complexity improvements. However, the software ecosystem for multi-state quantum systems is severely limited. In this paper, we highlight a quantum workflow for describing and compiling qudit systems. We investigate the design and implementation of a quantum compiler for qudit systems. We also explore several key theoretical properties of qudit computing as well as efficient optimization techniques. Finally, we provide demonstrations using physical quantum computers as well as simulations of the proposed quantum toolchain.
Qudit-based quantum computation offers unique advantages over qubit-based systems in terms of noise mitigation capabilities as well as algorithmic complexity improvements. However, the software ecosystem for multi-state quantum systems is severely limited. In this paper, we highlight a quantum workflow for describing and compiling qudit systems. We investigate the design and implementation of a quantum compiler for qudit systems. We also explore several key theoretical properties of qudit computing as well as efficient optimization techniques. Finally, we provide demonstrations using physical quantum computers as well as simulations of the proposed quantum toolchain.
Quantum computers have the potential to solve some important industrial and scientific problems with greater efficiency than classical computers. While most current realizations focus on two-level qubits, the underlying physics used in most hardware is capable of extending the concepts to a multi-level logic—enabling the use of qudits, which promise higher computational power and lower error rates. Based on a strong theoretical backing and motivated by recent physical accomplishments, this also calls for methods and tools for compiling quantum circuits to those devices. To enable efficient qudit compilation, we introduce the concept of an energy coupling graph for single-qudit systems and provide an adaptive algorithm that leverages this representation for compiling arbitrary unitaries. This leads to significant improvements over the state-of-the-art compilation scheme and, additionally, provides an option to trade-off worst-case costs and run-time. The developed compiler is available via github.com/cda-tum/qudit-compilation under an open-source license.
As quantum devices scale toward practical machine learning applications, the binary qubit paradigm faces expressivity and resource efficiency limitations. Multi-level quantum systems, or qudits, offer a promising alternative by harnessing a larger Hilbert space, enabling richer data embeddings, more compact variational circuits, and support for multi-valued problem structures. In this work, we review the role of qudits in quantum machine learning techniques, mainly variational quantum algorithms and quantum neural networks. Drawing on recent experimental demonstrations, including high-level superconducting transmons, qutrit-based combinatorial optimization, and single-qudit classifiers, we highlight how qudit architectures can reduce circuit depth and parameter counts while maintaining competitive fidelity. We further assess the evolving software ecosystem, from specialized simulators and differentiable-programming libraries to extensions of mainstream frameworks. We also identify key challenges in control complexity, noise management, and tooling maturity.
Quantum computing holds great promise for surpassing the limits of classical devices in many fields. Despite impressive developments, however, current research is primarily focused on qubits. At the same time, quantum hardware based on multi-level, qudit, systems offers a range of advantages, including expanded gate sets, higher information density, and improved computational efficiency, which might play a key role in overcoming not only the limitations of classical machines but also of current qubit-based quantum devices. However, working with qudits faces challenges not only in experimental control but particularly in algorithm development and quantum software. In this work, we introduce MQT Qudits, an open-source tool, which, as part of the Munich Quantum Toolkit (MQT), is built to assist in designing and implementing applications for mixed-dimensional qudit devices. We specify a standardized language for mixed-dimension systems and discuss circuit specification, compilation to hardware gate sets, efficient circuit simulation, and open challenges. MQT Qudits is available at github.com/cda-tum/mqt-qudits and on pypi at pypi.org/project/mqt.qudits.
This short report explores the (non exhaustive) current state of quantum technologies, their potential applications, and the challenges that must be addressed to harness their full potential. In particular we will focus on the quantum computer architecture and its ecosystem. Such architecture represents a complex, multi-layered system that integrates quantum and classical components to enable the execution of quantum algorithms. This manuscript is then organized as follows : first we will introduce the quantum processing unit, the lowest layer of a quantum computer. Then we will progress from the lowest to the higher layer of the system architectures : measurement, circuit control, error correction and mitigation system, the quantum compiler and finally the software stack, with particular emphasis on the interactions between these components
Abstract Quantum compilation, critical for bridging high-level quantum programming and physical hardware, faces unique challenges distinct from classical compilation. As quantum computing advances, scalable and efficient quantum compilation methods become necessary. This paper surveys the landscape of quantum compilation, detailing the processes of qubit mapping and circuit optimization, and emphasizing the need for integration with classical computing to harness quantum advantages. Techniques such as Variational Quantum Eigensolver (VQE) exemplify hybrid approaches, highlighting the potential synergy between quantum and classical systems. It is concluded that, while quantum compilation retains many classic methodologies, it introduces novel complexities and opportunities for optimization and verification, essential for the evolving field of quantum computing.