Qudit is a multi-level computational unit alternative to the conventional 2-level qubit. Compared to qubit, qudit provides a larger state space to store and process information, and thus can provide reduction of the circuit complexity, simplification of the experimental setup and enhancement of the algorithm efficiency. This review provides an overview of qudit-based quantum computing covering a variety of topics ranging from circuit building, algorithm design, to experimental methods. We first discuss the qudit gate universality and a variety of qudit gates including the pi/8 gate, the SWAP gate, and the multi-level controlled-gate. We then present the qudit version of several representative quantum algorithms including the Deutsch-Jozsa algorithm, the quantum Fourier transform, and the phase estimation algorithm. Finally we discuss various physical realizations for qudit computation such as the photonic platform, iron trap, and nuclear magnetic resonance.

Qudit是替代传统2级qubit的多级计算单元。与qubit相比，qudit提供了更大的状态空间来存储和处理信息，因此可以降低电路复杂性，简化实验设置并提高算法效率。这篇综述概述了基于qudit的量子计算，涵盖了从电路构建，算法设计到实验方法的各种主题。我们首先讨论qudit门的通用性和各种qudit门，包括pi / 8门，SWAP门和多级受控门。然后，我们介绍几种具有代表性的量子算法的qudit版本，其中包括Deutsch-Jozsa算法，量子傅立叶变换和相位估计算法。