A discussion of the gate efficiency of synthesizing an arbitrary unitary U using geometric method is given in Section 2.3. Then Section 2.2 lists various examples of qudit gates and discusses the difference and possible improvement of these gates over their qubit counterparts. The generalization of the universal gate set to qudit systems and several proposed sets are provided in Section 2.1. Definitions and properties of a qudit and related qudit gates are given in Section 2. Finally, we introduce various physical platforms that can implement qudit computation and compare their performances with their qubit counterparts. Qudit versions of three major classes of quantum algorithms-algorithms for the oracles decision problems (e.g., the Deutsch-Jozsa algorithm, algorithms for the hidden non-abelian subgroup problems (e.g., the phase-estimation algorithms (PEAs) and the quantum search algorithm (e.g., Grover’s algorithm -are discussed and the comparison of the qudit designs vs. In this article, high-dimensional generalizations of many widely used quantum gates are presented and the universality of the qudit gates is shown. This review article provides an overview of qudit-based quantum computing covering a variety of topics ranging from circuit building algorithm designs to experimental methods. Īlthough the qudit system’s advantages in various applications and potentials for future development are substantial, this system receives less attention than the conventional qubit-based quantum computing, and a comprehensive review of the qudit-based models and technologies is needed. The qudit-based quantum computing system can be implemented on various physical platforms such as photonic systems continuous spin systems ion trap nuclear magnetic resonance and molecular magnets. The advantage of the qudit not only applies to the circuit model for quantum computers but also applies to adiabatic quantum computing devices topological quantum systems and more. These features play an important role in the reduction of the circuit complexity, the simplification of the experimental setup and the enhancement of the algorithm efficiency. Due to its multi-level nature, qudit provides a larger state space to store and process information and the ability to do multiple control operations simultaneously. Qudit technology, with a qudit being a quantum version of d-ary digits for d > 2 is emerging as an alternative to qubit for quantum computation and quantum information science. Finally we discuss various physical realizations for qudit computation such as the photonic platform, iron trap, and nuclear magnetic resonance. 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. 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. This review provides an overview of qudit-based quantum computing covering a variety of topics ranging from circuit building, algorithm design, to experimental methods. 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. Qudit is a multi-level computational unit alternative to the conventional 2-level qubit. 3Institute for Quantum Science and Technology, University of Calgary, Calgary, AB, Canada.2Department of Physics and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN, United States.1Department of Chemistry, Purdue University, West Lafayette, IN, United States.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |