论文标题
使用Ququints的广义Toffoli门分解：实现Grover的算法使用Qudits
Generalized Toffoli gate decomposition using ququints: Towards realizing Grover's algorithm with qudits
论文作者
论文摘要
量子位是经典位的量子对应物，用作量子信息处理的基本信息单元，而基础的物理信息载体，例如（人工）原子或离子，接纳更复杂的多级状态的编码 - qudits。最近，对使用QUDIT编码作为进一步缩放量子处理器的一种方式非常关注。在这项工作中，我们在五级量子系统（所谓的Ququints）上呈现了广义Toffoli门的有效分解，该系统使用Ququints的空间作为具有关节辅助状态的两个量子的空间。我们使用的基本双Quition操作是受控阶段门的版本。拟议的$ n $ qubit Toffoli门分解具有$ O（N）$渐近深度，无需辅助尺寸。然后，我们将结果应用于Grover的算法，在该算法中，我们指出了使用基于QUDIT的方法和所提出的分解的可观优势。我们预计我们的结果适用于基于各种物理平台的量子处理器。
Qubits, which are quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g. (artificial) atoms or ions, admit encoding of more complex multilevel states -- qudits. Recently, significant attention is paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on the five-level quantum systems, so-called ququints, that uses ququints' space as the space of two qubits with a joint ancillary state. The basic two-qubit operation that we use is a version of controlled-phase gate. The proposed $N$-qubit Toffoli gate decomposition has $O(N)$ asymptotic depth using no ancillary qubits. We then apply our results for Grover's algorithm, where we indicate on the sizable advantage of the using qudit-based approach with the proposed decomposition. We expect that our results are applicable for quantum processors based on various physical platforms.
