论文标题
通过广义的Gell-Mann代表为一般非机构哈密顿量指定Qudit的统一演变
Specifying the unitary evolution of a qudit for a general nonstationary Hamiltonian via the generalized Gell-Mann representation
论文作者
论文摘要
对量子技术任务的最佳实现导致对在时间依赖性的哈密顿量下的$ d $级量子系统（QUDIT）行为进行详细的分析研究。在本文中，我们介绍了一种新的一般形式主义，描述了类似Bloch的矢量空间的Qudit $（D \ GEQ2）$的统一演变，并指定在一般情况下，这种形式主义与在任意时间依赖于时间依赖时间相关的Hamiltonian的进化过程中的时间相关参数有关。将这种新的常规形式主义应用于量子案例$（d = 2）$，我们通过在$ \ mathbb {r}^{4} $中的单位矢量的演化指定了量子的统一演变，这使我们能够得出Qubit Untartial Ottrolution Operation的精确分析，用于非阶级非阶级非阶级的非阶级Hamiltonary Hamilton hamilton。这种新的分析表达包括文献中已知的量子解决方案，仅作为特定情况。
Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a $d$-level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new general formalism describing the unitary evolution of a qudit $(d\geq2)$ in terms of the Bloch-like vector space and specify how in a general case this formalism is related to finding time-dependent parameters in the exponential representation of the evolution operator under an arbitrary time-dependent Hamiltonian. Applying this new general formalism to a qubit case $(d=2)$, we specify the unitary evolution of a qubit via the evolution of a unit vector in $\mathbb{R}^{4}$ and this allows us to derive the precise analytical expression of the qubit unitary evolution operator for a wide class of nonstationary Hamiltonians. This new analytical expression includes the qubit solutions known in the literature only as particular cases.
