标题： 四能级和两量子位系统、子代数以及单位积分 显示英文标题

标题： Four-level and two-qubit systems, sub-algebras, and unitary integration

摘要： 四能级系统在量子光学中以及用于表示量子计算中的两个量子位时，对于一般时间相关的哈密顿量难以求解。提出了一种系统的方法，该方法结合了代数算子方面的分析处理与经典一阶微分方程的简单解法。特别是，通过利用系统完整的SU(4)动力学群中的$su(2) \oplussu(2)$和$su(2) \oplus su(2) \oplus u(1)$子代数，最终计算的非平凡部分简化为一个单个的里卡蒂（一阶，二次非线性）方程，这个方程本身也很容易求解。文中提供了来自近期文献中的两个量子位问题的例子，包括使用约瑟夫森结实现两个量子位门。 显示英文摘要

摘要： Four-level systems in quantum optics, and for representing two qubits in quantum computing, are difficult to solve for general time-dependent Hamiltonians. A systematic procedure is presented which combines analytical handling of the algebraic operator aspects with simple solutions of classical, first-order differential equations. In particular, by exploiting $su(2) \oplus su(2)$ and $su(2) \oplus su(2) \oplus u(1)$ sub-algebras of the full SU(4) dynamical group of the system, the non-trivial part of the final calculation is reduced to a single Riccati (first order, quadratically nonlinear) equation, itself simply solved. Examples are provided of two-qubit problems from the recent literature, including implementation of two-qubit gates with Josephson junctions.