论文标题
三级系统的Magnus膨胀通过Magnus扩展
Coarse-grained effective Hamiltonian via the Magnus Expansion for a three-level system
论文作者
论文摘要
量子状态处理是量子技术的主要工具之一。尽管实际系统是复杂的和/或可能由非理想控制驱动的，但它们可能表现出大约局限于低能量希尔伯特子空间的简单动力学。绝热消除是最简单的近似方案，使我们能够在某些情况下得出有效的汉密尔顿人，在低维希尔伯特子空间中运行。但是，这些近似值可能会带来歧义性和困难，从而阻碍其在越来越大的系统中的准确性进行系统的改善。在这里，我们将Magnus扩展作为一种系统的工具来推导无歧义的有效哈密顿人。我们表明，近似值的有效性最终仅在确切动力学的时间内仅利用正确进行的粗粒。我们以适当量身定制的量子操作的保真度来验证获得有效的哈密顿量的准确性。
Quantum state processing is one of the main tools of quantum technologies. While real systems are complicated and/or may be driven by non-ideal control they may nevertheless exhibit simple dynamics approximately confined to a low-energy Hilbert subspace. Adiabatic elimination is the simplest approximation scheme allowing us to derive in certain cases an effective Hamiltonian operating in a low-dimensional Hilbert subspace. However, these approximations may present ambiguities and difficulties hindering a systematic improvement of their accuracy in larger and larger systems. Here we use the Magnus expansion as a systematic tool to derive ambiguity-free effective Hamiltonians. We show that the validity of the approximations ultimately leverages only on a properly done coarse-graining in time of the exact dynamics. We validate the accuracy of the obtained effective Hamiltonians with suitably tailored fidelities of quantum operations.
