Macrì Nicola, Giannelli Luigi, Paladino Elisabetta, Falci Giuseppe
Dipartimento di Fisica e Astronomia "Ettore Majorana", Università di Catania, 95123 Catania, Italy.
Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Catania, 95123 Catania, Italy.
Entropy (Basel). 2023 Jan 27;25(2):234. doi: 10.3390/e25020234.
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 proper coarse-graining in time of the exact dynamics. We validate the accuracy of the obtained effective Hamiltonians with suitably tailored fidelities of quantum operations.
量子态处理是量子技术的主要工具之一。虽然实际系统很复杂，并且/或者可能由非理想控制驱动，但它们仍可能表现出大致局限于低能希尔伯特子空间的简单动力学。绝热消去是最简单的近似方案，使我们能够在某些情况下推导出在低维希尔伯特子空间中运行的有效哈密顿量。然而，这些近似可能存在模糊性和困难，阻碍了在越来越大的系统中系统地提高其精度。在这里，我们使用马格努斯展开作为一种系统工具来推导无模糊的有效哈密顿量。我们表明，这些近似的有效性最终仅依赖于对精确动力学进行适当的时间粗粒化。我们用经过适当定制的量子操作保真度来验证所获得的有效哈密顿量的准确性。
