ArticleEntropy (Basel, Switzerland)2023
Coarse-Grained Effective Hamiltonian via the Magnus Expansion for a Three-Level System.
Article in Entropy (Basel, Switzerland), 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
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.
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