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arXiv · 2212.08508

Coarse-grained effective Hamiltonian via the Magnus Expansion for a three-level system

Nicola Macrì·Luigi Giannelli·Elisabetta Paladino·Giuseppe Falci
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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 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.

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Nicola Macrì, Luigi Giannelli, Elisabetta Paladino, Giuseppe Falci. 2022-12-16. Coarse-grained effective Hamiltonian via the Magnus Expansion for a three-level system. https://doi.org/10.3390/e25020234

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