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

• URL: http://arxiv.org/abs/2212.08508v1
• Date: Fri, 16 Dec 2022 14:41:10 GMT
• Title: Coarse-grained effective Hamiltonian via the Magnus Expansion for a three-level system
• Authors: Nicola Macr\`i, Luigi Giannelli, Elisabetta Paladino and Giuseppe Falci
• Abstract summary: We use the Magnus expansion as a systematic tool to derive ambiguity-free effective Hamiltonians. We validate the accuracy of the obtained effective Hamiltonians with suitably tailored fidelities of quantum operations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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