Quantum simulations of time-dependent Hamiltonians beyond the quasi-static approximation

• URL: http://arxiv.org/abs/2305.17097v3
• Date: Mon, 12 Feb 2024 00:57:58 GMT
• Title: Quantum simulations of time-dependent Hamiltonians beyond the quasi-static approximation
• Authors: Boyuan Shi and Florian Mintert
• Abstract summary: existing approaches to analogue quantum simulations of time-dependent quantum systems rely on perturbative corrections to quantum simulations of time-independent quantum systems. We overcome this restriction to perturbative treatments with an approach based on flow equations and a multi-mode Fourier expansion. The potential of the quantum simulations that can be achieved with our approach is demonstrated with the pedagogical example of a Lambda-system and the quench in finite time through a quantum phase transition of a Chern insulator in a driven non-interacting Hubbard system.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Existing approaches to analogue quantum simulations of time-dependent quantum systems rely on perturbative corrections to quantum simulations of time-independent quantum systems. We overcome this restriction to perturbative treatments with an approach based on flow equations and a multi-mode Fourier expansion. The potential of the quantum simulations that can be achieved with our approach is demonstrated with the pedagogical example of a Lambda-system and the quench in finite time through a quantum phase transition of a Chern insulator in a driven non-interacting Hubbard system. The example of the Lambda-system demonstrates the ability of our approach to describe situations beyond the validity of adiabatic approximations.

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