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Arbitrary High Order Low-rank Completely Positive and Trace Preserving (CPTP) Schemes for Lindblad Equations with Time-dependent Hamiltonian
Jiuhua Hu, Daniel Appelo, Yingda Cheng·November 15, 2025
math.NAQuantum Physics
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Abstract
In this paper, we develop a framework for designing arbitrary high order low-rank schemes for the Lindblad equation with time-dependent Hamiltonians. Our approach is based on nested Picard iterative integrators (NPI) and results in schemes in Kraus form that are completely positive and trace preserving (CPTP). The schemes are amenable to low rank formulations, making them suitable for problems where the matrix rank of the density matrix is small.