The time-evolving matrix product operator (TEMPO) method is a powerful tool for simulating open system quantum dynamics. Typically, it is used in problems with diagonal system-bath coupling, where analytical expressions for discretized influence functional are available. In this work, we aim to address issues related to off-diagonal coupling by extending the TEMPO algorithm to accommodate arbitrary basis sets. The proposed approach is based on computing the derivative of the discretized path-integral expression of a generalized influence functional when increasing one time step, which yields an equation of motion valid for a nondiagonal basis set and an arbitrary number of noncommuting baths. The generalized influence functional is then obtained by integrating the resulting differential equation. The applicability of the new method is then tested by simulating one- and two-qubit systems coupled to both $Z$- and $X$-type baths.

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• Open quantum systems & decoherence