Time evolving matrix product operator (TEMPO) method in a non-diagonal basis set based on derivative of the path integral expression

TL;DR

This paper extends the TEMPO method to handle non-diagonal basis sets and arbitrary baths by deriving a differential equation from the path integral, enabling simulations of more complex open quantum systems.

Contribution

The authors develop a generalized TEMPO algorithm that computes influence functionals in arbitrary basis sets, addressing off-diagonal system-bath couplings.

Findings

Successfully simulated one- and two-qubit systems with non-diagonal couplings.

Extended TEMPO accurately captures dynamics with X- and Z-type baths.

Demonstrated applicability to complex open quantum systems.

Abstract

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 non-diagonal basis set and arbitrary number of non-commuting baths. The generalized influence functional is then obtained by integrating the resulting differential equation. Applicability of the the new method is then tested by simulating one- and two- qubit systems coupled to both Z- and X-type baths.