  Multitime system correlations functions are relevant in various areas of
physics and science, dealing with system-bath interaction including
spectroscopy and quantum optics, where many of these schemes include an
off-diagonal system bath interaction. Here we extend the enhanced TEMPO
algorithm for quantum path integrals using tensor networks [Phys. Rev. Lett.
123, 240602 (2019)] to open quantum systems with off-diagonal coupling beyond a
single two level system. We exemplify the approach on a coupled cavity
waveguide system with spatially separated quantum two-state emitters, though
many other applications in material science are possible, including entangled
photon propagation, photosynthesis spectroscopy and on-chip quantum optics with
realistic dissipation.
