  Modeling open quantum systems -- quantum systems coupled to a bath -- is of
value in condensed matter theory, cavity quantum electrodynamics, nanosciences
and biophysics. The real-time simulation of open quantum systems was advanced
significantly by the recent development of chain mapping techniques and the use
of matrix product states that exploit the intrinsic entanglement structure in
open quantum systems. The computational cost of simulating open quantum
systems, however, remains high when the bath is excited to high-lying quantum
states. We develop an approach to reduce the computational costs in such cases.
The interaction representation for the open quantum system is used to
distribute excitations among the bath degrees of freedom so that the occupation
of each bath oscillator is ensured to be low. The interaction picture also
causes the matrix dimensions to be much smaller in a matrix product state of a
chain-mapped open quantum system than in the Schr\"odinger picture. Using the
interaction representation accelerates the calculations by 1-2 orders of
magnitude over existing matrix-product-state method. In the regime of strong
system-bath coupling and high temperatures, the speedup can be as large as 3
orders of magnitude. The approach developed here is especially promising to
simulate the dynamics of open quantum systems in the high-temperature and
strong-coupling regimes.
