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 Schrödinger picture. Using the interaction-representation accelerates the calculations by one to two 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 three 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 [1].

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In strong-coupling regimes, quantum dynamical effects can alter conventional physics described by perturbation theories, but the dynamical simulations of these quantum systems using matrix product states-such as multi-level vibronic systems that are relevant to energy and electron transfer reactions-suffer from rapid entanglement growth during their real-time evolution, impeding explorations of spectra, dynamics, and kinetics. We examine the possibility of using non-unitary transformations to alter dynamical entanglement growth in matrix-product-state simulations of quantum systems, using the spin-Boson model to showcase the reduced entanglement. By appropriately choosing the transformation, the entanglement growth rate is suppressed, improving the efficiency of quantum dynamical simulations. Entanglement control is achieved by the transformation-induced biased transitions among the system quantum states, and by "projecting" (approximately) the system quantum state to one of the eigenstates of the system-bath coupling operator, thus controlling the energy exchange between the system and bath. The transformation can be applied to quantum many-body systems, including spin chains and multi-level vibronic systems; the approach improves the numerical efficiency of the MPS simulations.

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