  We study quantum annealing of pure and random transverse Ising chains that
are coupled to boson baths, using a novel numerical method based on the
combination of the quasi-adiabatic propagation path integral (QUAPI) and the
matrix product state (MPS) formalisms. We present numerical results on systems
up to 64 spins and conclude that the baths disturb quantum annealing of pure
and random Ising chains. The numerical method to compute the reduced density
matrix is described in detail.

Statistical Mechanics;Quantum Physics