  We provide an efficient and accurate simulation scheme for the rough Heston
model in the standard ($H>0$) as well as the hyper-rough regime ($H > -1/2$).
The scheme is based on low-dimensional Markovian approximations of the rough
Heston process derived in [Bayer and Breneis, arXiv:2309.07023], and provides
weak approximation to the rough Heston process. Numerical experiments show that
the new scheme exhibits second order weak convergence, while the computational
cost increases linear with respect to the number of time steps. In comparison,
existing schemes based on discretization of the underlying stochastic Volterra
integrals such as Gatheral's HQE scheme show a quadratic dependence of the
computational cost. Extensive numerical tests for standard and path-dependent
European options and Bermudan options show the method's accuracy and
efficiency.
