  We investigate numerical approximations for the stochastic Burgers equation
driven by an additive cylindrical fractional Brownian motion with Hurst
parameter $H \in (\frac{1}{2}, 1)$. To discretize the continuous problem in
space, a spectral Galerkin method is employed, followed by the presentation of
a nonlinear-tamed accelerated exponential Euler method to yield a fully
discrete scheme. By showing the exponential integrability of the stochastic
convolution of the fractional Brownian motion, we present the boundedness of
moments of semi-discrete and full-discrete approximations. Building upon these
results and the convergence of the fully discrete scheme in probability proved
by a stopping time technique, we derive the strong convergence of the proposed
scheme.
