  Stochastic resonance is a phenomenon where the response signal to external
driving is enhanced by environment noise. In quantum regime, the effect of
environment is often intrinsically non-Markovian. Due to the combination of
such non-Markovian quantum noise and external driving force, it is difficult to
evaluate the correlation function and hence the power spectrum. Nevertheless, a
recently developed algorithm, which is called time-evolving matrix product
operators (TEMPO), and its extensions provide an efficient and numerically
exact approach for this task. Using TEMPO we investigate non-Markovian effects
in quantum stochastic resonance in a two level system. The periodic signal and
the time-averaged asymptotic correlation function, along with the power
spectrum, are calculated. From the power spectrum the signal-to-noise ratio is
evaluated. It is shown that both signal strength and signal-to-noise ratio are
enhanced by non-Markovian effects, which indicates the importance of
non-Markovian effects in quantum stochastic resonance. In addition, we show
that the non-Markovian effects can shift the peak position of the background
noise power spectrum.
