the Dirac equation, $$\label{eq:Impr7}
\psi^{(n)}(\vec{y},t|t_0) = \sum_{\vec{x}} D^{-1}(\vec{y},t; \vec{x},t_0) \eta^{(n)}(\vec{x},t|t_0).$$

\

With a random $Z(2) \otimes Z(2)$ wall source the solution for quark propagator needs only single inversion instead of $3\times 4=12$ corresponding to color and Dirac components required for a point source or smeared source. When the number of configurations in the ensemble is large enough, even if one uses a single random source for each configuration, (\[eq:Impr5\]) is expected to hold in the ensemble average. One may expect to obtain meson correlators of a similar statistical quality as with the traditional point source with only 1/12 of computing time.

In Fig. \[fig:C2ptPointVSZ2\], we compare the effective pion mass plot calculated on a set of 10 configurations at $\kappa_s=0.1364,\kappa_{ud}=0.13700$ ($M_\pi \approx 702~$MeV) from the PACS-CS ensemble using (a) point source, (b) single random $Z(2) \otimes Z(2)$ wall source, and (c) smeared source. We observe that the signal with the random $Z(2) \otimes Z(2)$ wall source is somewhat better than that for point source, while the signal for smeared source is better than that with the random $Z(2) \otimes Z(2)$ wall source. Using 4 random wall sources for each configuration, we observed that the quality of signal becomes comparable to 