a
Let the distance of the center from each corner be \(a\) . The the potential at the center is

\(V = \frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{{ - Q}}{a} + \frac{{ - q}}{a} + \frac{{2q}}{a} + \frac{{2Q}}{a}} \right)\)\( = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{Q + q}}{a}\)

This is zero if

\(Q+q=0\)