Solution:

The potential at the center of the square is the sum of the potentials due to each charge. Since potential is a scalar quantity, the total potential at the center is the algebraic sum of individual potentials.

For the potential to be zero, the sum of the potentials must cancel out. The relationship between \( Q \) and \( q \) for this condition is:

\[
\frac{-Q}{r} + \frac{-q}{r} + \frac{2q}{r} + \frac{2Q}{r} = 0
\]

Simplifying:

\[
(-Q + 2Q) + (-q + 2q) = 0
\]

\[
Q = -q
\]

Thus, the relation is \( Q = -q \).