Find the number of non-zero integral solutions of the equation.

$|1-i|^{x}=2^{x}$

$\Rightarrow\left(\sqrt{1^{2}+(-1)^{2}}\right)^{x}=2^{x}$

$\Rightarrow(\sqrt{2})^{x}=2^{x}$

$\Rightarrow 2^{\frac{x}{2}}=2^{x}$

$\Rightarrow \frac{x}{2}=x$

$\Rightarrow x=2 x$

$\Rightarrow 2 x-x=0$

$\Rightarrow x=0$

Thus, 0 is the only integral solution of the given equation. Therefore, the number of non-zero integral solutions of the given equation is 0.