smc

Expanding, we get that the expression is $x^2+2xy+y^2+x^2{y}^2-2xy+1$ or $x^2+y^2+x^2{y}^2+1$. By the Trivial Inequality (all squares are nonnegative) the minimum value for this is $\boxed{1}$, which can be achieved at $x=y=0$.