Quantum walk: transition matrix, negative or positive sign in the exponent?

Question

Why is it that in some papers the transition matrix of a continuous-time quantum walk is defined as $\exp(itH)$ and in other papers as $\exp(-itH)$?

Answer 1

Because the only thing which matters about $i$ is that $i^2=1$. You can always change $i$ to $-i$ as long as you do it consistently. While the convention is to use $e^{-iHt}$ for time evolution, nothing bad will happen if you take the $+$ sign.