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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 $\exp(-itH)$?

user823
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    $H$ is Hermitian and both $itH$ and $-itH$ are anti-Hermitian. Both $\exp(itH)$ and $\exp(-itH)$ are unitary. QM has no arrow of time. Nonetheless : do you have a reference where they use the plus sign? See also this post. – Kurt G. Mar 03 '22 at 08:38
  • A link is for example: https://www.math.uwaterloo.ca/~cgodsil/quagmire/QuantumWalks/pdfs/GrfSpc3.pdf (p. 3) – user823 Mar 03 '22 at 12:11

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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.

Norbert Schuch
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