  Given a conditionally completely positive map $\mathcal L$ on a unital
$\ast$-algebra $\A$, we find an interesting connection between the second
Hochschild cohomology of $\A$ with coefficients in the bimodule $E_{\mathcal
L}=\B^a(\A \oplus M)$ of adjointable maps, where $M$ is the GNS bimodule of
$\mathcal L$, and the possibility of constructing a quantum random walk (in the
sense of \cite{AP,LP,L,KBS}) corresponding to $\mathcal L$.
