  Quantum walk algorithms can speed up search of physical regions of space in
both the discrete-time [arXiv:quant-ph/0402107] and continuous-time setting
[arXiv:quant-ph/0306054], where the physical region of space being searched is
modeled as a connected graph. In such a model, Aaronson and Ambainis
[arXiv:quant-ph/0303041] provide three different criteria for a unitary matrix
to act locally with respect to a graph, called $Z$-local, $C$-local, and
$H$-local unitaries, and left the open question of relating these three
locality criteria. Using a correspondence between continuous- and discrete-time
quantum walks by Childs [arXiv:0810.0312], we provide a way to approximate
$N\times N$ $H$-local unitaries with error $\delta$ using
$O(1/\sqrt{\delta},\sqrt{N})$ $C$-local unitaries, where the comma denotes the
maximum of the two terms.
