  We study the computational complexity of zigzag sampling algorithm for
strongly log-concave distributions. The zigzag process has the advantage of not
requiring time discretization for implementation, and that each proposed
bouncing event requires only one evaluation of partial derivative of the
potential, while its convergence rate is dimension independent. Using these
properties, we prove that the zigzag sampling algorithm achieves $\varepsilon$
error in chi-square divergence with a computational cost equivalent to
$O\bigl(\kappa^2 d^\frac{1}{2}(\log\frac{1}{\varepsilon})^{\frac{3}{2}}\bigr)$
gradient evaluations in the regime $\kappa \ll \frac{d}{\log d}$ under a warm
start assumption, where $\kappa$ is the condition number and $d$ is the
dimension.
