@Mithrandir24601 Thanks for your response. So since I am working in base $2$ we are comparing $n = \log_2(m)$ to $\frac{2^{\frac{\log_2(m)}{4}}}{\log(m)}$, but if you plug this into wolfram or
desmos it shows that in the asymptotic limit $\log_2(m) \geq \frac{2^{\frac{\log_2(m)}{4}}}{\log(m)}$. How does it follow then that there is an exponential gap between the classical and quantum cases?