  Let $p\geq3$ be a large prime and let $n(p)\geq2$ denotes the least quadratic
nonresidue modulo $p$. This note sharpens the standard upper bound of the least
quadratic nonresidue from the unconditional upper bound $n(p)\ll
p^{1/4\sqrt{e}+\varepsilon}$ to the conjectured upper bound $n(p)\ll (\log
p)^{1+\varepsilon}$, where $\varepsilon>0$ is a small number, unconditionally.
This improvement breaks the exponential upper bound barrier.
