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In this article, we investigate properties of cyclic codes over a finitenon-chain ring$\mathbb{F}_q+v\mathbb{F}_q+v^2\mathbb{F}_q+v^3\mathbb{F}_q+v^4\mathbb{F}_q,$where $q=p^r,$ $r$ is a positive integer, $p$ is an odd prime, $4 \mid (p-1),$and $v^5=v.$ As an application, we construct several quantum error correctingcodes over the finite field $\mathbb{F}_q.$

Quantum codes constructed from cyclic codes over the ring $\mathbb{F}_q+v\mathbb{F}_q+v^2\mathbb{F}_q+v^3\mathbb{F}_q+v^4\mathbb{F}_q$