We study hulls of constacyclic codes of length n over a finite non-chain ring \({\mathbb {F}}_q+v{\mathbb {F}}_q\) with respect to the Euclidean and Hermitian inner products, where \(v^2=v\) . Under a special Gray map from \({\mathbb {F}}_q+v{\mathbb {F}}_q\) to \({\mathbb {F}}^2_q\) , dimensions of hulls of Gary images of constacyclic codes are obtained. Some new quantum error-correcting codes (QECCs) with good parameters are constructed by the quantum construction X method under the Euclidean and Hermitian inner products, respectively. Some of these QECCs are MDS with the minimum distance greater than \(\frac{q}{2}\) , and a few of these QECCs are MDS with the minimum distance equal to q.
