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Letq=pmq={p}^{m},ppbe an odd prime, andRk=Fq[u1,u2,…,uk]/⟨ui3=ui,uiuj=ujui⟩{R}_{k}={{\mathbb{F}}}_{q}\left[{u}_{1},{u}_{2},\ldots ,{u}_{k}]\hspace{-0.08em}\text{/}\hspace{-0.08em}\langle {u}_{i}^{3}={u}_{i},{u}_{i}{u}_{j}={u}_{j}{u}_{i}\rangle, wherek≥1k\ge 1and1≤i,j≤k1\le i,j\le k. In this article, we define a Gray map fromRkn{R}_{k}^{n}toFq3kn{{\mathbb{F}}}_{q}^{{3}^{k}n}. We study constacyclic codes overRk{R}_{k}and construct non-binary quantum codes overFq{{\mathbb{F}}}_{q}.

Non-binary quantum codes from constacyclic codes over 𝔽 q [ u 1 , u 2 ,…, u k ]/⟨ u i 3 = u i , u i u j = u j u i ⟩