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We investigate optimal decay rates for higher–order spatial derivatives of strong solutions to the 3D Cauchy problem of the compressible viscous quantum magnetohydrodynamic model in the  H  5  ×  H  4  ×  H  4  framework, and the main novelty of this work is three–fold: First, we show that fourth order spatial derivative of the solution converges to zero at theL  2   -  rate       (  1  +  t  )    -    11   4{L^2} - {\rm{rate}}\,{(1 + t)^{- {{11} \over 4}}}, which is same as one of the heat equation, and particularly faster than theL  2   -  rate       (  1  +  t  )    -   5  4{L^2} - {\rm{rate}}\,{(1 + t)^{- {5 \over 4}}}in Pu–Xu [Z. Angew. Math. Phys., 68:1, 2017] and theL  2   -  rate       (  1  +  t  )    -   9  4{L^2} - {\rm{rate}}\,{(1 + t)^{- {9 \over 4}}}, in Xi–Pu–Guo [Z. Angew. Math. Phys., 70:1, 2019]. Second, we prove that fifth–order spatial derivative of density  ρ  converges to zero at theL  2   -  rate       (  1  +  t  )    -    13   4{L^2} - {\rm{rate}}\,{(1 + t)^{- {{13} \over 4}}}, which is same as that of the heat equation, and particularly faster than ones of Pu–Xu [Z. Angew. Math. Phys., 68:1, 2017] and Xi–Pu–Guo [Z. Angew. Math. Phys., 70:1, 2019]. Third, we show that the high-frequency part of the fourth order spatial derivatives of the velocity  u  and magnetic  B  converge to zero at theL  2   -  rate       (  1  +  t  )    -    13   4{L^2} - {\rm{rate}}\,{(1 + t)^{- {{13} \over 4}}}, which are faster than ones of themselves, and totally new as compared to Pu–Xu [Z. Angew. Math. Phys., 68:1, 2017] and Xi–Pu–Guo [Z. Angew. Math. Phys., 70:1, 2019].

Optimal decay rate for higher–order derivatives of solution to the 3D compressible quantum magnetohydrodynamic model