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Abstract The finite dimension estimates of Hausdorff dimension and fractal dimension of the attractor of the dissipative quantum Zakharov equations are mainly studied by using the estimates of the Lyapunov exponents. The main results on the attractor are obtained through studying the linear system DS(t) $\operatorname{DS}(t)$, which is the differential system of solution operator S(t) $S(t)$ for the dissipative quantum Zakharov equations at the initial value (m0,n0,E0) $(m_{0},n_{0},E_{0})$.