We study the loop-induced decays $h^0 to gamma , gamma$ and $h^0 to g , g$ in the Minimal Supersymmetric Standard Model (MSSM) with quark flavour violation (QFV), identifying $h^0$ with the Higgs boson with a mass of 125 GeV, where $gamma$ and $g$ are photon and gluon, respectively. We perform a MSSM parameter scan and a detailed analysis around a fixed reference point respecting theoretical constraints from vacuum stability conditions and experimental constraints, such as those from B meson data and electroweak precision data, as well as recent limits on supersymmetric (SUSY) particle masses from LHC experiments. We find that (i) the relative deviation of the decay width $Gamma(h^0 to g , g)$ from the Standard Model value, $DEV(g)$, can be large and negative, $lesssim - 15%$, (ii) the analogous deviation of $Gamma(h^0 to gamma , gamma)$ is strongly correlated, $DEV(gamma) simeq -1/4,DEV(g)$ for $DEV(g) lesssim - 4%$, (iii) the relative deviation of the width ratio $Gamma(h^0 to gamma , gamma)/Gamma(h^0 to g , g)$ from the SM value, $DEV(gamma/g)$, can be large (up to $sim$ 20%), (iv) the deviations can be large due to the up-type squark loop contributions, (v) the SUSY QFV parameters can have a significant effect on these deviations. Such large deviations can be observed at a future $e^+e^-$ collider like ILC. Observation of the deviation patterns as shown in this study would favour the MSSM with flavour-violating squark mixings and encourage to perform further studies in this model.
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