Q-deformed Painleve tau function and q-deformed conformal blocks

We propose $q$-deformation of the Gamayun-Iorgov-Lisovyy formula for Painlev'e $\tau$ function. Namely we propose formula for $\tau$ function for $q$-difference Painlev'e equation corresponding to $A_7^{(1)}{}^{\mathrm{\prime }}$ surface (and $A_1^{(1)}$ symmetry) in Sakai’s classification. In this formula $\tau$ function equals the series of $q$-Virasoro Whittaker conformal blocks (equivalently Nekrasov partition functions for pure $SU(2)$ 5d theory).