$\xi > 0.3$. Then, the condition is equivalent to the 3D condition, namely, $na^3 = \xi \frac{a^2}{L^2} \ll 1 $ , which we assume. For smaller values of $\xi$, we can use analytical formulas given in Eqs. (\[e2d\]) and (\[e1d\]), which lead to the condition $ |\log(\xi)| \ll \frac{2L}{a} $ in the 3D-2D and $\sqrt{\xi} \gg \frac{a}{L}$ in the 3D-1D case.

*Conclusions.*—We analyzed the so far unexplored formation of quantum droplets in the Bose-Bose mixtures at dimensional crossover from 3D to 2D or 1D. Under the assumption, that the scattering processes are 3D, which happens when the spatial extent of a tight confinement $L$ is much larger than a 3D scattering length $a$, we have found expressions for the beyond-mean field correction to the system energy. These corrections generalize the Lee-Huang-Yang term as obtained for the 3D BEC. We show how this energy smoothly changes as a function of the parameter $\xi=(g_{11} n_1 + g_{22} n_2)/\varepsilon_0$.

The analysis of 3D-2D and 3D-1D crossovers revealed that the quasi-2D and quasi-1D regimes are accessed for values of $\xi\lesssim0.03$ and $\xi \lesssim 0.0004$, respectively, which are much smaller than expected. The naive prediction suggesting that for $\xi < 1 $, the excitations in 