  Ultradilute quantum droplets are intriguing new state of matter, in which the
attractive mean-field force can be balanced by the repulsive force from quantum
fluctuations to avoid collapse. Here, we present a microscopic theory of
ultradilute quantum droplets in three-, one- and two-dimensional two-component
Bose-Bose mixtures, by generalizing the conventional Bogoliubov theory to
include the bosonic pairing arising from the interspecies attraction. Our
pairing theory is fully equivalent to a variational approach and hence gives an
upper bound for the energy of quantum droplets. In three dimensions, we predict
the existence of a strongly interacting Bose droplet at the crossover from
Bose-Einstein condensates (BEC) to Bardeen--Cooper--Schrieffer (BCS)
superfluids and map out the bosonic BEC-BCS crossover phase diagram. In one
dimension, we find that the energy of the one-dimensional Bose droplet
calculated by the pairing theory is in an excellent agreement with the latest
diffusion Monte Carlo simulation {[}Phys. Rev. Lett. \textbf{122}, 105302
(2019){]}, for nearly all the interaction strengths at which quantum droplets
exist. In two dimensions, we show that Bose droplets disappear and may turn
into a soliton-like many-body bound state, when the interspecies attraction
exceeds a critical value. Below the threshold, the pairing theory predicts more
or less the same results as the Bogoliubov theory derived by Petrov and
Astrakharchik {[}Phys. Rev. Lett. \textbf{117}, 100401 (2016){]}. The predicted
energies from both theories are higher than the diffusion Monte Carlo results,
due to the weak interspecies attraction and the increasingly important role
played by the beyond-Bogoliubov-approximation effect in two dimensions.
