  Long-distance transfer of quantum information in architectures based on
quantum dot spin qubits will be necessary for their scalability. One way of
achieving it is to simply move the electron between two quantum registers.
Precise control over the electron shuttling through a chain of tunnel-coupled
quantum dots is possible when interdot energy detunings are changed
adiabatically. Deterministic character of shuttling is however endangered by
coupling of the transferred electron to thermal reservoirs: sources of
fluctuations of electric fields, and lattice vibrations. We theoretically
analyse how the electron transfer between two quantum dots is affected by
electron-phonon scattering, and interaction with sources of $1/f$ and Johnson
charge noise in both detuning and tunnel coupling. The electron-phonon
scattering turns out to be irrelevant in Si quantum dots, while a competition
between the effects of charge noise and Landau-Zener effect leads to an
existence of optimal detuning sweep rate, at which probability of leaving the
electron behind is minimal. In GaAs quantum dots, on the other hand, coupling
to phonons is strong enough to make the phonon-assisted processes of interdot
transfer dominate over influence of charge noise. The probability of leaving
the electron behind depends then monotonically on detuning sweep rate, and
values much smaller than in silicon can be obtained for slow sweeps. However,
after taking into account limitations on transfer time imposed by need for
preservation of electron's spin coherence, minimal probabilities of leaving the
electron behind in both GaAs- and Si-based double quantum dots turn out to be
of the same order of magnitude. Bringing them down below $10^{-3}$ requires
temperatures $\leq \! 100$ mK and tunnel couplings above $20$ $\mu$eV.
