Controlled adiabatic transfer of a single electron through a chain of quantum dots has been recently achieved in GaAs and Si/SiGe based quantum dots, opening prospects for turning stationary spin qubits into mobile ones and solving in this way the problem of long-distance communication between quantum registers in a scalable quantum computing architecture based on quantum dots. We consider theoretically the process of such an electron transfer between two tunnel-coupled quantum dots, focusing on control by slowly varying the detuning of energy levels in the dots. We take into account the fluctuations in detuning caused by
1/f-type noise that is ubiquitous in semiconductor nanostructures and analyze their influence on probability of successful transfer of an electron in a spin eigenstate. With numerical and analytical calculations we show that probability of electron not being transferred due to $1/{f}^{\ensuremath{\beta}}$ noise in detuning is $\ensuremath{\propto}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\sigma}}^{2}{t}^{\ensuremath{\beta}\ensuremath{-}1}/v$, where $\ensuremath{\sigma}$ characterizes the noise amplitude,
t is the interdot tunnel coupling, and
v is the detuning sweep rate. Interestingly, this means that the noise-induced errors in charge transfer are independent of
t for
1/f noise. For realistic parameters taken from experiments on silicon-based quantum dots, we obtain the minimal probability of charge transfer failure between a pair of dots is limited by
1/f noise in detuning to be the on the order of 0.01. This means that in order to reliably transfer charges across many quantum dots, charge noise in the devices should be further suppressed, or tunnel couplings should be increased, in order to allow for faster transfer (and less exposure to noise), while not triggering the deterministic Landau-Zener excitation.
Long-distance transfer of quantum information in architectures based on quantum dot spin qubits will be necessary for their scalability. One way of achieving this goal is to simply move the electron between two quantum registers. Precise control over the process of shuttling such a single electron through a chain of tunnel-coupled quantum dots is possible when interdot energy detunings are changed adiabatically. The deterministic character of shuttling is, however, endangered by the open nature of the system, as the transferred electron is coupled to thermal reservoirs: sources of fluctuations of electric fields and lattice vibrations. We present a comprehensive analysis showing how the electron transfer between two voltage-controlled 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, with charge noise dominating the dynamics of the system at slow detuning sweep, when the electron spends more time delocalized between the dots (i.e., near the anticrossing of the tunnel-coupled states). Competition between the effects of charge noise and the Landau-Zener effect leads to an existence of an optimal detuning sweep rate, leading to minimal probability of leaving the electron behind. In GaAs quantum dots, on the other hand, piezoelectric coupling to phonons is strong enough to make the processes of interdot transfer assisted by phonon emission and absorption dominate over transitions caused by charge noise. The probability of leaving the electron behind then depends monotonically on detuning the sweep rate over a broad range of rates, and values much smaller than in silicon can be obtained for slow sweeps. However, after taking into account limitations on transfer time imposed by the need for preservation of a shuttled electron's spin coherence, the 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 ${10}^{\ensuremath{-}3}$ requires temperatures $\ensuremath{\le}100$ mK and tunnel couplings above $20\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{eV}$.