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Controlled adiabatic transfer of a single electron through a chain of quantumdots has been recently achieved in GaAs and Si/SiGe based quantum dots, openingprospects for turning stationary spin qubits into mobile ones, and solving inthis way the problem of long-distance communication between quantum registersin a scalable quantum computing architecture based on quantum dots. We considertheoretically the process of such an electron transfer between twotunnel-coupled quantum dots, focusing on control by slowly varying the detuningof energy levels in the dots. We take into account the fluctuations in detuningcaused by $1/f$-type noise that is ubiquitous in semiconductor nanostructures,and analyze their influence on probability of successful transfer of anelectron in a spin eigenstate. With numerical and analytical calculations weshow that probability of electron not being transferred due to $1/f^\beta$noise in detuning is $\propto \sigma^2 t^{\beta-1}/v$, where $\sigma$characterizes the noise amplitude, $t$ is the interdot tunnel coupling, and $v$is the detuning sweep rate. Interestingly, this means that the noise-inducederrors in charge transfer are independent of $t$ for $1/f$ noise. For realisticparameters taken from experiments on silicon-based quantum dots, we obtain theminimal probability of charge transfer failure between a pair of dots islimited by $1/f$ noise in detuning to be the on order of $0.01$. This meansthat in order to reliably transfer charges across many quantum dots, chargenoise in the devices should be further suppressed, or tunnel couplings shouldbe increased, in order to allow for faster transfer (and less exposure tonoise), while not triggering the deterministic Landau-Zener excitation.

Adiabatic electron charge transfer between two quantum dots in presence of 1/f noise