  Independent component analysis (ICA) is a fundamental data processing
technique to decompose the captured signals into as independent as possible
components. Computing the contrast function, which serves as a measure of
independence of signals, is vital in the separation process using ICA. This
paper presents a quantum ICA algorithm which focuses on computing a specified
contrast function on a quantum computer. Using the quantum acceleration in
matrix operations, we efficiently deal with Gram matrices and estimate the
contrast function with the complexity of
$O(\epsilon_1^{-2}\mbox{poly}\log(N/\epsilon_1))$. This estimation subprogram,
combined with the classical optimization framework, enables our quantum ICA
algorithm, which exponentially reduces the complexity dependence on the data
scale compared with classical algorithms. The outperformance is further
supported by numerical experiments, while a source separation of a
transcriptomic dataset is shown as an example of application.
