  The imputation of missing data is a common procedure in data analysis that
consists in predicting missing values of incomplete data points. In this work
we analyse a variational quantum circuit for the imputation of missing data. We
construct variational quantum circuits with gates complexity $O(N)$ and
$O(N^2)$ that return the last missing bit of a binary string for a specific
distribution. We train and test the performance of the algorithms on a series
of datasets finding good convergence of the results. Finally, we test the
circuit for generalization to unseen data. For simple systems, we are able to
describe the circuit analytically, making possible to skip the tedious and
unresolved problem of training the circuit with repetitive measurements. We
find beforehand the optimal values of the parameters and we make use of them to
construct an optimal circuit suited to the generation of truly random data.
