Quantum Circuit for Imputation of Missing Data

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 analyze a variational quantum circuit for the imputation of missing data. We construct variational quantum circuits with gates complexity $\mathcal {O}(N)$ and $\mathcal {O}(N^{2})$ 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 it 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 make use of them to construct an optimal circuit suited to the generation of truly random data.