Quantum Circuit for Imputation of Missing Data

TL;DR

This paper explores a variational quantum circuit designed for imputing missing binary data, demonstrating its effectiveness, analytical tractability for simple systems, and potential for generating truly random data.

Contribution

The work introduces a quantum circuit with specific gate complexities for data imputation, including analytical solutions for simple cases and methods to optimize performance without extensive training.

Findings

Good convergence on datasets

Effective generalization to unseen data

Analytical solutions for simple systems

Abstract

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.