A Quantum Convolution Autoencoder for Handwritten Letters and Digits: A Case Study

The concept of an autoencoder is a key element of modern machine learning methods. It is used, e.g., to compress the input data into a lower-dimensional representation, which is later employed in other machine learning algorithms. In the area of quantum computing application methods, quantum machine learning is also developing dynamically, with the concept of a quantum autoencoder also present. In the article, we discuss a variant of building a quantum autoencoder based on a quantum convolutional network. The proposed autoencoder is characterized by an architecture based on adjacent quantum gates, which is especially important for the near-future noisy intermediate-scale hardware implementation of such a type of quantum circuits. The proposed circuits are built with an elementary set of gates, i.e., controlled negation gates and rotation gates. The described architecture of a quantum autoencoder properly uses the quantum phenomenon called quantum exponential capacitys, i.e., a linear number of qubits which allow encoding an exponential amount of classical information. In our case, for n qubit, it is possible to encode a classical gray coloured image with dimensionality 2ⁿ × 2ⁿ. The conducted numerical experiments on a set image of handwritten characters and letters show that, for a small number of parameters, the quantum autoencoder offers a reconstruction quality comparable to the currently used classical autoencoders. An important assumption is the omission of additional dimensionality reduction techniques, e.g., PCA, for the preparation of classical data. In the discussed experiment, the data after reconstruction can be read directly from the quantum register, through a series of quantum register measurements.