  The autoencoder is one of machine learning algorithms used for feature
extraction by dimension reduction of input data, denoising of images, and prior
learning of neural networks. At the same time, autoencoders using quantum
computers are also being developed. However, current quantum computers have a
limited number of qubits, which makes it difficult to calculate big data. In
this paper, as a solution to this problem, we propose a computation method that
applies a convolution filter, which is one of the methods used in machine
learning, to quantum computation. As a result of applying this method to a
quantum autoencoder, we succeeded in denoising image data of several hundred
qubits or more using only a few qubits under the autoencoding accuracy of 98%,
and the effectiveness of this method was obtained. Meanwhile, we have verified
the feature extraction function of the proposed autoencoder by dimensionality
reduction. By projecting the MNIST data to two-dimension, we found the proposed
method showed superior classification accuracy to the vanilla principle
component analysis (PCA). We also verified the proposed method using IBM Q
Melbourne and the actual machine failed to provide accurate results implying
high error rate prevailing in the current NISQ quantum computer.
