  Convolutional neural networks (CNNs) have rapidly risen in popularity for
many machine learning applications, particularly in the field of image
recognition. Much of the benefit generated from these networks comes from their
ability to extract features from the data in a hierarchical manner. These
features are extracted using various transformational layers, notably the
convolutional layer which gives the model its name. In this work, we introduce
a new type of transformational layer called a quantum convolution, or
quanvolutional layer. Quanvolutional layers operate on input data by locally
transforming the data using a number of random quantum circuits, in a way that
is similar to the transformations performed by random convolutional filter
layers. Provided these quantum transformations produce meaningful features for
classification purposes, then the overall algorithm could be quite useful for
near term quantum computing, because it requires small quantum circuits with
little to no error correction. In this work, we empirically evaluated the
potential benefit of these quantum transformations by comparing three types of
models built on the MNIST dataset: CNNs, quantum convolutional neural networks
(QNNs), and CNNs with additional non-linearities introduced. Our results showed
that the QNN models had both higher test set accuracy as well as faster
training compared to the purely classical CNNs.
