Quantum Convolutional Neural Networks¶
Convolutional neural networks (CNNs) are a type of classical machine learning model often used in computer vision and image processing applications. The structure of CNNs consists of applying alternating convolutional layers (plus an activation function) and pooling layers to an input array, typically followed by some fully connected layers before the output.
Convolutional layers work by sweeping across the input array and applying different filters (often 2x2 or 3x3 matrices) block by block. These are used to detect specific features of the image wherever they might appear. Pooling layers are then used to downsample the results of these convolutions to extract the most relevant features and reduce the size of the data, making it easier to process in subsequent layers. Common pooling methods involve replacing blocks of the data with their maximum or average values.
Quantum convolutional neural networks (QCNNs) were first introduced in Cong et al. (2018). The structure of QCNNs is motivated by that of CNNs:
Here, convolutions are operations performed on neighbouring pairs of qubits — they are parameterized unitary rotations, just like a regular variational circuit! These convolutions are followed by pooling layers, which are effected by measuring a subset of the qubits, and using the measurement results to control subsequent operations. The analogue of a fully-connected layer is a multi-qubit operation on the remaining qubits before the final measurement. Parameters of all these operations are learned during training.
One very natural application of QCNNs is classifying quantum states - for example, the original work used them to distinguish between different topological phases. QCNNs can also be used to classify images just like their classical counterparts.
Note
Quantum convolutional neural networks as presented here are different from quanvolutional neural networks. See the demo about quanvolutional networks to learn more!