Convolutional Neural Network (CNN) has achieved great success in areas such as computer vision. In the meantime, the rapid evolution of quantum computing hardware gives the possibility to enhance classical machine learning with quantum computing.
Inspired by classical CNN, this work proposes a hybrid quantum-classical convolutional neural network. This work also embeds the evaluation of the gradient of quantum expectation value into the classical automatic differentiation framework, such that the exact gradient of any hybrid loss function can be automatically computed using a hybrid quantum-classical computer.
QCCNN faithfully inherits the elementary structure of CNN, but replaces the feature map in CNN with the "quantum feature map". For example, for a window of size n×n , the quantum feature map first encodes it into a quantum state using qubit encoding, then evolves this state with a parametric quantum circuit, and finally computes the expectation value of a global quantum operator to output a scalar for the next layer.
QCCNN has 3 important features: 1) compared to other CNN inspired quantum machine learning algorithms, QCCNN largely inherits the architecture of CNN, for example nonlinearity and the multi-layer structure. Compared to CNN, QCCNN can explore a much larger feature space, thus more likely to achieve a higher learning accuracy, which is demonstrated numerically on a synthetic dataset in this work; 2) The window size used in CNN is often relatively small, such as from 3×3 to 9×9, thus the quantum feature map is friendly to current quantum computer with a few tens of qubits; 3) There is no input and output problem in QCCNN by design. Additional, QCCNN can easily accept quantum data as input, in which case quantum advantage in terms of computational efficiency could be realized.
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