Facial Expression Recognition (FER) is an extremely relevant task associated with human-computer interaction, with applications in predictive environments, content analysis, support for healthcare, behavioural description and many more. FER is a classification problem consisting in associating a face image with a category of expressions indicating anger, fear, surprise, sadness, happiness and so on.
This is a challenging problem when solved via computer models, due to the heterogeneity of human faces and the variety of poses and background.
The conventional approach to FER is based on three major steps: image preprocessing, feature extraction, and expression classification.
We describe here how a supervised classifier for expressions can be implemented on a quantum computer. The first preliminary step of image pre-processing is a classical task producing the items in the dataset, while the feature extraction phase is a mapping of such pre-processed images into graphs. The classification step is the quantum part of our implementation, where the features are mapped into the amplitudes of the quantum state forming the input to the quantum circuit representing the image classifier.
In our approach we take a subset of a dataset of pictures (for our experiments we have considered the FFHQ dataset ) and label the items in this subset. Then we encode the labelled instances and an unlabelled test instance into quantum states; these are then used as input to a quantum circuit in order to infer the test label. The circuit operates in a way that is similar to the nearest centroid technique  of classical machine learning, since the inferred label corresponds to the label of the closest item in terms of the Euclidean distance on a representation of the graphs . The quantum classifier we describe below extends the work in . As we will show later, the output obtained via the final measurement of this circuit can be seen as the minimization of a specific cost function expressing the distance of the unlabelled test from each class of labels, respectively. Thus, by interpreting the distance measure as a kernel, this model can be seen as a kernelized binary classifier.
The complexity (in terms of number of operations or gates) of the procedure we use to calculate the distance is linear in the number of qubits, while in general a classical procedure would use a number of instructions, which is linear in the number of features.
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