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Quantum machine Learning (QML) is an emerging technique that leverages quantum theory and the yet-to-be fully developed quantum computers. QML may help solve classification problems that cannot be resolved by deep neural network (DNN). However, QML suffers from a quantum aliasing problem that is created by the inevitable downsampling and binarization operations. QML takes classical data domain as its input, transforms it into a domain of quantum states (a subset of the Hilbert space) using quantum encoding, generates quantum feature vectors, and builds a quantum circuit on the quantum feature vectors—as a machine learning model—to perform classification tasks. Hence, quantum encoding is an important task in QML. However, in addition to the quantum aliasing problem created by the downsampling and binarization operations in the quantum encoding of the classical data to quantum bits, the data scarcity can intensify this problem into an uncontrollable state. This problem has been rarely studied in the QML research literature. Therefore, it is important to study this problem in depth and develop a robust quantum encoding scheme that improves the performance of QML under the influence of data scarcity. In this work, the performance instability of QML under the severity of quantum aliasing and the influence of data scarcity (a combined effect of data and quantum paucity) has been studied by using the TensorFlow Quantum software framework and the MNIST handwritten digits dataset. A quantum encoding—by leveraging Fast Fourier Transform (FFT) and Blackman-Harris window—that encodes the data into qubits to reduce quantum aliasing has been proposed. An empirical study shows that QML significantly improves its learning behavior and performs better than DNN under data scarcity with the use of the proposed FFT-based quantum encoding.
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