  Generating high-quality data (e.g. images or video) is one of the most
exciting and challenging frontiers in unsupervised machine learning. Utilizing
quantum computers in such tasks to potentially enhance conventional machine
learning algorithms has emerged as a promising application, but poses big
challenges due to the limited number of qubits and the level of gate noise in
available devices. In this work, we provide the first practical and
experimental implementation of a quantum-classical generative algorithm capable
of generating high-resolution images of handwritten digits with
state-of-the-art gate-based quantum computers. In our quantum-assisted machine
learning framework, we implement a quantum-circuit based generative model to
learn and sample the prior distribution of a Generative Adversarial Network. We
introduce a multi-basis technique that leverages the unique possibility of
measuring quantum states in different bases, hence enhancing the expressivity
of the prior distribution. We train this hybrid algorithm on an ion-trap device
based on $^{171}$Yb$^{+}$ ion qubits to generate high-quality images and
quantitatively outperform comparable classical Generative Adversarial Networks
trained on the popular MNIST data set for handwritten digits.
