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Although several models have been proposed towards assisting machine learning(ML) tasks with quantum computers, a direct comparison of the expressive powerand efficiency of classical versus quantum models for datasets originating fromreal-world applications is one of the key milestones towards a quantum readyera. Here, we take a first step towards addressing this challenge by performinga comparison of the widely used classical ML models known as restrictedBoltzmann machines (RBMs), against a recently proposed quantum model, now knownas quantum circuit Born machines (QCBMs). Both models address the same hardtasks in unsupervised generative modeling, with QCBMs exploiting theprobabilistic nature of quantum mechanics and a candidate for near-term quantumcomputers, as experimentally demonstrated in three different quantum hardwarearchitectures to date. To address the question of the performance of thequantum model on real-world classical data sets, we construct scenarios from aprobabilistic version out of the well-known portfolio optimization problem infinance, by using time-series pricing data from asset subsets of the S\&P500stock market index. It is remarkable to find that, under the same number ofresources in terms of parameters for both classical and quantum models, thequantum models seem to have superior performance on typical instances whencompared with the canonical training of the RBMs. Our simulations are groundedon a hardware efficient realization of the QCBMs on ion-trap quantum computers,by using their native gate sets, and therefore readily implementable innear-term quantum devices.

Classical versus Quantum Models in Machine Learning: Insights from a Finance Application