The search for an application of near-term quantum devices is widespread. Quantum machine learning is touted as a potential utilisation of such devices, particularly those out of reach of the simulation capabilities of classical computers. In this work, we study such an application in generative modelling, focussing on a class of quantum circuits known as Born machines. Specifically, we define a subset of this class based on Ising Hamiltonians and show that the circuits encountered during gradient-based training cannot be efficiently sampled from classically up to multiplicative error in the worst case. Our gradient-based training methods use cost functions known as the Sinkhorn divergence and the Stein discrepancy, which have not previously been used in the gradientbased training of quantum circuits, and we also introduce quantum kernels to generative modelling. We show that these methods outperform the previous standard method, which used maximum mean discrepancy (MMD) as a cost function, and achieve this with minimal overhead. Finally, we discuss the ability of the model to learn hard distributions and provide formal definitions for 'quantum learning supremacy'. We also exemplify the work of this paper by using generative modelling to perform quantum circuit compilation.

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Finding a concrete use case for quantum computers in the near term is still an open question, with machine learning typically touted as one of the first fields which will be impacted by quantum technologies. In this work, we investigate and compare the capabilities of quantum versus classical models for the task of generative modelling in machine learning. We use a real world financial dataset consisting of correlated currency pairs and compare two models in their ability to learn the resulting distribution—a restricted Boltzmann machine, and a quantum circuit Born machine. We provide extensive numerical results indicating that the simulated Born machine always at least matches the performance of the Boltzmann machine in this task, and demonstrates superior performance as the model scales. We perform experiments on both simulated and physical quantum chips using the Rigetti QCSTM platform, and also are able to partially train the largest instance to date of a quantum circuit Born machine on quantum hardware. Finally, by studying the entanglement capacity of the training Born machines, we find that entanglement typically plays a role in the problem instances which demonstrate an advantage over the Boltzmann machine.

The purpose of this study was to estimate the health burden imposed by Lyme disease (LD) in Maryland during 1992 and 1993. A cross-sectional 1-in-15 survey of physicians (total, 1200) in Maryland was conducted to estimate the incidence of diagnosed LD, presumptive cases of LD, patients with tick bites, and diagnostic tests ordered for LD. Results show that LD is underreported by 10- to 12-fold in Maryland, that 80% of cases are managed by primary care physicians, and that there is discordance between the actual clinical treatment of patients and the recommended approach. In addition, the much greater numbers of patients treated for presumptive LD, seen and given prophylaxis for tick bites, and having diagnostic tests indicate that real and perceived LD is a far greater public health problem and uses more medical resources than official surveillance data suggest.