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I'm inspired by [1] which clearly lays out near term applications of quantum computing: optimization, simulation and sampling. They claim that quantum sampling is likely to be the first application that achieves quantum supremacy "Our calculations show that, for relatively small circuits involving high-fidelity quantum gates, it will be possible to sample from probability distributions that are inaccessible classically, using a circuit of just 7 × 7 qubits in layers that are around 25 deep"

However, the authors only loosely describe potential applications of quantum sampling, viz. "inference and pattern recognition in machine learning". Can anyone describe the utility of quantum sampling in further depth?

[1] Mohseni, M., Read, P., Neven, H., Boixo, S., Denchev, V., Babbush, R., ... & Martinis, J. (2017). Commercialize quantum technologies in five years. Nature, 543(7644), 171-174.

Welcome to QCSE. Aaronson has a proposal, for sampling of the kind mentioned in your linked paper. E.g. he proposes to use random sampling from a quantum circuit as a source for "complexity-certified" randomness. This may be useful, for example, in some cryptocurrencies. Google lectures on "Quantum Supremacy and its Applications".

– Mark S – 2020-08-08T01:51:47.730one that comes to mind is (Huh et al. 2015), in the context of boson sampling

– glS – 2020-08-10T06:18:47.503