1 Despite the tremendous advances in quantum technologies 2 – 7 reported in the last few years, the implementation of a large-scale universal quantum computer is still far from our current capabilities. This effort is motivated by the promise of quantum algorithmic speed-up, with a notable early example provided by Shor’s algorithm for integer factoring. In recent years, much work has been directed to the development of suitable technologies for scalable quantum computation. We conclude by discussing the future application of photonic boson sampling devices beyond the original theoretical scope. We also discuss recent proposals and implementations of variants of the original problem, theoretical issues occurring when imperfections are considered, and advances in the development of suitable techniques for validation of boson sampling experiments. We review recent advances in photonic boson sampling, describing both the technological improvements achieved and the future challenges. This prospect has stimulated much effort resulting in the experimental implementation of progressively larger devices. There is strong evidence that such an experiment is hard to classically simulate, but it is naturally solved by dedicated photonic quantum hardware, comprising single photons, linear evolution, and photodetection. The problem consists in sampling from the output distribution of indistinguishable bosons in a linear interferometer. Boson sampling is a computational problem that has recently been proposed as a candidate to obtain an unequivocal quantum computational advantage.
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