A type of optics experiment called a boson sampler could be among the easiest routes to demonstrating the power of quantum computers. But recent work shows that super-classical boson sampling may be a long way off.
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Childs, A. Quantum advantage deferred. Nature Phys 13, 1148 (2017). https://doi.org/10.1038/nphys4272
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DOI: https://doi.org/10.1038/nphys4272