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A universal quantum computer of moderate scale is not available yet, howeverintermediate models of quantum computation would still permit demonstrations ofa quantum computational advantage over classical computing and could challengethe Extended Church-Turing Thesis. One of these models based on single photonsinteracting via linear optics is called Boson Sampling. Although Boson Samplingwas demonstrated and the threshold to claim quantum computational advantage wasachieved, the question on how to scale up Boson Sampling experiments remains.To make progress with this problem, here we present a practically achievablepathway to scale Boson Sampling experiments with current technologies bycombining continuous-variables quantum information and temporal encoding. Wepropose the combination of switchable dual-homodyne and single-photondetections, the temporal loop technique and scattershot-based Boson Sampling.We detail the required assumptions for concluding computational hardness forthis configuration. Furthermore, this particular combination of techniquespermits an efficient scaling and certification of Boson Sampling, all in asingle experimental setup.

Boson Sampling with Gaussian input states: efficient scaling and certification