Achieving a quantum computational advantage regime, and thus providing evidence against the extended Church-Turing thesis, remains one of the key challenges in modern science. Boson sampling seems to be a very promising platform in this regard, but to be confident of attaining the advantage regime, one must provide evidence of operating with the correct boson sampling distribution, and not with any of the distributions that admit efficient classical simulation. This problem is often called the validation problem, and it poses a major challenge to demonstrating unambiguous quantum advantage. In this work, using the recently proposed wave-function network approach, we study the sample space filling behavior with increasing the number of collected samples. We show that this allows for black-box data to exclude several undesired hypotheses, especially the distinguishable particles sampling. At this point, reference values corresponding to the true distribution are still required for the presented approach to be considered a complete validation protocol. Nevertheless, we show that it can instead be used for simple and efficient validation against a trusted sampling device. We also study the scaling of our approach with system size and under imperfections such as losses. These results highlight the potential of sample space filling analysis for addressing the validation problem.

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• Boson sampling
• Quantum verification