"Three decades ago, it was proposed that quantum computers (i.e. quantum systems where information can be encoded, processed and read out) could outperform classical devices for information processing. For instance, they may allow the factoring of integer numbers in a time which scales polynomially with the size of the input, while known classical algorithms require an exponential time. Problems of this kind are said to be hard to classically solve, while an efficient quantum solution theoretically exists for some of them, e.g. for factoring. However, in practice, it has not yet been possible to build a quantum computer large enough to beat classical machines. This has raised the question as to whether this difficulty is only technical, and will be overcome one day, or whether there are fundamental reasons why this would not be possible. In trying to answer this question, physicists and computer scientists have developed ""sub-universal"" quantum computing models, which aim at solving very specific problems, simpler than factoring, but still displaying a quantum advantage. Among those is the so-called boson sampling protocol, which enables to compute the permanent of a unitary matrix (a matrix property analogous to the determinant). In other words, scientists now seek for the observation of a minimal supremacy of quantum computers over classical ones.

Inspired by recent experimental achievements (Paris, Japan, Virginia), the goal of my project has been studying at the theoretical level new models of sub-universal quantum computers, based on original photonic architectures. Indeed, these models were only poorly studied, so far, in the promising context of the ""Continuous Variable"" (CV) encoding, which has recently allowed to reach the record-size for quantum computing resource states. This project has articulated through two main objectives: 1) The design of new sub-universal quantum circuits in CV, providing proof of their classical computational hardness 2) The study of viable experimental quantum optics platforms where these protocols may be efficiently implemented.

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