Nowadays, quantum computation and quantum communication problems are the central part of various researches in the world. This world-wide interest is due to the advantages and speedups that quantum features, like quantum entanglement and quantum superposition, may offer in solving those problems. Until now quantum superposition of quantum states has been extensively exploited to enable advantages, but quantum mechanics also allows to superimpose quantum operations in different orders, namely indefinite causal orders. This novel technique has already been demonstrated in theory to solve some computational problems with fewer resources than the conventional quantum computers, and to open new advantages for quantum communications in a new paradigm. However, no real experimental demonstration of sizeable (>2) superposition of quantum operations has been realized until now. The problem being addressed in InCaSQuC project is to go beyond of the state of the art by creating high-dimensional quantum systems with indefinite causal orders by using cutting-edge technology like Silicon photonics to lay the foundations for potential applications of superposition of quantum operations in different orders. The overall objectives were to establish the experimental bases, as for example single-photon sources, frequency-bin operations, best experimental design, to implement indefinite causal structures. Our project is a step forward to scale up the current implementations of superpositions of causal orders for real applications in quantum computation or quantum communications, which in the near future, could have far-reaching implications for our society in solving specific problems for chemistry, physics or computer science.
