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Indefinite Causal Structures on an Integrated Silicon Platform for Applications in Quantum Computing

Periodic Reporting for period 1 - InCaSQuC (Indefinite Causal Structures on an Integrated Silicon Platform for Applications in Quantum Computing)

Reporting period: 2018-08-07 to 2020-08-06

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.
From the beginning, the activities carried out in InCaSQuC project comprehend theoretical and experimental research. Our main theoretical result is the calculation of a general expression of the quantum N-switch (the only known experimentally relevant indefinite order structure) for an arbitrary number of channels N with any depolarizing strength, thus providing an operational formula enabling the exploration of communication channels controlled by causal orders. On the experimental research, the main result was the finding of a silicon source of appropriate free spectral range which perfectly matches our needs for the implementation of indefinite causal orders with three quantum operations.
InCaSQuC project made progress in the understanding of the experimental conditions for scaling up superposition of causal order with more than two quantum operations. Our calculations showed that there are communicational advantages by scaling, in number and dimensions, the causal orders in superposition. However, an experimental demonstration of these advantages is still in the process of improvement by the hosting team. If such a demonstration is carried out, it would open many possibilities towards the realisation of real applications in quantum communications and a large-scale computational device in quantum computing.
An indefinite causal order: the quantum 3-switch