While the technological development that has led us from the abacus to today’s supercomputers or even to the latest achievements of machine learning are quite spectacular, one should not forget that they all fit the very same model of computation, formalized by Turing in the 1930s, and therefore fall under the umbrella of classical computing. Quantum physics has played a major role in this story through the 1 st quantum revolution which gave birth to the transistor, the laser and the micro-processor. Rather surprisingly, the impact of quantum physics on the theory of computation is very likely still in its infancy. There is little doubt that an unprecedented shift will occur in the decades to come and that an entirely new form of computing will be dominant in 50 years (and probably much sooner). This is the object of the 2 nd quantum revolution which will harness the quantum properties of matter and light to process data much more efficiently than is possible by purely classical means. The scope of applications remains hard to delineate at this point but covers a large spectrum of human activities: simulation of quantum systems will be crucial to develop new medicine, help fighting climate change by developing better materials to store or transport energy, reducing CO2 emissions by developing efficient processes to capture CO2; quantum computing will also be instrumental to solve optimization problems intractable today. At the same time, quantum technologies will dramatically impact cryptography and requires to implement important changes right now.

If the first glimpse of this second quantum revolution can be traced back to visionaries like Feynman or Deutsch in the early 80s, the fields of quantum computation and quantum simulation really took off in the last decade or so. The long-term objective of this line of work is to build a large universal quantum computer and the main scientific challenges today are to identify potential approaches for scaling up the small quantum processors consisting of a few tens of qubits already available, to anticipate how to program these new machines, and to understand what new capabilities will become accessible once quantum
computing becomes available.

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