solve certain problems exponentially faster than the best known classical algorithms, a very large quantum computer is likely to be required to beat classical computers on a problem of intrinsic interest (as opposed to a made-up problem conceived to demonstrate a quantum advantage, e.g., [@A11; @BBB16]). There are basically two reasons for this. First, classical computers are extremely large and fast. The world’s fastest supercomputers operate at nearly 100 quadrillion (i.e. $10^{17}$) floating-point operations per second on a memory of nearly a quadrillion bytes. While this is largely achieved by parallelization, even the CPU used to write this article performs a few billion operations per second on a memory of a few tens of billions of bytes. In contrast, the typical clock rate of solid-state quantum computers enables a few million operations per second, and in this collection of articles we imagine an early generation of devices containing on the order of a thousand qubits.

While these quantum clock rates and memories sizes may appear reasonably large, we must not forget that quantum systems are highly susceptible to noise, which bring us to the second reason. As far as we know, quantum algorithms need to be implemented fault-tolerantly to provide 