The resource cost of large scale quantum computing

This thesis deals with the problematics of the scalability of fault-tolerant quantum computing. This question is studied under the angle of estimating the resources needed to set up such computers. What we call a resource is, in principle, very general; it could be the power, the energy, the total bandwidth allocated to the different qubits... However, we mainly focus on the energetic cost of quantum computing. In particular, we develop an inter-disciplinary approach that allows to minimize the resources required to implement algorithms on quantum computers. By asking to find the minimum amount of resources required to perform a computation under the constraint that the algorithm provides a correct answer with a targeted accuracy, it is possible to optimize the whole computer in order to minimize the resources spent, while being sure to have a correct answer with a high probability. We apply this approach to a complete model fault-tolerant quantum computer based on superconducting qubits. Our results indicate that for algorithms implemented on thousands of logical qubits, our method makes it possible to reduce the energetic cost by orders of magnitudes in regimes where, without optimizing, the power consumption could be close to the gigawatt. This work illustrates that the energetic cost of quantum computing should be a criterion in itself, allowing to evaluate the scaling potential of a given quantum computer technology. It also illustrates that optimizing the architecture of a quantum computer, via inter-disciplinary methods, including algorithms, error correction, qubit physics, engineering aspects, such as the ones that we propose, can prove to be a powerful tool, clearly improving the scaling potential of quantum computers. Finally, we provide general hints about how to make fault-tolerant quantum computers energy efficient.