Abstract
Quantum computing is a new paradigm that may be able to solve some very specific and interesting problems faster than classical computing. But to reach the regime where quantum computers can outperform their classical counterparts, several crucial milestones must be attained. Hardware needs to improve its error rates and qubit number, algorithms have to evolve in order to be able to run correctly on noisy hardware, implementations and compiler should be tailored to the targeted hardware, analysis of quantum programs and quantum states will likely need improvements.In this thesis, we study several of these milestones and extend over the state of the art, trying to get closer to the quantum supremacy regime. We first implemented a non-trivial quantum algorithm, analysed its behaviour and performed advanced resources estimation. From this implementation and analysis, we confirmed that current quantum hardware could not run such an implementation, even after taking into account hardware intricacies and an extensive and comprehensive optimisation efforts. These optimisation efforts revealed a lack of tools to synthetically visualise the quantum circuit that could guide optimisation similar to classical computing ones. This omission led to the development of qprof, a quantum program analysis tool able to efficiently provide a human-readable structure and cost report from the analysis of a given quantum circuit.Next, we present a classical algorithm to solve the qubit routing problem, one of the most costly steps in quantum compilers, by taking into account hardware calibrations to tailor the final solution to the targeted hardware. We describe how the algorithm works and find that it can improve the fidelity of the quantum computations when it is used.We also implement a variational algorithm to solve linear systems of equations and analyse its requirements and behaviour when executed on real quantum hardware. Finally, we performed an extensive study on single-qubit quantum noise and introduced a new visualisation of quantum states. Using this new representation, we isolated errors in qubits prepared in a known quantum state that are currently not corrected by the automatic calibration of quantum chips.