Quantum systems modelling and metrology with circuit quantum electrodynamics

A leading platform for quantum information processing are superconducting circuits, which can now comprise tenths of qubits. One of the key challenges in the design of these systems is balancing the tradeoff between access to the qubits for readout and control versus environment induced decoherence. In other words, the same lines used to access the information on the system, unavoidable induce losses and destroy the quantum information store on it. To mitigate this issue, nonreciprocal devices are included between the superconducting qubits and the control electronics. Commercially available microwave nonreciprocal devices are bulky, and impractical for scaling these systems to the scales necessary for the implementation of useful quantum computing algorithms. For this reason, efforts are being directed to the development of on-chip microwave nonreciprocal devices. However, due to the large scale of these systems, their design and modelling is an ongoing challenge. In this thesis, we show how effective dynamical models of superconducting qubits can be obtained when these are coupled by nonreciprocal linear responses, extending the previous work to include on-chip nonreciprocal devices, and more formally all kinds of effectively linear lossless microwave devices. Notably, our formalism quantitatively captures the tradeoff between control and dissipation induced by coupling to the external electronics. In addition, we provide a modern presentation of the theoretical background underpinning circuit synthesis and modelling. Additionally, while scaling to thousands of qubits is necessary for the implementation of useful quantum computing algorithms, this is not the only route where quantum information processing systems can find applications in other fields. In particular, quantum metrology offers a venue where only a few well-tuned qubits and oscillators are needed for a quantum sensing advantage. Examples where these advantages have been realize include dark-matter searches, satellite-free navigational systems, imaging of biological tissues, among others. Despite their promise, quantum sensors must balance the tradeoff between sensitivity to external perturbations and robustness against noise sources. A pathway to limit the detrimental effects of noise and maximize the achievable sensitivity is given by reservoir-engineering and quantum error-correction. Thus, the development of quantum sensors robust against noise is a promising venue with broad applications. In our work, we show how recent protocols developed for the stabilization of bosonic codes can be adapted for quantum sensing. In particular, we show how stabilizing protocols for the Gottesman-Kitaev-Preskill code can be adapted for the quantum sensing of displacements. Quantum sensing of displacement may find applications in for example electric field sensing, force sensing and gravitational waves sensing. Remarkably, the protocol we study nearly saturates the sensitivity allowed by quantum mechanics.