Long-Range Coupling of Electron Spins In the quest towards harnessing quantum systems to study quantum physical phenomena and eventually build a universal quantum computer, multiple promising platforms have emerged. Vast progress has been made on the circuit quantum electrodynamics (cQED) platform, where superconducting quantum bits (qubits) are already being used in networks of beyond 50. Another favored implementation is the spin of a single electron. While it is challenging to control due to its weak interactions with the environment, that property is a promising ingredient for long-lived and coherent qubits. Uniting these two platforms has the potential for a powerful symbiosis, combining the long-range networking via microwave photons with the coherence of a single electron spin.

In this thesis, we build upon first demonstrations of coherent coupling between individual electron spins with microwave photons. In this coupling approach, the electron is trapped inside a double quantum dot (DQD) and subjected to a strong magnetic field gradient, which enables coupling of the spin to the electric field of a superconducting resonator. We extend this hybrid cQED architecture by a new coupling approach that allows for scalable access to charge-photon coupling while retaining its coupling strength. We then utilize this architecture to demonstrate resonant long-distance coupling between two spins and a cavity photon across a distance of over 4 mm. This first link between two separated spins improves the range of interaction between two spins by more than 4 orders of magnitude compared to usual exchange based approaches with 100nm length scales.

We scale the architecture from using DQDs to triple quantum dots (TQDs) and study the valley states in the array. Using the high-resolution readout of the coupled resonator, we extract the inter-valley coupling elements between neighboring quantum dots, studying the complex-valued nature of the valley states. This new insight into the state landscape of electrons in silicon quantum dots can help feed back into substrate fabrication efforts and shed light onto interdot dynamics that also occur in quantum dot arrays without a cavity sensor. Finally, we utilize a cavity-coupled TQD to perform high-fidelity spin readout via a flexible gate-sensing approach.