Abstract: 
Scaling up quantum computers is a formidable task [Pre18, CKJ+20]. Quantum systems are extremely delicate and sensitive to environmental interactions [Nie02]. Ever since the first theoretical proposals for their construction in the early 1990s [CZ95], many platforms have arisen, and several of the original challenges addressed. However, while the first proof-of-concept quantum computers are already a reality, the question of how to scale up these prototypes to the dimensions needed for fault-tolerant computing remains largely open.
 
Distributed Quantum Computing (DQC) emerged as an alternative to expand the size and capabilities of quantum computers. The key idea is to distribute computations and memory across multiple medium-sized nodes, similar to classical computing. While this approach reduces cross-talk and control line overhead from placing many qubits on a single chip, it introduces new challenges. A distributed architecture needs fast, reliable, and synchronized information exchange between nodes to function effectively. In this thesis, we advocate for quantum state transfer, first proposed in [CZKM96], as a fundamental operation for transmitting quantum information deterministically and on demand. This constitutes the foundation of what we refer to as quantum state transfer networks, of which pioneering experimental realizations already exist [LLC+19, MSK+20, QLN+23]. In these networks, quantum information is transmitted by mapping states from stationary qubits to propagating ones. This requires strong and finely tuneable light-matter interactions, which make superconducting circuits an ideal platform for implementation.
 
The objective of this thesis is twofold. First, we construct a theoretical quantum optical model of a complete state transfer network based on microwave quantum links with the goal of understanding and providing theoretical insights for state-of-the-art experimental work. Secondly, we propose and design novel protocols and mitigation strategies for overcoming some of the most critical challenges affecting this platform nowadays.

Through detailed modeling of the experiments, we identified sources of error that are often overlooked in the superconducting circuits literature, such as wavepacket distortion caused by non-linear dispersion relations and non-uniform couplings. These limitations add on top of the commonly recognized issues, such as poor measurement fidelities, limited qubit coherence times, and the challenge of maintaining the entire network at cryogenic temperatures [BGGW21]. Beyond these imperfections, the field also faces ongoing challenges, particularly the need for multiplexing information through quantum links and the generation and distribution of entanglement across the network. Addressing both error mitigation and protocol design is crucial for building a functional, scalable quantum state transfer network.

Equipped with the tools of quantum optics and building on the complete modeling of existing experiments, we addressed both issues. By accurately characterizing the emission process and exploiting the explicit relationship between the couplings and the shape of the produced electromagnetic field, we were able to leverage the flexibility of the light-matter couplings for various purposes. Through careful engineering of the phase profile, we designed a family of predistorted photons that are resilient to propagation distortions. This method applies to any quantum communication channel, provided the distortion behavior of the photon within the channel is known...