Tailoring Tunable Interactions in Superconducting Circuits Using Many to No Modes

Tunable couplings are a central requirement for scalable quantum processing with superconducting quantum circuits. Practical quantum processors must dynamically reconfigure their interaction landscape to accommodate different quantum operations, including idle, single-qubit gates, two-qubit gates, readout, and reset, while maintaining high coherence and suppressing spurious couplings. While widely used tunable interaction approaches rely on single-mode mediation, they are often constrained by nearest-neighbor connectivity, limited on-off ratios, and stringent requirements on qubit frequency allocation. This thesis develops and studies novel strategies for tailoring tunable interactions by moving beyond single-mode mediation, spanning multimode engineered interactions and modeless interaction schemes ("many to no modes"), while accounting for realistic constraints in superconducting hardware. Using a microwave metamaterial waveguide realized by coupled resonator arrays, I demonstrate tunable dissipative interactions that allow on-demand, fast, and high switching-ratio photon emission from a transmon used as a multi-level quantum emitter. This capability is leveraged to achieve deterministic generation of multidimensional photonic cluster states, as well as unconditional reset and leakage reduction of frequency-tunable superconducting qubits. Complementary to these multimode dissipative tunable interactions, this thesis also introduces architectures that realize tunable interactions mediated by many coherent modes or by no mediating modes. I discuss a long-range interaction scheme between superconducting dual-rail qubits mediated by spatially extended eigenmodes of a coupled-resonator array bus. Finally, I propose and analyze a novel modeless coupling architecture based on a SQUID coupler which provides intrinsic cross-Kerr interactions, enabling fast, hybridization-free CZ gates for far-detuned pairs, and discuss its implications for miniaturization of superconducting quantum processors.