Continuous-variable quantum computation has emerged as a promising paradigm for scalable, fault-tolerant, measurement-based quantum computing. Key resources for this approach are cluster states, which are multipartite entangled states characterized by a specific correlation structure. In this thesis we use microwave digital signal processing techniques and a superconducting parametric oscillator to generate, measure, and analyze continuous-variable cluster states in the frequency domain.

We employ a Josephson parametric amplifier with a phase-controlled multifrequency pump waveform to engineer connections between modes in a microwave frequency comb multiplexed in a single transmission line. Mode-coupling theory and the scattering formalism are applied to model these connections, showing good agreement with experiments. The scattering framework provides an effective tool to explore parametric interactions, and we extend it to include non-reciprocal scattering between modes. Through programming the phase and amplitude of the multifrequency components of the pump waveform, we demonstrate the directionality of mode coupling, realizing two-mode isolation and a three-mode circulation.

The scattering measurements and simulations provide a foundation to explore quantum correlations within the Gaussian quantum information framework. We characterize entanglement through measurement and analysis of the covariance matrix in our frequency-comb mode basis, demonstrating up to 1.4 dB of squeezing in a square-ladder cluster state containing 94 modes. Our work represents a scalable and hardware-efficient method for creating large-scale entanglement with possible applications in quantum computation, sensing, and communication.