We describe an experiment demonstrating the generation of three independent square-ladder continuous-variable cluster states with up to 94 qumodes of a microwave frequency comb. This entanglement structure at a large scale is realized by injecting vacuum fluctuations into a Josephson Parametric Amplifier pumped by three coherent signals around twice its resonance frequency, each having a particular well-defined phase relation. We reach up to 1.4 dB of squeezing of the nullifier that verifies the cluster state on the square ladder graph. Our results are consistent with a more familiar measure of two-mode squeezing, where we find up to 5.42 dB for one pump, and up to 1 dB for three pumps.

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.

We investigate nonreciprocal scattering within the modes of a microwave frequency comb. Adjusting the pump frequencies, amplitudes, and phases of a Josephson parametric oscillator, we control constructive interference for the m--> pound scattering processes, while concurrently achieving destructive interference for the inverse process pound --> m. We outline the methodology for realizing nonreciprocity in the context of two-mode isolation and a three-mode circulation, which we extend to multiple modes. We find good agreement between the experiments and a linearized theoretical model. Nonreciprocal scattering expands the toolset for parametric control, with the potential to engineer alternative quantum correlations.

Two-level system (TLS) loss typically limits the coherence of superconducting quantum circuits. The loss induced by TLS defects is nonlinear, resulting in quality factors with a strong dependence on the circulating microwave power. We observe frequency mixing due to this nonlinearity by applying a two-tone drive to a coplanar waveguide resonator and measuring the intermodulation products using a multifrequency lock-in technique. This intermodulation spectroscopy method provides an efficient approach to characterizing TLS loss in superconducting circuits. Using harmonic balance reconstruction, we recover the nonlinear parameters of the device-TLS interaction, which are in good agreement with the standard tunneling model for TLSs.

Significant progress has been made with multipartite entanglement of discrete qubits, but continuous variable systems may provide a more scalable path toward entanglement of large ensembles. We demonstrate multipartite entanglement in a microwave frequency comb generated by a Josephson parametric amplifier subject to a bichromatic pump. We find 64 correlated modes in the transmission line using a multifrequency digital signal processing platform. Full inseparability is verified in a subset of seven modes. Our method can be expanded to generate even more entangled modes in the near future.

Exploiting multiple modes in a quantum acoustic device could enable applications in quantum information in a hardware-efficient setup, including quantum simulation in a synthetic dimension and continuous-variable quantum computing with cluster states. We develop a multimode surface acoustic wave (SAW) resonator with a superconducting quantum interference device (SQUID) integrated in one of the Bragg reflectors. The interaction with the SQUID-shunted mirror gives rise to coupling between the more than 20 accessible resonator modes. We exploit this coupling to demonstrate two-mode squeezing of SAW phonons, as well as four-mode multipartite entanglement. Our results open avenues for continuous-variable quantum computing in a compact hybrid quantum system.