Programmable Microwave Cluster States via Josephson Metamaterials

Cluster states are a key resource for continuous-variable quantum computing, enabling measurement-based protocols that can scale beyond qubit-based architectures. Here, we demonstrate the on-demand generation of multimode entangled microwave cluster states using a programmable Josephson Traveling-Wave Parametric Amplifier (JTWPA) operated in the three-wave mixing regime. By injecting a tailored set of pump tones with an arbitrary waveform generator, we engineer frequency-specific nonlinear couplings between multiple modes, allowing different graph topologies. Entanglement is verified via frequency-resolved heterodyne detection of quadrature nullifiers, confirming the target graph structures. Our scheme is reconfigurable via the pump spectrum and supports scalability by exploiting the wide bandwidth and spatial homogeneity of the JTWPA. This platform enables scalable measurement-based quantum information processing in the microwave domain, fully compatible with superconducting circuits.