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#### Quantum Models for the Optimization of Superconducting Traveling Wave Parametric Amplifiers

Quantum-limited amplifiers are a key component in the readout chain of superconducting quantum computers. Their unprecedented noise performance, close to the quantum limit, however, requires the respective amplifier models to account for the intricate quantum nature of the electromagnetic field in the amplifier. Parametric amplifiers can also be used to generate entangled pairs of microwave photons. We present an approach for the self-consistent quantum modeling of traveling wave parametric amplifiers with different junction topologies.