<p>High-fidelity qubit measurement is a critical element of all quantum computing architectures. In superconducting systems, qubits are typically measured by probing a readout resonator with a weak microwave tone that must be amplified before reaching the room-temperature electronics. Superconducting parametric amplifiers have been widely adopted as the first amplifier in the chain, primarily because of their low-noise performance, approaching the quantum limit. However, they require isolators and circulators to route signals up the measurement chain and to protect qubits from amplified noise. Although these commercial components are wideband and simple to use, their intrinsic loss, size and magnetic shielding requirements impact the overall measurement efficiency and scalability. Here we report a parametric amplifier that achieves both broadband forward amplification and backward isolation in a single, compact, non-magnetic circuit that could be integrated on chip with superconducting qubits. The approach relies on a nonlinear transmission line that supports the travelling-wave parametric amplification of forward propagating signals and isolation via the frequency conversion of backward propagating signals. This travelling-wave parametric amplifier and converter has the potential to reduce the readout hardware overhead when scaling up the size of superconducting quantum computers.</p>