  Low-noise microwave amplifiers are crucial for detecting weak signals in
quantum technologies and radio astronomy. Building an ideal device is
challenging as it must amplify a broad range of frequencies while adding
minimal noise. The amplification must also be directional so that it favors the
observer's direction while protecting the source from its environment. Here, we
introduce a fundamentally new type of superconducting Josephson traveling-wave
parametric amplifier that fulfills all these requirements by exploiting
non-Hermitian topological effects and time-reversal symmetry breaking via the
phase of the four-wave-mixing pump. In the topological amplification phase, the
device acquires an unprecedented performance such as a gain growing
exponentially with system size and largely surpassing 20 dB, exponential
suppression of back-wards noise below -30 dB, a bandwidth of GHz, and
topological protection against disorder. This opens the door for integrating
near-ideal and compact pre-amplifiers on the same chip as quantum processors.
