  Josephson junctions (JJ) and their tunable properties, including their
nonlinearities, form the core of superconducting circuit quantum
electrodynamics (cQED). In quantum circuits, low-noise amplification of feeble
microwave signals is essential and the Josephson parametric amplifiers (JPA)
are the widely used devices. The existing JPAs are based on Al-AlOx-Al tunnel
junctions realized in a superconducting quantum interference device geometry,
where magnetic flux is the knob for tuning the frequency. Recent experimental
realizations of 2D van der Waals JJs provide an opportunity to implement
various cQED devices with the added advantage of tuning the junction properties
and the operating point using a gate potential. While other components of a
possible 2D van der Waals cQED architecture have been demonstrated -- quantum
noise limited amplifier, an essential component, has not been realized. Here we
implement a quantum noise limited JPA, using a graphene JJ, that has linear
resonance gate tunability of 3.5 GHz. We report 24 dB amplification with 10 MHz
bandwidth and -130 dBm saturation power; performance on par with the best
single-junction JPAs. Importantly, our gate tunable JPA works in the
quantum-limited noise regime which makes it an attractive option for highly
sensitive signal processing. Our work has implications for novel bolometers --
the low heat capacity of graphene together with JJ nonlinearity can result in
an extremely sensitive microwave bolometer embedded inside a quantum
noise-limited amplifier. In general, our work will open up exploration of
scalable device architecture of 2D van der Waals materials by integrating a
sensor with the quantum amplifier.
