  Superconducting quantum circuits are a natural platform for quantum
simulations of a wide variety of important lattice models describing
topological phenomena, spanning condensed matter and high-energy physics. One
such model is the bosonic analogue of the well-known fermionic Kitaev chain, a
1D tight-binding model with both nearest-neighbor hopping and pairing terms.
Despite being fully Hermitian, the bosonic Kitaev chain exhibits a number of
striking features associated with non-Hermitian systems, including chiral
transport and a dramatic sensitivity to boundary conditions known as the
non-Hermitian skin effect. Here, using a multimode superconducting parametric
cavity, we implement the bosonic Kitaev chain in synthetic dimensions. The
lattice sites are mapped to frequency modes of the cavity, and the $\textit{in
situ}$ tunable complex hopping and pairing terms are created by parametric
pumping at the mode-difference and mode-sum frequencies, respectively. We
experimentally demonstrate important precursors of nontrivial topology and the
non-Hermitian skin effect in the bosonic Kitaev chain, including chiral
transport, quadrature wavefunction localization, and sensitivity to boundary
conditions. Our experiment is an important first step towards exploring genuine
many-body non-Hermitian quantum dynamics.
