  Topology, like symmetry, is a fundamental concept in understanding general
properties of physical systems. In condensed matter systems, non-trivial
topology may manifest itself as singular features in the energy spectrum or the
quantization of observable quantities such as electrical conductance and
magnetic flux. Using microwave spectroscopy, we show that a superconducting
circuit with three Josephson tunnel junctions in parallel can possess energy
degeneracies indicative of $\textrm{\emph{intrinsic}}$ non-trivial topology. We
identify three topological invariants, one of which is related to a hidden
quantum mechanical supersymmetry. Depending on fabrication parameters, devices
are gapless or not, and fall on a simple phase diagram which is shown to be
robust to perturbations including junction imperfections, asymmetry, and
inductance. Josephson tunnel junction circuits, which are readily fabricated
with conventional microlithography techniques, allow access to a wide range of
topological systems which have no condensed matter analog. Notable spectral
features of these circuits, such as degeneracies and flat bands, may be
leveraged for quantum information applications, whereas quantized transport
properties could be useful for metrology applications.
