  Topological insulators are materials that have a gapped bulk energy spectrum,
but contain protected in-gap states appearing at their surface. These states
exhibit remarkable properties such as unidirectional propagation and robustness
to noise that offer an opportunity to improve the performance and scalability
of quantum technologies. For quantum applications, it is essential that the
topological states are indistinguishable. Here we report high-visibility
quantum interference of single photon topological states in an integrated
photonic circuit. Two topological boundary-states, initially at opposite edges
of a coupled waveguide array, are brought into proximity, where they interfere
and undergo a beamsplitter operation. We observe $93.1\pm2.8\%$ visibility
Hong-Ou-Mandel (HOM) interference, a hallmark non-classical effect that is at
the heart of linear optics-based quantum computation. Our work shows that it is
feasible to generate and control highly indistinguishable single photon
topological states, opening pathways to enhanced photonic quantum technology
with topological properties, and to study quantum effects in topological
materials.
