  The search for topological insulators has been actively promoted in the field
of condensed matter physics for further development in energy-efficient
information transmission and processing. In this context, recent studies have
revealed that not only electrons but also bosonic particles such as magnons can
construct edge states carrying nontrivial topological invariants. Here we
demonstrate topological triplon bands in the spin-1/2 two-dimensional dimerized
quantum antiferromagnet Ba$_2$CuSi$_2$O$_6$Cl$_2$, which is closely related to
a pseudo-one-dimensional variant of the Su-Schrieffer-Heeger (SSH) model,
through inelastic neutron scattering experiments. The excitation spectrum
exhibits two triplon bands and a clear band gap between them due to a small
alternation in interdimer exchange interactions along the $a$-direction, which
is consistent with the crystal structure. The presence of topologically
protected edge states is indicated by a bipartite nature of the lattice.
