  The non-Bloch topology leads to the emergence of various counter-intuitive
phenomena in non-Hermitian systems under the open boundary condition (OBC),
which can not find a counterpart in Hermitian systems. However, in the
non-Hermitian system without chiral symmetry, being ubiquitous in nature,
exploring its non-Bloch topology has so far eluded experimental effort. Here by
introducing the concept of non-chiral non-Bloch invariants, we theoretically
predict and experimentally identify the non-Bloch topological phase diagram of
a one-dimensional (1D) non-Hermitian system without chiral symmetry in
discrete-time non-unitary quantum walks of single photons. Interestingly, we
find that such topological invariants not only can distinguish topologically
distinct gapped phases, but also faithfully capture the corresponding gap
closing in open-boundary spectrum at the phase boundary. Different topological
regions are experimentally identified by measuring the featured discontinuities
of the higher moments of the walker's displacement, which amazingly match
excellently with our defined non-Bloch invariants. Our work provides a useful
platform to study the interplay among topology, symmetries and the
non-Hermiticity.
