  Quantum walks, whose dynamics is prescribed by alternating unitary coin and
shift operators, possess topological phases akin to those of Floquet
topological insulators, driven by a time-periodic field. While there is ample
theoretical work on topological phases of quantum walks where the coin
operators are spin rotations, in experiments a different coin, the Hadamard
operator is often used instead. This was the case in a recent photonic quantum
walk experiment, where protected edge states were observed between two bulks
whose topological invariants, as calculated by the standard theory, were the
same. This hints at a hidden topological invariant in the Hadamard quantum
walk. We establish a relation between the Hadamard and the spin rotation
operator, which allows us to apply the recently developed theory of topological
phases of quantum walks to the one-dimensional Hadamard quantum walk. The
topological invariants we derive account for the edge state observed in the
experiment, we thus reveal the hidden topological invariant of the
one-dimensional Hadamard quantum walk.
