  We demonstrate the quantum fidelity approach for exploring and mapping out
quantum phases. As a simple model exhibiting a number of distinct quantum
phases, we consider the alternating-bond Ising chain using the infinite time
evolving block decimation method in the infinite matrix product state
representation. Examining the quantum fidelity with an arbitrary reference
state in the whole range of the interaction parameters leads to the explicit
detection of the doubly degenerate groundstates, indicating a $Z_2$ broken
symmetry. The discontinuities of the fidelity indicate a first-order quantum
phase transition between the four ordered phases. In order to characterize each
phase, based on the spin configurations from the spin correlations, even and
odd antiferromagnetic order parameters are introduced. The four defined local
order parameters are shown to characterize each phase and to exhibit
first-order quantum phase transitions between the ordered phases.
