  The quantum walk is a dynamical protocol which describes the motion of
spinful particles on a lattice. Also, it has been demonstrated to be a powerful
platform to explore topological quantum matter. Recently, the quantum walk in
coherent state space has been proposed theoretically and realized
experimentally. However, due to the inherent characteristics of coherent
states, it is challenging to control the number of photons when we need the
coherent space to be a nearly orthogonal space in practice. Here, we
demonstrate that the nonorthogonality of coherent sates, on the one hand can be
cancelled by multiple measurement, on the other hand, it is useful resource to
characterize the nature of the system. Thus the number of photons of the system
is controllable. We first present a feasible scheme to measure the wave
function of quantum walks. Then we show that the expected number of photons of
the coherent space is good observable to represent topological properties of
the system, which reflected the advantage of coherent state space quantum
walks. In addition, we propose an experimental protocol in a circuit quantum
electrodynamics architecture, where a superconducting qubit is a coin while the
cavity mode is used for quantum walk.
