  Cluster state plays a crucial role in the one-way quantum computation. Here,
we propose and experimentally demonstrate a new scheme to prepare an
ultrahigh-fidelity four-photon linear cluster state via spontaneous parametric
down-conversion process. The state fidelity is measured to be
$0.9517\pm0.0027$. Our scheme can be directly extended to more photons to
generate N-qubit linear cluster state. Furthermore, our scheme is optimal for
generating photonic linear cluster states in the sense of achieving the maximal
success probability and having the simplest strategy. The key idea is that the
photon pairs are prepared in some special non-maximally entangled states
instead of the normal Bell states. To generate a 2N-qubit linear cluster state
from N pairs of entangled photons, only (N-1) Hong-Ou-Mandel interferences are
needed and a success probability of $(\frac{1}{4})^{N-1}$ is achieved.
