  A new scheme of realizing the nonadiabatic conditional geometric phase shift
via a noncoplanar (and coiled) fiber system is presented in this Letter. It is
shown that the effective Hamiltonian that describes the interaction of
polarized photons with the fiber medium is just the Wang-Keiji type of
Hamiltonian. This, therefore, means that the coiled fiber system may be an
ideal implementation of realizing the nonadiabatic geometric phase gates for
the topological quantum computation. The remarkable feature of the present
method is that it can automatically meet the conditions and requirements
proposed in the Wang-Keiji scheme: (i) in the coiled fiber system, the
dynamical phase of photon wavefunction caused by the interaction Hamiltonian
automatically vanishes; (ii) the Wang-Keiji requirement for the parameters in
the Wang-Keiji Hamiltonian can be exactly satisfied automatically in the fiber
system; (iii) the conditional initial state can be easily achieved by
manipulating the initial wave vector of polarized photons. Due to these three
advantages, the coiled fiber system may be a potentially practical way of
achieving the nonadiabatic conditional geometric phase shift (and hence the
nonadiabatic geometric quantum gates).
