Due to strong zero-phonon line emission, narrow inhomogeneous broadening, and
stable optical transition frequencies, the quantum system consisting of
negatively charged silicon-vacancy (SiV) centers in diamond is highly expected
to develop universal quantum computation. We propose to implement quantum
computation for the first time using SiV centers placed in a one-dimensional
phononic waveguide, for which quantum gates are realized in a nonadiabatic
geometric way and protected by dynamical decoupling (DD). The scheme has the
feature of geometric quantum computation that is robust to control errors and
the advantage of DD that is insensitive to environmental impact. Furthermore,
the encoding of qubits in long-lifetime ground states of silicon-vacancy
centers can reduce the effect of spontaneous emission. Numerical simulations
demonstrate the practicability of the SiV center system for quantum computation
and the robustness improvement of quantum gates by DD pulses. This scheme may
provide a promising path toward high-fidelity geometric quantum computation in
solid-state systems