© 2020 American Physical Society. The silicon-vacancy center in diamond has recently attracted significant attention as a candidate for quantum information processing as it overcomes many of the optical issues present in the nitrogen-vacancy center. Historically it has been hampered by short dephasing times; however the recent development of high-purity samples at low temperatures resolves this issue. Hence it is timely to explore whether silicon-vacancy centers are useful for quantum tasks beyond single-photon sources. Here we investigate the potential of the silicon-vacancy center to realize two important operations required for quantum information processing: High-efficiency projective measurement and efficient single-qubit rotations. Due to its similar nature, the germanium-vacancy center is discussed as a point of comparison.