  Holonomic quantum computation is a quantum computation strategy that promises
some built-in noise-resilience features. Here, we propose a scheme for
nonadiabatic holonomic quantum computation with nitrogen-vacancy center
electron spins, which are characterized by fast quantum gates and long qubit
coherence times. By varying the detuning, amplitudes, and phase difference of
lasers applied to a nitrogen-vacancy center, one can directly realize an
arbitrary single-qubit holonomic gate on the spin. Meanwhile, with the help of
cavity-assisted interactions, a nontrivial two-qubit holonomic quantum gate can
also be induced. The distinct merit of this scheme is that all the quantum
gates are obtained via an all-optical geometric manipulation of the solid-state
spins. Therefore, our scheme opens the possibility for robust quantum
computation using solid-state spins in an all-optical way.
