  Experimental realization of a universal set of quantum logic gates is the
central requirement for implementation of a quantum computer. An all-geometric
approach to quantum computation offered a paradigm for implementation where all
the quantum gates are achieved based on the Berry phases and their non-abelian
extensions, the holonomies, from geometric transformation of quantum states in
the Hilbert space. Apart from its fundamental interest and rich mathematical
structure, the geometric approach has some built-in noise-resilient features.
On the experimental side, geometric phases and holonomies have been observed
using nuclear magnetic resonance with thermal ensembles of liquid molecules,
however, such systems are known to be non-scalable for quantum computing. There
are proposals to implement geometric quantum computation in scalable
experimental platforms such as trapped ions, superconducting qubits, or quantum
dots, and a recent experiment has realized geometric single-bit gates with the
superconducting system. Here, we report the experimental realization of a
universal set of geometric quantum gates with solid-state spins of the diamond
defects. The diamond defects provide a scalable experimental platform with the
potential for room-temperature quantum computing, which has attracted strong
interest in recent years. Based on advance of coherent control in this system,
our experiment shows that all-geometric and potentially robust quantum
computation can be realized with solid-state spin qubits.
