  Holonomic quantum computation exploits a quantum state's non-trivial,
matrix-valued geometric phase (holonomy) to perform fault-tolerant computation.
Holonomies arising from systems where the Hamiltonian traces a continuous path
through parameter space have been well-researched. Discrete holonomies, on the
other hand, where the state jumps from point to point in state space, have had
little prior investigation. Using a sequence of incomplete projective
measurements of the spin operator, we build an explicit approach to universal
quantum computation. We show that quantum error correction codes integrate
naturally in our scheme, providing a model for measurement-based quantum
computation that combines the passive error resilience of holonomic quantum
computation and active error correction techniques. In the limit of dense
measurements we recover known continuous-path holonomies.
