Universal quantum computation and quantum error correction using discrete holonomies

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