Topos logic in measurement-based quantum computation
  We report first steps towards elucidating the relationship between contextuality, measurement-based quantum computation (MBQC) and the non-classical logic of a topos associated with the computation. We show that, in a class of MBQC, classical universality requires non-classical logic, which is 'consumed' during the course of the computation, thereby pinpointing another potential quantum computational resource. 
Leon Loveridge, Raouf Dridi and Robert Raussendorf
quant-ph