Probabilistic generation of quantum contextual sets

We give a method for exhaustive generation of a huge number of Kochen–Specker contextual sets, based on the 600-cell, for possible experiments and quantum gates. The method is complementary to our previous parity proof generation of these sets, and it gives all sets while the parity proof method gives only sets with an odd number of edges in their hypergraph representation. Thus we obtain 35 new kinds of critical KS sets with an even number of edges. We also give a statistical estimate of the number of sets that might be obtained in an eventual exhaustive enumeration. ► We generate millions of new Kochen–Specker noncontextual set. ► We find thousands of novel critical Kochen–Specker (KS) sets. ► We give algorithms for generating KS sets from a new 4-dim class. ► We represent KS sets by means of hypergraphs and their figures. ► We give a new exact estimation method for random sampling of sets.