# Vector Generation of Contextual Sets

## TL;DR

This paper introduces a comprehensive vector generation method for Kochen-Specker contextual sets, enabling the creation of all known and new sets from minimal initial components, advancing quantum computation and communication.

## Contribution

A novel, unified vector generation approach that surpasses previous methods, allowing complete and customizable generation of KS sets from minimal starting points.

## Key findings

- Can generate all known KS sets from minimal vectors
- Enables creation of large and feature-specific KS sets
- Facilitates diverse quantum computation implementations

## Abstract

As quantum contextuality proves to be a necessary resource for universal quantum computation, we present a general method for vector generation of Kochen-Specker (KS) contextual sets in the form of hypergraphs. The method supersedes all three previous methods: (i) fortuitous discoveries of smallest KS sets, (ii) exhaustive upward hypergraph-generation of sets, and (iii) random downward generation of sets from fortuitously obtained big master sets. In contrast to previous works, we can generate master sets which contain all possible KS sets starting with nothing but a few simple vector components. From them we can readily generate all KS sets obtained in the last half a century and any specified new KS sets. Herewith we can generate sufficiently large sets as well as sets with definite required features and structures to enable varieties of different implementations in quantum computation and communication.