Abstract
In this short talk we motivate the study of noncommutative constraint satisfaction problems. Constraint satisfaction problems from theoretical computer science have a natural framing as optimization of polynomials in commuting variables. Noncommutativity is one of the defining features of quantum mechanics. So it is not surprising that noncommutative polynomial optimization plays an important role in quantum computer science. At a first glance it seems that noncommutative polynomial optimization must be more complex. However this is not always true for example when the polynomial is coming from certain constraint satisfaction problems ...