Generating ray class fields of real quadratic fields via complex equiangular lines

Let K be a real quadratic field. For certain K with sufficiently small discriminant we produce explicit unit generators for specific ray class fields of K using a numerical method that arose in the study of complete sets of equiangular lines in C^d (known in quantum information as symmetric informationally complete measurements or sics). The construction in low dimensions suggests a general recipe for producing unit generators in infinite towers of ray class fields above arbitrary K and we summarise this in a conjecture. Such explicit generators are notoriously difficult to find, so this recipe may be of some interest. In a forthcoming paper we shall publish promising results of numerical comparisons between the logarithms of these canonical units and the values of L-functions associated to the extensions, following the programme laid out in the Stark Conjectures.