The QLA interface operates on single node data. Data objects are primitives, such as SU(N) matrices or SU(N) vectors, or arrays of such objects. Linear algebra operations, such as products of matrices and vectors, are carried out either on single objects or arrays of objects. For arrays of objects a variety of indirect addressing schemes is supported, including indirect indexing (gathers and scatters) and pointers. Various reduction operations (e.g. global sums) and fill operations (e.g. setting values to zero) are also included. It is intended that a subset of operations in this interface be optimized for specific architectures, with attention paid to efficient cache loading and fast instructions.