I offer a case that quantum query complexity still has loads of enticing and fundamental open problems—from relativized QMA versus QCMA BQP IP , to time/space tradeoffs for collision element distinctness, polynomial degree partial functions, the Unitary Synthesis Problem more.

Given a set of n integer-valued coin types and target value t, the well-known change-making problem asks for minimum number coins that sum to assuming an unlimited in each type. In more general all-targets version problem, we want summing j, every j=0,…,t. We obtain new results on these problems, including (i) algorithm with running time O˜(t4/3) (improving previous O˜(t3/2)-time algorithm), (i...