Higher-order quantum computing with known input states

In higher-order quantum computing (HOQC), one typically considers the universal transformation of unknown quantum operations, treated as blackboxes. It is also implicitly assumed that the resulting operation must act on arbitrary—and thus unknown—input states. In this work, we explore a variant of this framework in which the operation remains unknown, but the input state is fixed and known. We argue that this assumption is well-motivated in certain practical contexts, such as unitary programming, and show that classical knowledge of the input state can significantly enhance performance. Moreover, this assumption allows us to distinguish protocols designed for pure, bipartite, and mixed states, which enabled us to identify the class of mixed states for which deterministic and exact implementation becomes possible.

arXiv:2510.20530 [quant-ph]