Higher-order quantum computing with known input states

Understand

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.