A Semantic Gap in QRAM Storage Assumptions

Block-encoding constructions are often stated as: if a normalized matrix is stored in a quantum-accessible data structure (QRAM), then efficient state preparation or blockencoding can be achieved. We show that “stored” admits two distinct interpretations. In the oracle reading, the required normalized object is assumed, and the implication holds. In the operational reading, storage is the outcome of a discrete preprocessing map applied to classical data, and the conclusion need not follow. Using an order-theoretic circuit-schedule formalism for QRAM-based access, we formalize this gap and show that these constructions hold only under oracle semantics.