Universal Quantum Random Access Memory: A Data-Independent Unitary with a Commuting-Projector Hamiltonian

Quantum random access memory (QRAM) is a central primitive for coherent data access in quantum algorithms, yet it remains controversial in practice because the wall-clock cost of "one lookup" can hide routing depth, control overhead, and geometric constraints. We present a universal QRAM construction (U-QRAM) in which the database is a physical memory register that participates in the lookup unitary as quantum control. This yields a single fixed, data-independent lookup unitary on $A \otimes D \otimes M$ that is correct for all basis-encoded databases. Our first contribution is an explicit, exact Hamiltonian realization: U-QRAM equals a single time-independent evolution $U_{QRAM} = \exp(-iH_{tot})$ where $H_{tot}$ is a sum of mutually commuting projector terms, one per memory cell, and the construction avoids control-dependent phase ambiguities. Our second contribution is an architectural sharpening: under unary (one-hot, mode-addressed) encoding of the address, each cell term becomes uniform and 3-local, delineating the most direct path toward constant-latency interpretations. We keep claims conservative by separating latency from work and stating explicit hardware assumptions required for constant wall-clock queries.