  Quantum random-access memory (QRAM) is a mechanism to access data (quantum or
classical) based on addresses which are themselves a quantum state. QRAM has a
long and controversial history, and here we survey and expand arguments and
constructions for and against.
  We use two primary categories of QRAM from the literature: (1) active, which
requires external intervention and control for each QRAM query (e.g. the
error-corrected circuit model), and (2) passive, which requires no external
input or energy once the query is initiated. In the active model, there is a
powerful opportunity cost argument: in many applications, one could repurpose
the control hardware for the qubits in the QRAM (or the qubits themselves) to
run an extremely parallel classical algorithm to achieve the same results just
as fast. Escaping these constraints requires ballistic computation with passive
memory, which creates an array of dubious physical assumptions, which we
examine in detail. Considering these details, in everything we could find, all
non-circuit QRAM proposals fall short in one aspect or another. We apply these
arguments in detail to quantum linear algebra and prove that most asymptotic
quantum advantage disappears with active QRAM systems, with some nuance related
to the architectural assumptions.
  In summary, we conclude that cheap, asymptotically scalable passive QRAM is
unlikely with existing proposals, due to fundamental limitations that we
highlight. We hope that our results will help guide research into QRAM
technologies that attempt to circumvent or mitigate these limitations. Finally,
circuit-based QRAM still helps in many applications, and so we additionally
provide a survey of state-of-the-art techniques as a resource for algorithm
designers using QRAM.
