Define the exact classical/quantum access interface.
Acceptance: Separate data construction, coherent calls, memory and update costs.
planned; no claimed closure
Structure before circuit tricks
Data loading without a free QRAM assumption
An algorithm with few abstract queries can still be expensive when the query unitary is built from real data.
research target setting:explicit-data-charged-access
\[T_{\rm total}=T_{\rm build}+Q\,T_{\rm query}+T_{\rm update}+T_{\rm readout}\]
Frozen target and input model
Identify succinct data classes for which explicit access construction preserves the intended algorithmic advantage.
Access model: Classical stored arrays, QROM, arithmetic formulas and physical QRAM are separate settings with explicit initialization, updates and memory costs.
- Fix data bit length, update frequency and reuse count
- Charge controlled/inverse queries when the algorithm uses them
- Compare against a classical algorithm with the same access assumptions
Desired result, not an achieved bound
A full cost theorem for one succinct data representation, not universal polylogarithmic loading of an arbitrary array.
General sparse-access and block-encoding constructions can require near-linear cost in matrix dimension. Sparsity does not make all entries free.
Dependency-ready execution route
Compile one formula, sparse-index or repeated-block supplier.
Acceptance: Basis-action theorem and count of actual access primitives.
planned; no claimed closure
Reinsert access costs into a downstream algorithm.
Acceptance: A comparison using the same input/output model and total cost, not query count alone.
planned; no claimed closure
Next bounded advance: Reuse existing sparse/LCU routes only after auditing their oracle contracts and compiler frontiers.
Reusable mathematics
No local transport theorem is bound to this record. Do not infer formal truth from its position in the atlas.
Lower-bound comparison contract
source-audit-pending
Port a pinned circuit-capacity/access lower bound with precision and ancilla assumptions intact.
Same-model key: setting:explicit-data-charged-access
Diagnostic examples, not proofs
- Repeated structured blocks
- Sparse matrices with formulaic index/value access
- Amortized repeated-query workloads
Primary-source ledger
primary-text-checked Results: circuit complexity lower bound; construction of LCU-based block-encoding; Methods: state preparation
Explicit access construction is not a free oracle. PREPARE together with SELECT and uncomputation can supply a block encoding; a single prepared state alone does not determine an arbitrary operator.
primary-metadata-checked Abstract and publication version notice: published arXiv v2; later v3 exists
Baseline for arbitrary and controlled state preparation and ancilla/depth trade-offs. Pin a version and gate model before comparing bounds.
Download bounded agent / contributor packet
python3 website/scripts/research_atlas.py context --route spw-no-qram