Define the coherent family contract including phases and clean workspace.
Acceptance: One matrix action for arbitrary parameter superpositions.
planned; no claimed closure
Structure before circuit tricks
Coherent parameter-dependent families
Parameterized PDEs, source histories and Bayesian conditional states require superpositions of inputs, not separate classically compiled circuits.
research target setting:joint-parameter-data-supplier
\[U:\sum_a c_a|a\rangle|0\rangle\longmapsto\sum_a c_a|a\rangle|f_a\rangle\]
Frozen target and input model
Produce one coherent template for jointly structured parameters and data with a uniform error bound.
Access model: Parameter a is a quantum register; one shared joint coefficient/core supplier is provided with a uniform norm bound.
- Relative phases are fixed across a
- Norms stay bounded away from zero on the promised parameter domain
- Branch selection and numerical rank changes are controlled coherently or avoided
Desired result, not an achieved bound
Polynomial dependence on the joint structural parameters and parameter bit length, rather than a table of independent preparations.
A family of individually easy states need not have an easy coherent supplier. Per-parameter correctness up to phase is insufficient.
Dependency-ready execution route
Derive a joint tensor/polynomial representation.
Acceptance: Uniform rank/degree and nonzero normalization proof over all allowed parameters.
planned; no claimed closure
Compile with uniform error and cost.
Acceptance: Operator-action error on the whole parameter-data subspace, not only sampled parameter values.
planned; no claimed closure
Next bounded advance: Use an affine parameterized Hermite or Gaussian family as a small exact model before time-dependent PDE source histories.
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
model-definition-pending
Keep arbitrary CQSP lower bounds separate from the restricted joint-structure promise.
Same-model key: setting:joint-parameter-data-supplier
Diagnostic examples, not proofs
- Width-dependent Gaussians
- Parameter-dependent Hermite smoothing
- Time-dependent source terms
Primary-source ledger
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.
primary-text-checked Abstract, Introduction and Discussion: shallow compositional state preparation
Composition-dependent bounds, not an efficient preparation theorem for every continuous multivariate function.
Download bounded agent / contributor packet
python3 website/scripts/research_atlas.py context --route spw-controlled