Formalize support-aware coherent reweighting and its exact success probability.
Acceptance: All amplitudes including zero-reference entries and complex phases agree; normalizer nonzero.
planned; no claimed closure
Structure before circuit tricks
Preconditioned function preparation with an explicit envelope
Uniform-state postselection can have exponentially small filling fraction in dimension; a reference should match localization without hiding an equally hard preparation problem.
research target setting:coherent-envelope-ratio
\[\kappa_{\rm env}=\frac{C\|g\|_2}{\|f\|_2},\quad p_{\rm succ}=\kappa_{\rm env}^{-2},\quad C\ge\max_{g_j\ne0}|f_j/g_j|\]
Frozen target and input model
Construct g for one useful localized function class so that reference preparation, ratio implementation and amplification are all controlled.
Access model: A clean U_g and U_g-dagger with charged construction; coherent access to a bounded complex ratio; classical or certified scalar C.
- support(f) subset support(g); define the ratio as zero off support(g)
- f and g nonzero and C>0
- A constructive domination certificate, not an empirical maximum on a few grid points
Desired result, not an achieved bound
For a selected class, prove kappa_env and reference/ratio costs polynomial in declared class parameters; add a model-matched obstruction or lower bound.
Coherent rejection and reweighting are prior art. Uniform g recovers kappa_env=1/F2 where F2=||f||2/(sqrt(M)||f||infinity). A small ratio on average does not imply a valid pointwise envelope.
Dependency-ready execution route
Build a certified reference for a restricted localized class.
Acceptance: A concrete supplier for g, a global domination proof and kappa bound.
planned; no claimed closure
Add robust ratio approximation and amplification.
Acceptance: State error and actual query/primitive costs, including U_g inversion and repeated calls.
planned; no claimed closure
Next bounded advance: First close the support-aware probability identity, then study anisotropic product envelopes and a controlled perturbation class.
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
Audit the quantum rejection-sampling query lower bound and prove whether its oracle assumptions match this structured envelope model before transferring it.
Same-model key: setting:coherent-envelope-ratio
Diagnostic examples, not proofs
- Localized Gaussian profiles
- Boundary-layer initial data
- Piecewise payoff functions with declared phase convention
Primary-source ledger
primary-metadata-checked Authors' publication page: quantum state generation, query characterization and matching lower bound
Prior art for coherent amplitude reweighting. Novelty must be in an explicit structured envelope, guarantees, implementation or model-matched bound, not in rejection sampling itself.
primary-metadata-checked Abstract; Physical Review Letters 136, 240603, published 18 June 2026
QET-based function preparation with few ancillas. Approximation, normalization and success probability remain separate costs.
primary-metadata-checked Abstract and article record
Multivariate preparation baseline; a tensor-product coefficient count is not automatically polynomial in dimension.
Download bounded agent / contributor packet
python3 website/scripts/research_atlas.py context --route spw-envelope