Formalize one pinned filtering theorem with exact promises.
Acceptance: Gap, overlap, energy information and success convention match the source.
planned; no claimed closure
Structure before circuit tricks
Useful trial states for strong-correlation ground-state preparation
Near-optimal filtering is only useful when trial-state and spectral promises are available.
research target setting:ground-filter-overlap-gap
\[\gamma=\|\Pi_0|\psi_{\rm trial}\rangle\|,\qquad \Delta=E_1-E_0\]
Frozen target and input model
For a specified physical family, construct a cheap trial-state supplier with a proved useful overlap or target-subspace guarantee.
Access model: Hamiltonian access, a charged trial-state circuit and explicit energy/gap information; target may be a ground subspace rather than a unique vector.
- Hamiltonian family and locality stated
- Overlap convention and gap promise stated
- Trial-state optimization and evaluation costs included
Desired result, not an achieved bound
A class-specific overlap and total preparation theorem; no unconditional removal of inverse-overlap or inverse-gap barriers.
Lin–Tong provides algorithms and lower bounds under overlap/gap assumptions. Strong correlation does not itself certify an MPS rank or overlap.
Dependency-ready execution route
Prove an overlap bound for a concrete trial family.
Acceptance: The trial circuit and overlap certificate are both explicit.
planned; no claimed closure
Compose trial preparation and filtering.
Acceptance: All repeated preparations, oracle calls, error and workspace are charged.
planned; no claimed closure
Next bounded advance: Begin with a controlled family with a rigorous trial-state overlap, not arbitrary strongly correlated molecules.
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
external-baseline
Retain search/approximate-counting barriers from the pinned source and test whether extra structure changes their applicability.
Same-model key: setting:ground-filter-overlap-gap
Diagnostic examples, not proofs
- Gapped one-dimensional families with a supplied rank certificate
- Small selected-CI/MPS trial models with explicit overlap
Primary-source ledger
primary-metadata-checked Abstract: initial overlap, spectral-gap promise, energy information and lower bounds
Use the promised overlap/gap model; do not erase these costs in a generic strong-correlation claim.
primary-metadata-checked Article record and abstract
Application motivation for trial-state construction, assessment and refinement; not a proved overlap guarantee for arbitrary molecules.
Download bounded agent / contributor packet
python3 website/scripts/research_atlas.py context --route spw-ground