Structure before circuit tricks
Research targets with explicit access models, acceptance tests and model-matched lower-bound obligations. A candidate route is not a proved open-problem classification.
Priority 1 · research target
Produce one coherent template for jointly structured parameters and data with a uniform error bound.
A family of individually easy states need not have an easy coherent supplier. Per-parameter correctness up to phase is insufficient.
Priority 1 · research target
Construct g for one useful localized function class so that reference preparation, ratio implementation and amplification are all controlled.
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.
Priority 1 · research target
Prove a constructive cost and state-error theorem for a precisely specified low-rank, sparse-frequency, mixed-smoothness or compositional class; do not equate these assumptions.
Generic tensor-product degree-q expansions have (q+1)^D coefficients; smoothness alone does not remove dimensionality. Hermite's one-dimensional exact-real compiler is a substrate, not this multivariate theorem.
Priority 2 · research target
Relate a declared finite-energy oscillator encoding to qubit-grid preparation with a rigorous embedding and separate resource budgets.
The finite Hermite state is a useful first example. No CV–DV equivalence or GKP preparation theorem is currently supplied by this route.
Priority 2 · research target
Compile the exact-real structured route into a finite gate set with a proved error budget and declared connectivity.
The Hermite exact-real primitive theorem is already a useful substrate. Full bit complexity and stable angle generation are additional obligations.
Priority 2 · research target
Identify succinct data classes for which explicit access construction preserves the intended algorithmic advantage.
General sparse-access and block-encoding constructions can require near-linear cost in matrix dimension. Sparsity does not make all entries free.
Priority 2 · research target
Automatically derive a low-sample fidelity witness for a precisely defined structured state class.
A Lean ideal-circuit proof does not certify noisy hardware. The user-supplied 2609.08414 reference remains primary-source-unavailable in this ledger.
Priority 3 · research target
For a restricted noncommuting local Hamiltonian family, prove a mixing certificate and implemented-channel error bound.
KMS detailed balance and stationarity are not polynomial mixing. Classical sampling inequalities cannot be transferred to quantum operators without a hypothesis map.
Priority 3 · research target
For a specified physical family, construct a cheap trial-state supplier with a proved useful overlap or target-subspace guarantee.
Lin–Tong provides algorithms and lower bounds under overlap/gap assumptions. Strong correlation does not itself certify an MPS rank or overlap.
primary-metadata-checked Abstract: explicit function to MPS to circuit; requested v1 HTML was unavailable in this audit
Prior art for function-to-MPS preparation. The ASPBE Hermite specialization must not be credited with inventing polynomial-to-MPS or sequential MPS preparation.
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 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; 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
Piecewise function preparation baseline; partition access, degree, success amplification and primitive compilation must be specified before a resource comparison.
primary-metadata-checked Abstract and article record
Multivariate preparation baseline; a tensor-product coefficient count is not automatically polynomial in dimension.
primary-text-checked Abstract, Introduction and Discussion: shallow compositional state preparation
Composition-dependent bounds, not an efficient preparation theorem for every continuous multivariate function.
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: 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.
primary-text-checked Article abstract and Gibbs-sampler construction; Communications in Mathematical Physics 406, 67
Invariant Gibbs state and efficient mixing are different obligations. A low-temperature polynomial mixing claim needs additional model-specific evidence.
primary-source-unavailable User-supplied arXiv identifier; primary fetch failed; do not use reported hardware numbers as evidence
Retained in the candidate queue rather than silently promoted from secondary indexing.
primary-text-checked Author once; graph contribution; independent encoder–denoiser; unchanged historical audit debt
Design attribution. QuantumComputinglib has its own register, oracle, clean-ancilla and resource contracts; Samplinglib is not an imported Lean dependency.
primary-text-checked Sections 2–6; Figures 3–5; Eq. (16) controlled-adder rewrite; Eq. (17) quantum–quantum comparator contract
Primary source for the partial PromiseGateOptimization route and the planned source-faithful adder/comparator/incrementer formalization. Existing generic controlled-conjugation and dirty-flag lemmas do not certify the complete paper circuits or optimality claims.
primary-text-checked Course notes: finite-dimensional QIT foundations, representation theory, Schur–Weyl duality and symmetry-based QIT applications
Planned curriculum anchor for a future Quantum Information part. Source registration is not a claim that its theorems have been formalized locally.
primary-text-checked 29 April 2026 public 447-page edition; Parts I–IV from background/foundations through block encoding, QSP/QSVT, simulation, linear systems/differential equations and open systems
Planned curriculum anchor for quantum scientific computing. Reuse existing ASPBE state-preparation/block-encoding nodes; do not duplicate Chapter 9 under a second API. The user-supplied PDF is not vendored because this edition is publicly hosted.