Freeze the source's unitary and non-unitary operator contracts.
Acceptance: Versioned equation anchors, scalar phase conventions, dilation scale and signal-register order are reconciled with the local matrix API.
planned; no claimed closure
Structure before circuit tricks
Diagonal operators: space, depth, accuracy and success
The same diagonal supplier can serve function loading, block encoding and non-unitary evolution, without duplicating the underlying finite-matrix library.
research target setting:diagonal-supplier-space-time-accuracy
\[\Pi U_D(|0\rangle|\psi\rangle)=D|\psi\rangle/\alpha,\quad p=\|D\psi\|^2/\alpha^2\]
Frozen target and input model
Formalize unitary phase synthesis and non-unitary diagonal dilation as separate suppliers, then derive a state-preparation consumer with full resource accounting.
Access model: Specified diagonal data or function, gate set, coefficient/angle preprocessing, explicit input state, and sequential/parallel circuit schedule with clean ancilla policy.
- Unit-modulus phase operators are distinguished from general bounded diagonals; V.1 handles signed real entries, while the complex extension needs a separate modulus–phase supplier with a zero-entry convention
- Workspace fanout/unfanout, connectivity and angle synthesis are counted
- State infidelity, operator error and normalized-branch error are separate contracts; source Eq. (18) normalized-block error delta corresponds to unscaled-operator error alpha_total times delta
- Quantitative output-norm or success lower bounds accompany efficiency claims
Desired result, not an achieved bound
Source-faithful size/depth/ancilla/accuracy tradeoffs and a separately costed SP consumer; exact arbitrary diagonals are not claimed poly(n).
Reduced depth may require much more workspace without reducing total size. A non-unitary diagonal is an accepted block, not a deterministic system-only gate; approximation may require stronger smoothness for transformed angle functions. Local staging checks the literal Figure3 accepted1<-0 action, success mass and normalized branch. Printed rejected-phase and clean0<-0 discrepancies are retained as source gaps; no scalable resource theorem or full-paper admission follows.
Dependency-ready execution route
Prove a sequential/parallel supplier and workspace cleanup.
Acceptance: Composed gate semantics, copy/uncompute action and emitted-list cost under a fixed connectivity model; no no-cloning shortcut.
planned; no claimed closure
Apply the diagonal block to a charged input and normalize.
Acceptance: Nonzero branch, exact probability, robust state error and all repeated/inverse/control calls in the successful-preparation resource tuple.
planned; no claimed closure
Next bounded advance: Review the staged literal Figure3 chain and zero-angle mismatch; supply the actual dmax/alpha scale and a reviewed clean-sector adapter before approximate/parallel-resource translation.
Reusable mathematics
Named Lean substrates below have their own exact signatures. They do not certify every sentence or proposed generalization on this page.
QuantumBlockEncoding.CubicDiagonalOracle.cubicN2PrimitiveProgram_cleanEntry
Lower-bound comparison contract
source-audit-pending
Pin size/depth/ancilla/precision promises before comparing the paper's regimes or arbitrary-diagonal lower bounds.
Same-model key: setting:diagonal-supplier-space-time-accuracy
Diagnostic examples, not proofs
- Pure global phase used under control
- Bounded diagonal with zero entries and a nonzero accepted branch
- Zero accepted branch rejection
- Same operator and accuracy under two clean-workspace budgets
Primary-source ledger
primary-text-checked arXiv v4, 21 January 2025; checked 29 September 2026: II.1, III.1–III.2, IV.1 Eqs. (15)–(16), V.1 Eqs. (19)–(21), VI A, VIII.1 and Tables I–II. Figure 4 signal-sector and III.2/VIII.1 accounting ambiguities remain explicit source obligations.
Parallel scheduling trades ancillas for depth, not automatically total size. Table I uses spectral-norm error; Eq. (18) bounds normalized-block error delta, corresponding to total-scale times delta in the unscaled-operator convention. Exact-block success in source notation is ||D psi||^2/(alpha^2 dmax^2); alpha>1 controls the transformed-angle derivative in smooth approximation. No local source theorem or resolution of source ambiguities is claimed.
primary-text-checked arXiv v3, 9 November 2023; checked 29 September 2026: Theorem 1, Corollary 1, Table I and Appendix B (B14–B19, B28).
Walsh Series Loader: epsilon is state infidelity. Smooth fixed-function single-attempt depth O(epsilon^-1/2), size O(n+epsilon^-1/2), success Theta(epsilon); expected depth O(epsilon^-3/2), expected size O((n+epsilon^-1/2)/epsilon). Constants retain function/derivative/nonzero-mass assumptions. Sparse variants require supplied coefficients and Hamming-weight bounds. Amplification also charges reflections and inverses.
primary-text-checked 29 April 2026 public 447-page edition; PDF SHA256 56825000d53025dea4c2998dd6a061592b8fb2b9a446c3194c5f408183327599. First bounded source slice: Chapter 9 Section 9.1, printed pages 141–143, equations (9.2), (9.9), (9.10), (9.12); standing partial-application convention Definition 2.25, page 37. Parts I–IV remain curriculum anchors, not completed formalisation.
Peer Part IV curriculum anchor, reusing existing ASPBE state-preparation/block-encoding APIs. New Chapter 9 adapters, operator-norm approximation, scientific constructions and resource certificates still require separate production admission. No whole-section/book completion is claimed.
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python3 website/scripts/research_atlas.py context --route spw-diagonal