Theory-Hook Promotion Matrix¶

BL-98 distinguishes a useful research routine from an admitted product or control capability. Importability is not promotion. Every reviewed hook has a machine-readable tier, one permitted role, explicit forbidden claims, and a small local fixture that proves only the bounded software path.

The current matrix is fail-closed: no hook is admitted for actuation, publication claims, hardware performance, or differentiable execution. A passing fixture does not change those permissions.

Current decisions¶

Hook	Tier	Status	Permitted role	Current evidence
Quantum speed limit	B	`bounded_candidate`	Optional offline control constraint candidate	Two-qubit closed-system threshold fixture
Hamiltonian learning	B	`bounded_candidate`	Synthetic inverse problem	Exact two-qubit correlators, initialized at the generating coupling
Koopman closure	B	`diagnostic_only`	Classical local baseline	Finite two-oscillator observable matrix and Hermitian projection
Minimum bipartite QMI	D	`research_only`	Mutual-information diagnostic	Bell-state QMI identity plus tier-D policy check
Stabilizer Rényi entropy	B	`diagnostic_only`	Resource-theory diagnostic	Stabilizer/T-state contrast
Spectral form factor	B	`diagnostic_only`	Finite-size spectral diagnostic	Four-qubit exact spectrum with magnetisation-sector spacing ratio

The canonical records are returned by list_theory_hook_promotions(). The committed result is regenerated from code, not edited by hand:

python scripts/run_theory_hook_promotion_evidence.py --check

The byte-checked outputs are data/theory_hook_promotion/evidence.json and data/theory_hook_promotion/evidence.md in the repository.

Reading the tiers¶

Tier B means the implementation has a bounded, testable mathematical role. It does not mean production-ready, differentiable, experimentally validated, or publication-ready. Tier D means research-only: the present semantics are not sufficient for promotion, regardless of whether the code executes correctly.

Statuses add a second axis:

bounded_candidate permits future evaluation against named promotion gates;
diagnostic_only permits the current observable or baseline but not its use as a certification;
research_only prevents promotion until the semantic gap itself is closed.

All six records expose admitted_for_control = false, admitted_for_publication_claim = false, and differentiable = false.

Quantum speed limit¶

compute_qsl() evolves a finite closed Kuramoto-XY model and reports a sampled local-phase-order threshold time. tau_MT is the Mandelstam–Tamm lower bound for the actual initial/target overlap in that simulation.

The legacy tau_ML field is more limited: it evaluates the traditional Margolus–Levitin orthogonalization-time expression. If the final state is not orthogonal to the initial state, that value is not an arbitrary-fidelity bound for the target. It is retained for compatibility and labelled as an orthogonalization reference. The distinction matters because extensions of the Margolus–Levitin result to arbitrary fidelity require additional semantics.

Allowed now:

finite closed-system MT and legacy ML diagnostic calculation;
offline evaluation as a possible lower-bound feature after an independent control contract is defined.

Not allowed now:

measured synchronization time;
a critical exponent or BKT certificate;
automatic rejection or actuation inside a controller;
arbitrary-fidelity interpretation of tau_ML.

Primary mathematical context: Levitin and Toffoli, Phys. Rev. Lett. 103, 160502 (2009).

Hamiltonian learning¶

learn_hamiltonian() fits a symmetric non-negative coupling matrix by matching ground-state XX+YY correlators. The current objective repeatedly performs dense exact diagonalization and reports an in-sample residual.

The BL-98 fixture deliberately starts the optimizer at the generating two-qubit coupling. It proves end-to-end wiring and self-consistency, not identifiability. Distinct couplings may yield similar observables, and the current routine has no shot-noise model, calibration model, posterior, confidence region, held-out objective, or misspecification test.

Before promotion, this route needs:

identifiability and uncertainty analysis;
held-out noisy and misspecified synthetic systems;
measured-data calibration with no fit/evaluation leakage.

Hamiltonian-learning context: Wiebe, Granade, Ferrie, and Cory, Phys. Rev. A 89, 042314 (2014).

Koopman local closure¶

The exact Koopman operator is linear but generally infinite-dimensional. The repository routine uses a finite basis containing phase identities and pairwise sine/cosine observables. Its matrix is reference-point-dependent and truncates higher-order terms. It is therefore described as a finite local Koopman-style closure.

koopman_to_hamiltonian() constructs i(L-L†)/2. This is a Hermitian projection: it discards the symmetric part of L. It is useful for bounded matrix and spectral experiments but is not dynamically equivalent to the complete nonlinear Kuramoto flow.

Allowed now:

a classical local observable-space baseline;
closure-matrix and projected-matrix diagnostics.

Explicitly forbidden:

an exact finite Koopman invariant subspace;
full nonlinear dynamics;
BQP-completeness or quantum advantage.

Finite approximation context: Williams, Kevrekidis, and Rowley, J. Nonlinear Sci. 25, 1307–1346 (2015).

Minimum bipartite mutual information is not IIT Φ¶

The legacy quantum_phi module computes

\[ I(A:B) = S(\rho_A) + S(\rho_B) - S(\rho_{AB}) \]

for every non-trivial bipartition and returns the minimum and maximum. This is quantum mutual information. It is not Integrated Information Theory Φ.

No causal model, intervention repertoire, cause-effect structure, exclusion postulate, or IIT composition calculation is implemented. Consequently:

the route is permanently labelled tier D under its current semantics;
IntegratedInformationPhi fails closed unless a caller explicitly requests a labelled entropy or mutual-information diagnostic;
proxy results set phi_available = 0.0 and is_integrated_information = 0.0;
proxy results never use the key phi;
no consciousness, sentience, cognition, or clinical interpretation is allowed.

Legacy PhiResult, compute_quantum_phi(), and phi_* field names remain only for import and serialization compatibility. Their API documentation identifies the values as QMI.

IIT 3.0 illustrates the causal-structure semantics absent from this code: Oizumi, Albantakis, and Tononi, PLOS Computational Biology 10, e1003588 (2014). That citation documents the semantic mismatch; it is not endorsement or validation of IIT claims by this package.

Stabilizer Rényi entropy¶

magic_nonstabilizerness enumerates all 4**n Pauli strings for a pure state and evaluates the documented stabilizer Rényi-2 quantity. This is a bounded resource-theory diagnostic. The exact fixture distinguishes a computational stabilizer state from a T state.

A maximum over a finite coupling grid is only the grid argmax. It is not a critical-point estimate and does not establish fault-tolerant resource cost, classical hardness, or quantum advantage. Criticality work requires a preregistered finite-size protocol and uncertainty-aware measurement route.

Primary definition: Leone, Oliviero, and Hamma, Phys. Rev. Lett. 128, 050402 (2022).

Spectral form factor and adjacent-gap ratio¶

compute_sff() evaluates the normalized finite-spectrum form factor. The reported adjacent-gap ratio defaults to a magnetisation sector because mixing independent symmetry sectors can distort level statistics. Full-spectrum and selected-sector ratios remain separate in the result.

The compatibility field chaos_onset_K is a fixed-threshold crossing on the provided grid. It is not a statistical certificate of quantum chaos, a Poisson-to-random-matrix transition, a BKT transition, or a coincidence between chaos and synchronization.

Promotion requires a preregistered ensemble, energy window, symmetry policy, null distribution, finite-size scaling plan, and held-out replication. For the adjacent-gap-ratio statistic, see Atas et al., Phys. Rev. Lett. 110, 084101 (2013).

Programmatic use¶

Inspect policy without running numerical fixtures:

from scpn_quantum_control.analysis import get_theory_hook_promotion

policy = get_theory_hook_promotion("koopman_local_closure")
assert policy.status.value == "diagnostic_only"
assert policy.admitted_for_control is False
assert "BQP-completeness" in policy.forbidden_claims

Run all local fixtures and build a digest-locked report:

from scpn_quantum_control.analysis import build_theory_hook_promotion_report

report = build_theory_hook_promotion_report()
assert report.passed
assert all(not row.admitted_for_control for row in report.records)
print(report.content_digest)

report.passed means only that the six named fixtures passed. Always evaluate the corresponding policy record before using a metric downstream.

Promotion procedure¶

A future change to a row must provide all of the following:

a new versioned schema when semantics change;
an exact claim and review of the affected source, tests, docs, and evidence;
held-out evidence satisfying every listed promotion_requirement;
an updated forbidden-claim audit;
independent review before any publication or control admission;
explicit authority for provider, hardware, actuation, or publication work.

Local evidence never supplies those external authorities.