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© Concepts 1996–2026 Miroslav Šotek. All rights reserved.

© Code 2020–2026 Miroslav Šotek. All rights reserved.

ORCID: 0009-0009-3560-0851

Contact: www.anulum.li | protoscience@anulum.li

SCPN Quantum Control — SCPN/FIM Claim Boundary

SCPN/FIM Claim Boundary

Date: 2026-05-05

This document converts the generated SCPN/FIM artefacts into manuscript-safe claim language. It is deliberately conservative: a claim is usable only if it is backed by a committed artefact and does not exceed the evidence boundary.

Artefact base

Artefact group Files Status
Exact spectra fim_spectrum_summary_2026-05-05.json, .csv generated
Magnetisation-sector spectra fim_sector_spectrum_summary_2026-05-05.csv generated
Adjacent-gap ratios fim_level_spacing_summary_2026-05-05.json, .csv generated
Bipartition entropy fim_entanglement_summary_2026-05-05.json, rows/aggregate CSV generated
Sector-conservation checks fim_sector_survival_prediction_2026-05-05.json, summary/rows CSV generated
VQE ground-state scoring fim_vqe_ground_state_summary_2026-05-05.json, rows/aggregate CSV generated
IBM pilot candidate fim_ibm_candidate_protocol_2026-05-05.json, .csv generated, not submitted

Manuscript-safe claims

Claim Status Supporting artefact Safe wording Limitation
The FIM term changes the exact small-n energy landscape. validated offline fim_spectrum_summary_2026-05-05.json For n=4,6,8, increasing lambda lowers the ground energy and increases the spectral gap/width in the generated dense exact spectra. Exact dense small-n only.
The FIM term creates explicit magnetisation-sector energy shifts. validated offline fim_sector_spectrum_summary_2026-05-05.csv The -lambda M^2/n term separates magnetisation sectors by a known diagonal energy contribution. This is a Hamiltonian-structure statement, not a hardware robustness result.
The ideal Hamiltonian conserves total magnetisation. validated offline fim_sector_survival_prediction_2026-05-05.json The generated commutator and off-sector block checks are zero for the tested grid, so ideal H_XY + H_FIM has no unitary sector leakage. Hardware leakage must be treated as noise/circuit/readout behaviour.
Low-energy entanglement changes with larger lambda in the tested grid. validated offline fim_entanglement_summary_2026-05-05.json For n=4, the mean low-energy bipartition entropy decreases from about 0.676 bits at lambda=0 to about 0.490 bits at lambda=8. Low-energy exact eigenstate diagnostic only; not a universal localisation proof.
Adjacent-gap ratios shift on n=6 and n=8 as lambda increases. validated offline fim_level_spacing_summary_2026-05-05.json The full-spectrum adjacent-gap mean is lower at large lambda for n=6 and n=8 in the generated artefact. Small-n exact diagnostic; use "localisation-like" only with caveats.
A topology-informed ansatz performs better than generic baselines in the n=4 FIM VQE grid. validated offline fim_vqe_ground_state_summary_2026-05-05.json In the n=4, reps=2, three-seed benchmark, the K_nm-informed ansatz has lower median relative energy error than TwoLocal and EfficientSU2 for lambda in {0,1,4}. Small optimiser budget and n=4 only; not an ansatz theorem.
The IBM pilot is ready as a candidate protocol. protocol-ready, not executed fim_ibm_candidate_protocol_2026-05-05.json A non-submitting n=4 pilot protocol exists with lambda/depth/state/readout controls and a falsification rule. Requires backend selection, live transpilation, QPU-time estimate, and explicit approval.
The IBM pilot raw counts exist. data collected, analysis pending fim_ibm_pilot_raw_counts_2026-05-05_ibm-run-4c0bd60c3fc2c532.json The n=4 SCPN/FIM pilot completed on ibm_kingston with 61 circuits and 249856 shots. No result claim is promoted until the analysis and readout-control scripts are run.

Claims that remain blocked

Blocked claim Reason
The FIM term improves real IBM hardware coherence. FIM IBM raw counts now exist, but the analysis/readout-control result has not yet been computed or promoted.
The FIM term causes ideal magnetisation-sector leakage suppression. The ideal Hamiltonian has zero sector leakage; suppression is not the correct framing.
The result demonstrates quantum advantage. All current SCPN/FIM artefacts are exact small-n offline computations or protocol design.
The model proves strict many-body localisation. Current evidence is level-spacing and entanglement diagnostics on n=4,6,8 only.
The FIM mechanism is universally protective. No multi-size hardware or open-system validation exists.

Quantitative anchors for the current draft

Exact spectrum:

  • n=4: spectral gap increases from 1.1317 at lambda=0 to 12.6060 at lambda=4.
  • n=6: spectral gap increases from 0.4468 at lambda=0 to 13.7801 at lambda=4.
  • n=8: spectral gap increases from 0.2827 at lambda=0 to 13.7173 at lambda=4.

Adjacent-gap ratios:

  • n=6 full-spectrum mean adjacent-gap ratio changes from 0.4334 at lambda=0 to 0.4071 at lambda=4.
  • n=8 full-spectrum mean adjacent-gap ratio changes from 0.4368 at lambda=0 to 0.4048 at lambda=4 and 0.3852 at lambda=8.

Entanglement:

  • n=4 mean low-energy bipartition entropy is about 0.676 bits for lambda <= 1.
  • n=4 mean low-energy bipartition entropy decreases to about 0.584 bits at lambda=2, 0.502 bits at lambda=4, and 0.490 bits at lambda=8.

VQE:

  • K_nm-informed ansatz median relative error is 0.372%, 0.413%, and 0.848% at lambda=0, lambda=1, and lambda=4, respectively.
  • Generic baselines in the same grid remain at multi-percent median error.

IBM candidate:

  • n=4.
  • lambda in {0, 1, 4}.
  • depths {2, 4, 6}.
  • five representative magnetisation sectors.
  • full 16-state readout baseline.
  • 4096 shots per candidate circuit.
  • 61 candidate circuits and 249856 candidate shots.
  • submission status: not_submitted.
  • local circuit-preparation artefact exists with max local transpiled depth 262 and max local two-qubit gate count 144; live backend transpilation is still required before any QPU submission.
  • live non-submitting backend transpilation on ibm_kingston exists with max depth 540 and max two-qubit gate count 157; QPU submission still requires review and explicit approval.

Use:

We introduce and characterise a collective Fisher-information-inspired magnetisation-feedback term in a Kuramoto-XY Hamiltonian. Exact small-n artefacts show sector-energy separation, gap widening, shifts in spectral and low-energy entanglement diagnostics, and a hardware-facing pilot protocol.

Avoid:

The FIM term has been shown to protect quantum coherence on hardware.

Avoid:

The model demonstrates quantum advantage or strict many-body localisation.

Next decision

The project can now either:

  1. Draft the paper as an offline theory/computation note with a proposed IBM pilot.
  2. Refine the pilot through live backend/transpilation checks before writing the hardware-facing section.
  3. Add a noise-model sector-survival harness before spending QPU time.

2026-05-05 IBM pilot boundary update

The n=4 SCPN/FIM pilot on ibm_kingston completed as job ibm-run-4c0bd60c3fc2c532. It is a valid hardware pilot, but it is not a positive hardware-protection result.

Allowed claims:

  • The SCPN/FIM circuit family was executed on IBM Heron r2 hardware.
  • The raw count dictionaries, row metrics, lambda-trend comparisons, and readout-baseline summaries are archived in data/scpn_fim_hamiltonian/.
  • The run is useful for protocol debugging and for designing a repeated, randomized follow-up campaign.

Blocked claims:

  • Do not claim that H_FIM = -lambda M^2 / n improved hardware coherence in this pilot.
  • Do not claim hardware many-body localisation.
  • Do not report hardware p-values from this pilot; there is one sample per lambda/depth/state condition.
  • Do not describe the readout correction as full confusion-matrix mitigation.

2026-05-05 repeated follow-up boundary update

The repeated/randomized SCPN/FIM follow-up completed as IBM job ibm-run-cf4835290f607387.

This is now stronger than a pilot boundary: the simple hardware-protection interpretation is falsified for the tested ibm_kingston circuit family.

Allowed claims:

  • The repeated run gives evidence that, in the tested implementation, lambda = 4 increases leakage relative to lambda = 0.
  • The result is a valid negative hardware result for this backend/circuit family.

Blocked claims:

  • Do not claim that FIM improves hardware coherence in this implementation.
  • Do not claim backend-general behaviour.
  • Do not claim hardware many-body localisation.
  • Do not generalize the negative result to all possible FIM Hamiltonian implementations; it applies to this digital Trotter construction, depth set, backend, calibration window, and observable set.