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SPDX-License-Identifier: AGPL-3.0-or-later

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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 Hamiltonian Paper Plan

SCPN/FIM Self-Referential Hamiltonian Paper Plan

Date: 2026-05-05

Working title

Fisher-information-inspired collective feedback in Kuramoto-XY quantum Hamiltonians

Alternative:

Magnetisation-sector structure induced by a self-referential FIM term in Kuramoto-XY quantum simulation

Purpose

This paper is the theory and computational-mechanism track behind the SCPN quantum-control programme. It studies whether a collective Fisher-information-inspired feedback term changes synchronisation, spectral statistics, magnetisation-sector structure, localisation-like diagnostics, and hardware-facing decoherence predictions in Kuramoto-XY quantum simulations.

The paper must remain separate from the DLA-parity hardware paper and the Rust/VQE methods paper:

  • The DLA-parity paper is the real-hardware phenomenology and validation anchor.
  • The Rust/VQE methods paper is the reproducible software and benchmark anchor.
  • This paper is the Hamiltonian-mechanism and falsifiable-prediction anchor.

Core Hamiltonian

The model family is:

H(lambda) = H_XY + H_FIM(lambda)
H_FIM(lambda) = -lambda * M^2 / n
M = sum_i Z_i

where H_XY is the Kuramoto-derived heterogeneous XY Hamiltonian and M is the total magnetisation operator. The FIM term is interpreted conservatively as a collective magnetisation-feedback term inspired by information geometry.

Safe claim boundary at project start

Safe now:

  • The Hamiltonian family is mathematically definable.
  • The term creates an explicit sector-dependent energy contribution through M^2.
  • The existing package has the infrastructure needed to generate Hamiltonians, VQE ansaetze, exact small-n references, benchmark artefacts, and IBM hardware packages.
  • The previous DLA-parity study demonstrates that hardware claims must be controlled for depth, popcount, layout, readout, and calibration context.

Not safe yet:

  • Do not claim a demonstrated universal protection principle.
  • Do not claim quantum advantage.
  • Do not claim strict many-body localisation unless the diagnostics support the term and the limitations are stated.
  • Do not claim hardware robustness until equal-depth IBM runs exist.
  • Do not use old internal or application numbers as paper claims unless they are regenerated into committed JSON/CSV artefacts.

Scientific questions

  1. Does H_FIM produce a predictable magnetisation-sector energy structure?
  2. Does increasing lambda change level-spacing statistics relative to plain heterogeneous XY?
  3. Does the FIM term reduce entanglement growth or scrambling in a way that is visible in small-n exact simulation?
  4. Does the term predict sector-resolved survival or leakage differences under calibrated noise models?
  5. Which predicted effects are large enough to justify a minimal IBM pilot?
  6. If IBM hardware disagrees with simulation, which confound explains the failure: excitation count, circuit depth, layout, readout, calibration drift, or the absence of a real FIM mechanism?

Required offline artefacts before IBM runs

Every numerical paper claim must come from committed artefacts.

Minimum artefact set:

  • data/scpn_fim_hamiltonian/fim_spectrum_summary_2026-05-05.json — generated initial n=4,6,8 exact spectrum artefact.
  • data/scpn_fim_hamiltonian/fim_spectrum_summary_2026-05-05.csv — generated compact spectrum table.
  • data/scpn_fim_hamiltonian/fim_sector_spectrum_summary_2026-05-05.csv — generated magnetisation-sector spectrum table.
  • data/scpn_fim_hamiltonian/fim_level_spacing_summary_2026-05-05.json — generated full-spectrum and sector adjacent-gap-ratio artefact.
  • data/scpn_fim_hamiltonian/fim_level_spacing_summary_2026-05-05.csv — generated adjacent-gap-ratio table.
  • data/scpn_fim_hamiltonian/fim_entanglement_summary_2026-05-05.json — generated low-energy eigenstate bipartition-entropy artefact.
  • data/scpn_fim_hamiltonian/fim_entanglement_rows_2026-05-05.csv — generated per-eigenstate entropy table.
  • data/scpn_fim_hamiltonian/fim_entanglement_aggregate_2026-05-05.csv — generated entropy aggregate table.
  • data/scpn_fim_hamiltonian/fim_sector_survival_prediction_2026-05-05.json — generated commutator and sector-conservation artefact.
  • data/scpn_fim_hamiltonian/fim_sector_survival_summary_2026-05-05.csv — generated commutator and maximum off-sector-coupling table.
  • data/scpn_fim_hamiltonian/fim_sector_survival_rows_2026-05-05.csv — generated per-sector energy-barrier table.
  • data/scpn_fim_hamiltonian/fim_vqe_ground_state_summary_2026-05-05.json — generated small-n FIM VQE ground-state comparison artefact.
  • data/scpn_fim_hamiltonian/fim_vqe_ground_state_rows_2026-05-05.csv — generated per-seed VQE table.
  • data/scpn_fim_hamiltonian/fim_vqe_ground_state_aggregate_2026-05-05.csv — generated aggregate VQE table.
  • data/scpn_fim_hamiltonian/fim_ibm_candidate_protocol_2026-05-05.json — generated non-submitting IBM pilot candidate protocol.
  • data/scpn_fim_hamiltonian/fim_ibm_candidate_protocol_2026-05-05.csv — generated candidate circuit table.

Initial artefact hashes:

Artefact SHA256
fim_spectrum_summary_2026-05-05.json 451442c677b73419a5826fd22d3426f498a5e1186545987067ee2f3e240cef5e
fim_spectrum_summary_2026-05-05.csv aadcd6426c66967f3f92441c2114def324c68199958dff5d6a23acf586efcc9f
fim_sector_spectrum_summary_2026-05-05.csv 9e957d1d16e16cf3f41bec0644cdc508586ff716e52f61810d723c91dcdddc53
fim_level_spacing_summary_2026-05-05.json dfcc2882e561100c6c07afc2518e5b35c863628dc015c22f2d12e75ad931f959
fim_level_spacing_summary_2026-05-05.csv 4874687619524561b819e7397d5e6c599e35e9ea569015149c0f076a6dec1cf8
fim_entanglement_summary_2026-05-05.json ea9a8b81ecad09b9e354e50e61053f816263e44686660e5a3fc6fcb147c2692a
fim_entanglement_rows_2026-05-05.csv 980e54502b61f409d2d631cc2cdc136ed841e16273702f247864a8a0772b9e5b
fim_entanglement_aggregate_2026-05-05.csv 3f0c1951e7491b0ec0cde01cd7abe0914cd598e7c91d2e57bf5c745187d109f5
fim_sector_survival_prediction_2026-05-05.json addfa842cd81e1f38f3582baabf7cc3fdffc250ceeae66f922f61c6abde7fd72
fim_sector_survival_summary_2026-05-05.csv a27931c7add47c08c3a3545a5e79952f73ce63e10dddc495bbddbab23623095e
fim_sector_survival_rows_2026-05-05.csv d2f243c11a73b98851c436528328ac5345b665506bd27cf792209b904a4f65be
fim_vqe_ground_state_summary_2026-05-05.json 8d25ed4ba4593778b5f96b88ed1c571ebb04e03bcf779bdc0911a160e6792ecf
fim_vqe_ground_state_rows_2026-05-05.csv c8ab197a7c7f5a60783ae76dc6f8d7c9eeb5abc75ae987ced721d9be81bdf759
fim_vqe_ground_state_aggregate_2026-05-05.csv cf6305f59c7b207b41eda11654e9a15df176f65cd97404140e935657f0bb2d51
fim_ibm_candidate_protocol_2026-05-05.json 9b76136c7bc090f9738fcad58eab7f5b1b8bb5f26ede7ebfc32c114234407839
fim_ibm_candidate_protocol_2026-05-05.csv a577bfbd082d4528ed6471dfa95ac186b7619fd1822be99a08cf5b160eda4ac4

Minimum scripts:

  • scripts/analyse_fim_spectrum.py — implemented initial exact spectrum and magnetisation-sector summaries.
  • scripts/analyse_fim_level_spacing.py — implemented initial adjacent-gap ratio summaries for full spectra and magnetisation sectors.
  • scripts/analyse_fim_entanglement.py — implemented low-energy eigenstate bipartition-entropy summaries.
  • scripts/analyse_fim_sector_survival.py — implemented commutator, ideal-sector-conservation, and per-sector energy-barrier summaries.
  • scripts/benchmark_fim_vqe_ground_state.py — implemented small-n VQE ground-state scoring against exact dense diagonalisation.
  • scripts/prepare_fim_ibm_pilot.py — implemented a non-submitting IBM pilot candidate protocol with QPU gates and falsification rule.

Proposed paper structure

  1. Introduction and motivation.
  2. Kuramoto-XY mapping and collective FIM-inspired feedback.
  3. Magnetisation-sector decomposition induced by M^2.
  4. Exact small-n spectral and localisation-like diagnostics.
  5. VQE and ansatz implications.
  6. Noise-model survival predictions and IBM pilot design.
  7. Discussion: what the term supports, what it does not support, and what the hardware can falsify.
  8. Data and code availability.

Initial manuscript draft:

  • paper/scpn_fim_hamiltonian/scpn_fim_hamiltonian.tex
  • paper/scpn_fim_hamiltonian/scpn_fim_hamiltonian_refs.bib

Publication stance

The paper should be framed as a theoretical/computational physics note with hardware-facing predictions. It should not be framed as a hardware-confirmed result until the IBM pilot exists.

The current manuscript-safe claim boundary is recorded in docs/scpn_fim_claim_boundary_2026-05-05.md.

The first IBM-readiness step is also complete: local, non-submitting circuit preparation generated fim_ibm_circuit_preparation_2026-05-05.json and .csv. This does not replace live backend transpilation.

Recommended venues after artefacts exist:

  • arXiv preprint first.
  • Quantum Science and Technology, Physical Review A, or New Journal of Physics depending on final scope and whether IBM data are included.
  • If the result remains purely computational, SoftwareX/JOSS is not the right target; the methods paper already covers software.

Decision gate for IBM runs

IBM runs are justified only after offline artefacts identify the smallest falsification experiment with a predicted effect large enough to survive hardware noise.

Minimum IBM pilot:

  • n=4 only.
  • lambda = 0 plus two non-zero values selected from offline artefacts.
  • Equal-depth circuits.
  • Matched qubit layout where possible.
  • Explicit magnetisation/popcount controls.
  • Same-day readout calibration or parity-readout correction.
  • Fixed shot budget and pre-registered stop rule.

Continuation to n=6 or n=8 requires the n=4 pilot to show a stable sign or a clear falsification that motivates the next experiment.

Immediate next step

Inspect the generated artefacts and draft the manuscript claim table. The current generated artefacts establish the exact small-n spectrum, magnetisation-sector energy structure, adjacent-gap diagnostics, low-energy bipartition entropy, ideal sector-conservation checks, VQE ground-state baseline, and a non-submitting IBM pilot candidate protocol.

Important scientific boundary: in the ideal model, H_XY, H_FIM, and H_XY + H_FIM conserve total magnetisation. The FIM term changes sector energies and low-energy structure, but it does not create ideal unitary leakage between magnetisation sectors. Any IBM leakage or survival asymmetry must therefore be tested as a noise, state-preparation, transpilation, layout, or readout phenomenon.