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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 — Strategic Roadmap (post-v1.0 differentiation)

Strategic Roadmap — Post-v1.0 Differentiation

Canonical status note (2026-05-06): active task selection is consolidated in ROADMAP.md. This document remains the detailed deferred/CEO-gated strategic catalogue; items here are not activated unless copied into the canonical work queue.

Fifty-three differentiation items scoped beyond the feature list in ROADMAP.md. Each item is a multi-week-to-multi-month track with explicit prerequisites, deliverables, and risks. None is scheduled yet; this document is the bill of work so future sessions can prioritise, scope, and sequence without re-deriving the case.

Status: all fifty-three are DEFERRED / CEO-gated. No execution until each item is individually activated.

Execution note (2026-04-29): the preprint Figure 17 exact-simulation crossover closes a manuscript resource-boundary figure only. It does not activate S2 or claim broad quantum advantage; S2 still requires the full N=4--20 exact/MPS/GPU/noisy-hardware benchmark matrix and CEO approval.

Methods-paper follow-up candidates (2026-05-05): the Rust/VQE methods papers identify four concrete next steps: a one-command reproducibility CLI, a public benchmark dashboard, n=6--12 ansatz scaling with tensor-network baselines, and an optional Pulser/Bloqade analog XY bridge. The CLI and dashboard are publication infrastructure. The scaling study maps to S2/S20, and the analog bridge maps to S10; both require separate activation before heavy benchmark or dependency work.

SCPN/FIM Hamiltonian paper track (2026-05-05): the third paper is activated as a documentation and offline-validation track. It covers the collective Fisher-information-inspired term H_FIM = -lambda * M^2 / n, its magnetisation-sector consequences, and hardware-facing predictions. IBM runs are not activated by this note; they require offline artefacts, equal-depth circuit protocols, QPU-time estimates, and explicit approval.

Relationship to ROADMAP.md: that file tracks release-scoped work (v0.9.x → v1.0). This file tracks post-v1.0 differentiation work that pushes the project into novel territory rather than closing gaps.

Priority matrix

Ordering below is by expected research/adoption impact per effort unit. Ordering is not fixed — re-evaluate each quarter as the scientific landscape moves.

# Track Impact Effort Dependencies
S1 Hybrid classical–quantum feedback loop high 6–10 weeks runner refactor, latency budget, IBM Dynamic Circuits
S2 Quantum advantage benchmarks at scale medium-high 4–6 weeks IBM credits, MPS/GPU baselines
S3 ML-augmented pulse / ansatz design medium-high 8–12 weeks JAX tier, DLA-closure data
S4 Multi-hardware + pulse-level control medium 6–8 weeks PennyLane adapter, OpenPulse docs
S5 Open-data + classical validation harness medium 3–5 weeks Zenodo DOI, QuTiP/Dynamiqs already wired
S6 Decoupled quantum-kuramoto subpackage medium 2–3 weeks import-graph audit
S7 Fault-tolerant / logical-level extension strategic 12+ weeks surface code + DLA theory pass
S8 Mid-circuit adaptive branching (Dynamic Circuits) high 4–6 weeks (after S1) S1 feedback runner, Dynamic Circuits API
S9 Quantum thermodynamics of sync transitions medium-high 6–8 weeks LindbladSyncEngine ✓, GUESS ✓, OTOC ✓
S10 Analog-native backends (Rydberg / neutral-atom / CV photonic) high (post-NISQ positioning) 8–12 weeks per backend vendor SDK access, analog mapper
S11 DLA-driven quantum sensing (sync-as-sensor) medium 3–4 weeks qfi_criticality.py ✓, witnesses ✓
S12 Automated phase-diagram exploration via Bayesian optimisation medium-high 6–8 weeks persistent-homology gem ✓, Krylov complexity ✓, Rust Hamiltonian builder ✓
S13 Bosonic / continuous-variable quantum Kuramoto medium-high 8–10 weeks photonic SDK access, Rust hypergeometric pulse ✓
S14 Hybrid quantum-classical forecasting engine medium-high 6–8 weeks OTOC ✓, DLA invariants ✓, sc-neurocore / SSGF / SPO bridges ✓
S15 DLA-protected many-body scars for long-lived sync medium-high 6–8 weeks DLA machinery ✓, Rust drive shaping ✓
S16 Quantum network tomography (reconstruct K_nm from observables) high 5–7 weeks witnesses ✓, OTOC ✓, differentiable Rust backend (new)
S17 Higher-order (simplicial / hypergraph) quantum Kuramoto medium 5–7 weeks mapper refactor, future Heron / Loon multi-qubit gates
S18 Sync-protected quantum memories and repeaters medium-high 6–8 weeks witnesses ✓, qec/ ✓
S19 Entanglement phase diagram + magic + Krylov complexity medium 4–5 weeks magic_sre ✓, krylov_complexity ✓, entanglement_entropy ✓
S20 Quantum Kuramoto universal control-benchmark suite high (community) 6–8 weeks scpn_quantum_engine ✓, HardwareRunner ✓, S5 harness
S21 Multi-scale quantum → classical bridging layer high 6–8 weeks DLA invariants ✓, bridge/* ✓, large-N classical Kuramoto (ext dep)
S22 Non-Hermitian / PT-symmetric Kuramoto + exceptional points medium-high 6–8 weeks LindbladSyncEngine ✓, Rust pulse ✓, dilation primitive (new)
S23 Quantum reservoir computing on Kuramoto transients medium-high 5–6 weeks qrc_phase_detector ✓, OTOC ✓, witnesses ✓
S24 Quantum speed limits for collective sync medium 4–5 weeks quantum_speed_limit ✓, DLA ✓, OTOC ✓
S25 Topological defects + vortex dynamics on 2D quantum lattices medium-high 6–8 weeks vortex_detector ✓, wilson_loop ✓, mapper 2D extension
S26 Entanglement-mediated long-range synchronisation medium 5–6 weeks Bell pair prep ✓ (crypto/bell_test), Heron topology constraints
S27 Hardware-in-the-loop inverse design of oscillator networks high 6–8 weeks S1 feedback ✓, Rust mapper ✓, VQE ✓
S28 Sync-enhanced distributed quantum metrology medium-high 5–6 weeks QFI ✓, witnesses ✓, sensor-array topology design
S29 Floquet Kuramoto time crystals + subharmonic sync medium 4–5 weeks floquet_kuramoto ✓, Rust hypergeometric pulse ✓
S30 Quantum Kuramoto for community detection + modularity medium 5–6 weeks witnesses ✓, DLA invariants ✓, graph-benchmark corpus
S31 DLA-protected MBL / delocalisation transitions medium 5–7 weeks DLA ✓, OTOC ✓, disorder-sweep harness (new)
S32 Monitored quantum Kuramoto (measurement-induced transitions) medium-high 5–7 weeks Dynamic Circuits ✓ (S1/S8), witnesses ✓
S33 Quantum-enhanced Lyapunov spectra for chaotic Kuramoto medium 5–6 weeks OTOC ✓, DLA ✓, classical large-N solver
S34 Self-organising Kuramoto (autonomous drive engineering) medium 4–5 weeks S1 + S8 feedback plumbing (prerequisite)
S35 Quantum Kuramoto native simulator for active matter (non-reciprocal) medium 5–6 weeks non-reciprocal K extension, S22 dilation primitive
S36 Information geometry on quantum sync manifolds (Fisher tensor) medium-high 5–6 weeks QFI ✓, Rust engine ✓
S37 Categorical / compositional quantum Kuramoto medium 5–7 weeks mapper refactor, category-theory formalism
S38 Quantum Kuramoto field theory (QKFT) continuum limit + RG flows high 8–12 weeks tensor networks (quimb ✓), DLA ✓, QuTiP ✓
S39 Autopoietic / self-referential networks (sync-driven K rewriting) medium 5–6 weeks S1 feedback + S34 autonomous (prereq)
S40 Holographic duals via quantum sync (AdS/CFT-style) strategic / exploratory 8–12 weeks DLA invariants ✓, theorist pass
S41 Quantum causal discovery with intervention medium-high 5–7 weeks extends S16, requires Dynamic Circuits ✓
S42 Symplectic structure-preserving Trotterization medium 5–7 weeks Rust pulse ✓, geometric-integrator theory
S43 Full resource theory of quantum synchronisation medium-high 6–8 weeks witnesses ✓, OTOC ✓, DLA ✓
S44 Objective collapse / macroscopic foundations testbed (GRW, Penrose OR, CSL; Quantum Darwinism angle) high (foundations) 8–12 weeks DLA parity ✓, large-N hardware time
S45 Biologically faithful Kuramoto simulator + IIT consciousness angle medium-high 6–8 weeks EEG / connectome benchmarks ✓, applications/ ✓
S46 Phase-transition / attractor-landscape quantum programming medium-high (paradigm) 6–8 weeks witnesses ✓, floquet_kuramoto ✓
S47 Analogue gravity: relativistic metrics, cosmological phase transitions, baryogenesis, emergent spacetime high (foundations) 10–12 weeks QKFT (S38), theorist pass
S48 Self-healing qubit fabrics + continuous QEC via sync medium-high 6–8 weeks qec/ ✓, S18 sync memories (prereq)
S49 Quantum fluctuation theorems (Jarzynski, Crooks) across sync transitions medium-high 5–6 weeks extends S9 thermodynamics, LindbladSyncEngine ✓
S50 Quantum kernels from sync manifolds (ML) medium-high 4–5 weeks DLA ✓, Rust forward mapper ✓
S51 Hayden–Preskill / black-hole info dynamics simulator medium-high 5–6 weeks OTOC ✓, DLA scrambling ✓
S52 Distributed quantum consensus via global sync (quantum internet timing) high (infrastructure) 8–10 weeks S1 async runner ✓, Bell pair ✓, modular topology
S53 Engineered self-organised criticality in oscillator networks medium-high 5–7 weeks SOC literature, OTOC ✓, witness ✓

S1 — Hybrid classical–quantum feedback loop

Motivation

Current pipeline is batch (submit → wait → analyse). A closed loop where a classical sync observer feeds back into pulse shaping on the next shot / circuit unlocks a class of adaptive experiments that are not currently covered by any polished open-source quantum-Kuramoto tool. Adaptive measurement protocols (Bayesian phase estimation, reinforcement-learning pulse shaping, active decoherence tracking) all require sub-second feedback.

Deliverables

  1. hardware/feedback_loop.py — classical observer API plus a FeedbackRunner(scheduler, observer) orchestrator that submits one circuit, receives counts, feeds them into the observer callback, updates the circuit parameters, and submits the next shot.
  2. IBM Dynamic Circuits integration — leverage mid-circuit measurement + conditional gates available on Heron r2+ for intra-shot feedback within a single circuit, not only across-shot.
  3. Reference classical observer: Kalman-filtered Kuramoto sync-R estimator written in Rust (hot-loop code) and exposed through the multi-language dispatcher.
  4. Two end-to-end demos:
  5. Cross-shot closed-loop: 20-shot Bayesian refinement of the K_ij coupling estimate on a small network.
  6. Intra-shot Dynamic-Circuits demo: mid-circuit parity measurement gates the subsequent RZZ angle.
  7. Benchmark: wall-time budget per feedback cycle, amortised over 1 000 shots. Document in docs/pipeline_performance.md.

Risks

  • IBM Runtime session-mode latency is bounded below by ~200 ms round-trip even on Session. Real-time sub-kHz feedback is infeasible without hardware-side primitives.
  • Dynamic Circuits API surface is still evolving; pin qiskit-ibm-runtime version in the feedback module's own importlib.metadata check.

Prerequisites

  • Runner refactor to support Session + callback protocol.
  • Explicit latency budget ≤ 1 s per feedback cycle documented and benchmarked.
  • IBM credits allocation or paid Runtime window (this burns session minutes fast).

Acceptance

A 20-step Bayesian-refinement demo completes end-to-end in ≤ 5 minutes on ibm_kingston (or equivalent Heron r2+) with the feedback loop demonstrably converging to a ground-truth K_ij within 10 %. Notebook + raw data archived to Zenodo.

S2 — Quantum advantage benchmarks at scale

Motivation

The project currently demonstrates scientific fidelity (DLA parity, BKT, CHSH) but does not publish an explicit scaling curve showing where classical ODE / MPS / sparse methods break down and the quantum approach wins. That scaling study is the single most compelling evidence for a post-NISQ audience and is also the foundation for the Phase 2 IBM credits justification.

Deliverables

  1. Sweep script scripts/bench_advantage_scaling.py that builds the same K_nm physics at N = 4, 6, 8, 10, 12, 14, 16, 18, 20 and measures wall-time + memory for each of:
  2. Classical exact diagonalisation (numpy eigh).
  3. Classical Trotter via dense matrix exponential.
  4. Classical sparse MPS (quimb already wired via [tensor]).
  5. GPU-accelerated paths where available.
  6. Quantum Trotter + ZNE on ibm_kingston (noisy) and AerSimulator (ideal).
  7. Explicit crossover table: memory breakpoint, wall-time breakpoint, noisy vs. ideal gap as a function of N.
  8. Figure set: log-log scaling plots plus a combined panel figure for publication.
  9. Short paper section + preprint integration — the scaling curve is the headline plot for the expanded paper/ draft.
  10. tests/test_advantage_scaling_regression.py — a tight regression test that catches unintended classical-speedup regressions in future refactors.

Risks

  • Phase 2 IBM credits are pending; without them, the hardware column caps at ≤ 4 qubits on the free tier.
  • Some classical baselines (quimb, JAX) have distinct memory models that make "memory footprint at N" comparisons unfair without careful instrumentation.

Prerequisites

  • IBM Credits decision (currently pending since 2026-03-29).
  • quimb + dynamiqs + jax already wired (done).
  • MPS memory profiler + GPU memory profiler harness.

Acceptance

Published scaling figure with every column populated up to N = 20 (with the hardware column graceful-degrading to its accessible subset). Raw data archived to Zenodo DOI. Figure + table embedded in the paper.

S3 — ML-augmented pulse / ansatz design

Motivation

Hand-crafted Kuramoto-XY ansätze (structured_ansatz.py) and hand-chosen pulse shapes (pulse_shaping.py: PMP-ICI, hypergeometric) leave performance on the table for networks with non-trivial topology. Reinforcement learning + differentiable programming can discover better mappings for large networks, exploiting the DLA closure structure as an implicit symmetry prior. The project already has the JAX tier wired — the differentiable-programming substrate is in place.

Deliverables

  1. ml/ansatz_rl.py — PPO-style RL agent that takes a K_nm coupling matrix as state and proposes ansatz parameter schedules. Reward: VQE ground-state fidelity on the classical reference.
  2. ml/pulse_diff.py — JAX-based differentiable pulse shaper that trains a parameterised pulse envelope (hypergeometric family is the natural candidate; JAX autodiff through the Rust hypergeometric path via a custom VJP).
  3. DLA-symmetry prior — bake the build_xy_generators output into the RL policy as a mask over allowed operator classes; agent chooses coefficients, not operators.
  4. Benchmark vs. hand-designed baselines on the N=4 DLA-parity task and on a new 6-oscillator "mixed-parity" benchmark.
  5. Reproducibility harness: saved weights + training logs + one-command replay script.
  6. docs/ml_ansatz_design.md — theory note explaining the RL formulation, the DLA mask, and the differentiable-pulse backward pass.

Risks

  • RL on quantum circuits has a well-known sample-efficiency problem. If classical-reference reward takes > 1 s per candidate, training on realistic N quickly becomes compute-bound.
  • "Learned ansatz beats hand-crafted" is a non-trivial claim that needs falsification criteria (track under docs/falsification.md).

Prerequisites

  • JAX tier already installed ([jax] extra exists).
  • stable-baselines3 or cleanrl added as a new [rl] extra.
  • GPU access (mining rig or ML350; not laptop CPU).

Acceptance

On the N=6 mixed-parity benchmark, the learned ansatz achieves ≥ 5 % lower VQE energy error than structured_ansatz on ≥ 80 % of 50 randomised K_nm instances. Signed reproducibility run on the mining rig, logs + weights archived.

S4 — Multi-hardware backend + pulse-level control

Motivation

The PennyLane adapter advertises IBM / IonQ / Rigetti / Quantinuum / Braket / Cirq vendor strings and a 67-test cross-vendor mock suite exists (commit c3dcbf6), but no real hardware run has been made against a non-IBM backend. Pulse-level control on IBM is similarly under-exploited: the Rust hypergeometric pulse engine would compose cleanly with OpenPulse for custom DRAG / Gaussian envelopes.

Deliverables

  1. Two non-IBM hardware runs, mock → real promotion:
  2. IonQ Aria (trapped-ion, PennyLane ionq.qpu route).
  3. Rigetti Aspen-M-3 or Quantinuum H1-1 (superconducting or trapped-ion, TBD by quota).
  4. OpenPulse integration on IBM — plug the Rust ici_three_level_evolution_batch output into a qiskit.pulse.Schedule; measure a Rabi-equivalent on-hardware calibration of a custom hypergeometric pulse.
  5. hardware/pulse_compiler.py — thin compiler from the existing pulse_shaping.py numeric envelope to a vendor's pulse format (OpenPulse for IBM, native sequence for IonQ via PennyLane).
  6. Cross-vendor replication of the Phase 1 DLA-parity result at N = 4 on at least one non-IBM backend. Fidelity degradation attribution separated per vendor.
  7. docs/multi_vendor_hardware.md — operator manual: how to acquire credits, how to transpile, per-vendor gotchas (IonQ's all-to-all connectivity, Quantinuum's mid-circuit measurement, Braket's cost accounting).

Risks

  • Vendor costs are not free. IonQ QPU time is expensive; Quantinuum requires a commercial relationship. Without a research credit programme, hardware costs cap what runs.
  • PennyLane adapter wraps Qiskit + vendor plugins — plugin version drift is a chronic risk (cf. the Pennylane adapter fix in v0.9.4).

Prerequisites

  • IonQ research credits application (currently no relationship).
  • Quantinuum research credits application.
  • The Rust hypergeometric → OpenPulse converter pass needs a local calibration against a known ibm_kingston backend before external submission.

Acceptance

DLA parity asymmetry measured on two distinct hardware backends at N = 4, qualitative direction agrees (both positive, both in the 5–20 % band). Raw data archived to Zenodo.

S5 — Open-data + classical validation harness

Motivation

Phase 1 raw data lives in data/phase1_dla_parity/*.json and has a Zenodo DOI (Zenodo record 18821929). A community-usable benchmark would ship: the raw data, the classical reference solvers, a reproducer script, and a diff-check harness against the published statistics — all in one pip install-able subpackage. This positions the repo as a reference benchmark for "quantum synchronisation dynamics on NISQ" the way QED-C positions itself for application-oriented QC benchmarks.

Deliverables

  1. scpn_quantum_control.benchmark_harness subpackage:
  2. load_phase1_dataset() — loads raw JSON, returns a typed pandas DataFrame plus metadata.
  3. reproduce_phase1_statistics() — runs Welch + Fisher + readout-baseline correction, asserts published values within tolerance. Already partially in tests/test_phase1_dla_parity_reproduces.py; promote to public API.
  4. classical_baselines — thin wrappers around QuTiP, Dynamiqs, MPS (quimb), and our own Python-floor dispatcher for apples-to-apples comparison.
  5. scripts/run_benchmark_suite.py — one-command reproduction of every published claim (DLA parity, CHSH, BKT, OTOC, DLA dim).
  6. docs/benchmark_harness.md — operator manual: how to install, how to run, what each output means, how to contribute new benchmarks.
  7. Submission to Papers With Code and Qiskit Ecosystem after the harness lands.
  8. Zenodo deposit refreshed with tagged benchmark snapshot.

Risks

  • "Community resource" only works if the community adopts it. Visibility campaign (launch copy drafts already in .coordination/launch_copy/) is a prerequisite.
  • Reproducibility-at-a-distance is brittle — CI must exercise the harness on every release.

Prerequisites

  • B9 (Phase 1 reproducer) — done, commit 16b3f8e.
  • C7 (cross-validation vs QuTiP / Dynamiqs) — done, commit 82b51d9.
  • Zenodo GitHub integration re-enabled by CEO.

Acceptance

A clean-room user with only pip install scpn-quantum-control[benchmark] can reproduce every published number within documented tolerance on the first run. CI gate runs the harness on every release tag.

S6 — Decoupled quantum-kuramoto subpackage

Motivation

scpn_quantum_control carries a mix of core XY / Kuramoto infrastructure and SCPN-specific research code (K_nm from Paper 27, the 16-layer UPDE, SCPN mapping modules). A user who only wants "quantum Kuramoto on superconducting hardware" has to take the whole stack, which increases the adoption barrier. A lightweight quantum-kuramoto subpackage — just phase/, bridge/ minus SCPN-specific parts, hardware/ core, and the accel dispatcher — would let that user opt in without the SCPN research baggage.

Deliverables

  1. src/quantum_kuramoto/ sub-distribution — separate pyproject.toml inside the same monorepo publishing as a second PyPI package that depends only on the reusable parts of scpn_quantum_control.
  2. Import-graph audit — measure exactly which modules depend on SCPN-specific symbols (K_nm, OMEGA_N_16, build_knm_paper27, SSGF, FIM) and mark them out of scope for the subpackage.
  3. Re-export surface in scpn_quantum_control — keep existing users unchanged; scpn_quantum_control.phase continues to work.
  4. Separate README for quantum-kuramoto that targets the general quantum-simulation audience (not SCPN-specific).
  5. Dual-publish pipeline — the existing publish workflow forks to produce two wheels from the same source.

Risks

  • Package boundary discipline is a maintenance cost — once there are two published packages, API breakage audits have to run on both.
  • "Adoption explosion" is hypothetical; reconfirm with user research (Qiskit Ecosystem post-submission feedback, downloads telemetry) before committing to dual-publish.

Prerequisites

  • Import-graph audit (2 days of work) — needs to be the first step to confirm the split is feasible.
  • Version-sync policy decision — the two packages share a SemVer or diverge?

Acceptance

pip install quantum-kuramoto installs without pulling any SCPN-specific module. import quantum_kuramoto; print(dir(...)) surfaces the documented public API (Kuramoto solver, VQE, Trotter, HardwareRunner, accel dispatcher). The existing scpn_quantum_control package continues to work unchanged for existing users.

S7 — Fault-tolerant / logical-level extension roadmap

Motivation

The DLA parity asymmetry is a physical-qubit phenomenon; its survival under error correction is not guaranteed and is not yet theoretically analysed. Positioning the project for the post-NISQ era requires (i) an explicit theory of which DLA-parity features survive at the logical level and (ii) a resource-estimation model for the surface-code implementation. The project already has qec/ scaffolding (repetition code UPDE, surface code UPDE, multi-scale QEC) — the logical-level theory is the missing piece.

Deliverables

  1. docs/logical_dla_parity.md — theory note on whether / under what conditions DLA parity survives logical-qubit encoding. Follow-up to Sec. 4.2 of the Phase 1 short paper.
  2. qec/dla_parity_logical.py — simulation of DLA parity on logical qubits under a configurable Pauli noise model.
  3. Resource-estimation table:
  4. Physical qubits needed for N = 16 oscillators at code distance d = {3, 5, 7}.
  5. Wall-clock for a single Trotter step at each distance.
  6. Expected fidelity under the Pauli noise model.
  7. Explicit cross-check against the multiscale_qec hierarchy already in the repo — does hierarchical encoding buy us a lower overhead than flat surface code?
  8. paper/logical_dla_parity.md — short-paper continuation for the post-v1 release cycle.

Risks

  • Full-scale logical simulation at N = 16 is compute-bound even on the mining rig; requires careful truncation.
  • The theory step may conclude that DLA parity does NOT survive a given code — in which case the result is still publishable (a negative result on a prominent conjecture), but needs careful framing.

Prerequisites

  • A theorist's pass on the representation theory of the XY Hamiltonian under the surface-code stabiliser group (this is a multi-week analytical task, not engineering).
  • qec/ subpackage is already wired but untested at logical scale; the multi-scale QEC modules need benchmarking first.

Acceptance

Publishable theory note with a clean positive or negative result on "does DLA parity survive surface-code encoding", accompanied by reproducible simulation code. Resource-estimation table cited in the v1.0 paper as an explicit "post-NISQ outlook" section.

S8 — Mid-circuit adaptive branching for real-time sync stabilisation

Motivation

Follow-up to S1. S1 establishes a cross-shot feedback loop (measure → observer → next shot). S8 collapses the loop into a single circuit: partial order-parameter measurements mid-Trotter feed a classical branch condition evaluated on the IBM classical register, and conditional gates apply corrective drives when a local desync metric crosses a threshold. IBM Dynamic Circuits on Heron r2+ support the required mid-circuit measurement + conditional gate primitives. A hardware demo of this kind of intra-circuit adaptive branching on a Kuramoto / XY Hamiltonian has not surfaced in the open literature we have surveyed (2026-04; the field moves, re-check before activation).

Deliverables

  1. control/adaptive_trotter.py — AdaptiveTrotterRunner that composes a branched Qiskit circuit: per-slice mid-circuit measurement on a chosen sub-register → classical-register condition → conditional RZZ / RX correction → next Trotter slice.
  2. Partial order-parameter measurement primitive (library): k-qubit projective X/Y readout that reconstructs \(R_{local}\) for a chosen subset of oscillators without destroying the rest of the state.
  3. Branch-condition library — three policies committed out of the box:
  4. Threshold on local R (corrective kick when \(R < R_*\)).
  5. Threshold on DLA-parity leakage between sectors.
  6. Chimera-state detector (clustered desync; triggers a topology-aware pulse from pulse_shaping.py).
  7. Rust pre-compute helper: scpn_quantum_engine function that, given a K_nm matrix and a target \(R_*\), emits the mid-circuit condition table (look-up for the classical branch logic).
  8. Hardware demo on ibm_kingston at N = 4: show that the adaptive path achieves a higher final R than the open-loop Trotter baseline at equal circuit depth.
  9. docs/adaptive_branching.md — operator manual explaining the API, the Dynamic Circuits constraints on the target backend, and the decision trade-off between "more branches = more reactive" vs. "more branches = more classical stalls".

Risks

  • Dynamic Circuits latency per branch is backend-dependent; the feature is most capable on Heron r2+. Older systems reject the conditional pattern entirely.
  • Mid-circuit measurement collapses the measured register; accidentally measuring the wrong sub-register destroys the Trotter state. The partial-order-parameter primitive needs a formal proof that only the targeted sub-register is projected.
  • Circuit compilation overhead grows with branch count; an eight- branch Trotter may exceed the 5-minute IBM Runtime soft-cap.

Prerequisites

  • S1 (hybrid feedback loop) must land first — S8 reuses the runner-level observer plumbing that S1 introduces. Activating S8 before S1 is feasible but duplicates work.
  • Dynamic Circuits support confirmed on the target backend.
  • Rust-side branch-table generator — 2 weeks on top of the existing scpn_quantum_engine build.

Acceptance

On a pre-registered N = 4 benchmark with controlled frequency spread, the adaptive branched circuit outperforms the open-loop Trotter baseline on final R at equal circuit depth in ≥ 70 % of 50 random \(\omega\) realisations. Raw data archived to Zenodo. Applications crossover panel — if the same adaptive pattern improves fidelity on a disruption-proxy ITER workload or a power-grid cascade toy model, it is evidence that the primitive generalises beyond Kuramoto.

Falsification

  • New entry for docs/falsification.md as C12 when S8 activates: "Adaptive branching improves final R over open-loop Trotter at equal depth." Falsifier — win-rate ≤ 50 % on the pre-registered benchmark.

S9 — Quantum thermodynamics of synchronisation transitions

Motivation

The repo already ships the machinery a quantum-thermodynamics study needs: LindbladSyncEngine (v0.9.5) for open-system dynamics, mitigation/symmetry_decay (GUESS) for a magnetisation-based ZNE that cleanly isolates a symmetry-protected sector, and analysis/otoc.py for information-scrambling probes. What is missing is the physical thermodynamic framing: entropy-production rates, irreversibility measures, heat dissipation signatures across the quantum Kuramoto transition — and how the DLA-parity constraint shapes them.

Standalone quantum-thermodynamics literature is mature on harmonic oscillators and simple qubit systems; heterogeneous Kuramoto order parameters on real hardware is a gap we are positioned to close.

Deliverables

  1. thermodynamics/ subpackage (new, per monolith rule — no single-file dump):
  2. entropy_production.py — Landi-Paternostro formalism for bipartite open-system entropy-production rate, applied to the two DLA parity sectors as the bipartition.
  3. irreversibility.py — Jarzynski / Crooks work-fluctuation estimators specialised for Kuramoto-XY quenches.
  4. heat_dissipation.py — scalar observable based on the Lindblad jump statistics already exposed by LindbladSyncEngine.
  5. Tests: multi-angle (deterministic reference at \(T = 0\), fluctuation identities at finite \(T\), DLA-sector invariance).
  6. Hardware demo at N = 4 on ibm_kingston: measure entropy production across the sync transition (\(K\)-sweep), using GUESS
  7. readout-baseline correction. Companion classical baseline from QuTiP Lindblad.
  8. Short paper: "Quantum thermodynamic signatures of synchronisation transitions on superconducting hardware". Target venue: PRX Quantum or npj Quantum Information.
  9. docs/quantum_thermo.md — theory note: derivation of the bipartite entropy-production rate on the heterogeneous Kuramoto-XY model, DLA-sector decomposition, experimental protocol.

Risks

  • Thermodynamic observables are notoriously noise-sensitive; hardware readout bias can mimic entropy-production signatures. Mitigation: GUESS plus a noise-free AerSimulator control run.
  • "Preprint would dominate citations" is a marketing claim, not a scientific one — the realistic framing is "fills a specific gap; expected to land on the lower rungs of the quantum-thermo citation tree".

Prerequisites

  • LindbladSyncEngine (already in repo).
  • GUESS ZNE (already in repo).
  • OTOC (already in repo).
  • Dedicated CEO / theorist time for the formalism derivation (the engineering port is trivial; the theory is not).

Acceptance

A reproducible hardware + classical pipeline that computes the entropy-production rate at five \(K\) values straddling the Kuramoto transition, with a classical reference within 2 \(\sigma\) of the hardware point. Paper draft circulated for internal review.

Falsification

  • New entry C13 in docs/falsification.md: "Entropy production rate peaks at the Kuramoto transition." Falsifier — no statistically significant peak above the classical baseline across the \(K\)-sweep.

S10 — Analog-native Kuramoto backends (Rydberg / neutral-atom / CV photonic)

Status 2026-05-20: first release gate landed as scpn-bench s10-analog-native-readiness. The gate publishes primitive accounting and no-submit provider-readiness artefacts for neutral-atom, Bloqade, and IBM Pulse export targets while keeping provider execution and analog-advantage claims blocked.

Motivation

Every Kuramoto / XY implementation in this repo today is digital- circuit based: K_nm and ω compile into sequences of RZZ / RX / CX gates, Trotterised. Analog-native platforms — Rydberg arrays, neutral-atom tweezers, continuous-variable photonic modes — are literally built out of interacting oscillators. A direct map from K_nm + ω to native Rydberg blockade / optical lattice / photonic coupling bypasses Trotter entirely and inherits hardware-native physics.

The post-NISQ simulation landscape (~2027–2030) is moving toward analog and hybrid-analog machines. Owning the software layer that compiles a Kuramoto coupling matrix directly onto a Rydberg / photonic simulator is a long-horizon positioning move.

Deliverables

  1. hardware/analog/ subpackage (new):
  2. rydberg.py — compile K_nm → Rydberg array geometry + detuning schedule. Integrate via QuEra Bloqade or pennylane-rydberg plugin.
  3. photonic.py — compile K_nm → CV-mode coupling schedule. Integrate via Xanadu Strawberry Fields / Bosonic-Qiskit / PennyLane default.gaussian.
  4. mapping.py — unit-conversion and topology-fitting helpers (not every K_nm is physically realisable on a fixed lattice; document which subset is).
  5. Three end-to-end demos:
  6. Rydberg simulator (Bloqade or equivalent): DLA parity asymmetry on a 6-atom chain at N = 6.
  7. CV photonic simulator: Kuramoto synchronisation with three modes, heterogeneous frequencies.
  8. Hybrid digital-analog: portion of the K_nm in Rydberg, the sync observables read via a digital Pauli readout.
  9. Pulse shaping via the existing scpn_quantum_engine hypergeometric pulse envelope — native to analog platforms.
  10. docs/analog_backends.md — operator manual: vendor SDK install instructions, per-platform caveats, the mapping trade-offs.

Risks

  • Vendor SDK access is non-trivial. QuEra Bloqade is open but requires a Julia runtime (our Julia tier helps). Xanadu Strawberry Fields is maintenance-mode since 2024; a more actively maintained photonic alternative may need identification.
  • "Analog is 10–100× more natural than anyone else's" is unfalsifiable as a marketing claim. The falsifiable version: on a fixed Kuramoto benchmark, the analog compilation uses fewer primitives (detunings / beam-splitters) than the digital Trotter at matched fidelity.
  • Post-NISQ adoption timeline for analog machines is a bet.

Prerequisites

  • Julia tier landed — helps with Bloqade integration.
  • PennyLane adapter (67-test cross-vendor suite in commit c3dcbf6) is the structural starting point.
  • Rust hypergeometric pulse engine (already shipped in v0.9.5).

Acceptance

DLA parity asymmetry reproduced on at least one analog platform at N ≥ 4 with a direction agreeing with the IBM digital-circuit baseline. Photonic CV demo shows order-parameter synchronisation with three heterogeneous-frequency modes. docs/analog_backends.md published.

Falsification

  • New entry C14 in docs/falsification.md: "Analog compilation of K_nm uses fewer primitive operations than the Trotter digital compilation at matched fidelity." Falsifier — digital Trotter hits a lower gate count at the same fidelity on the benchmark.

S11 — DLA-driven quantum sensing via sync order parameter

Status 2026-05-20: first release gate landed as scpn-bench s11-quantum-sensing-readiness. The gate publishes a no-submit QFI/classical-Fisher proxy scan and keeps hardware execution plus sensing-advantage claims blocked behind preregistration, shot budgeting, and raw-count uncertainty evidence.

Motivation

The sync order parameter R (global) and its DLA-protected fluctuations are a natural quantum sensor for external perturbations — noise, applied fields, parameter drifts. The project already has analysis/qfi_criticality.py (quantum Fisher information at the Kuramoto transition) plus the witness machinery in analysis/sync_witness.py. A small addition — quantify the metrological gain of the sync observable as a function of K near the transition, then demonstrate it on hardware — converts the synchronisation demo into a quantum-enhanced sensor.

Applied targets: EEG connectivity drift, power-grid spectral perturbations, tokamak plasma-mode drift.

Deliverables

  1. analysis/sensing.py (new):
  2. metrological_gain_vs_K(K_array, omega, perturbation) — returns \(F_Q(K)\) of R under a parametric perturbation, using the QFI tooling already in qfi_criticality.py.
  3. optimal_sensing_K(K_grid, omega, target) — finds the K value that maximises the QFI-per-shot for a given sensing target.
  4. Hardware demo at N = 4 on ibm_kingston: measure \(F_Q(K)\) at five \(K\) values; confirm the expected peak near the critical coupling.
  5. Application cross-overs (one each):
  6. Injected classical perturbation on an EEG PLV matrix — demonstrate detection above classical baseline.
  7. Injected topology perturbation on the Josephson array benchmark.
  8. docs/quantum_sensing.md — theory note tying QFI \(\to\) sync observable \(\to\) real-world sensing use case.

Risks

  • QFI estimation on hardware needs careful shot-budget management; classical shadows (shadow_tomography already in repo) may be required for statistical sensitivity.
  • "Quantum-enhanced for real-world oscillator networks" must not be over-claimed; the rigorous claim is "QFI gain above classical Fisher information on a pre-registered benchmark".

Prerequisites

  • analysis/qfi_criticality.py — already in repo.
  • analysis/sync_witness.py — already in repo.
  • analysis/shadow_tomography.py — already in repo.

Acceptance

Published figure: hardware-measured \(F_Q(K)\) vs. K with a peak-detection test that isolates the transition region to within \(\Delta K = 0.1\). Cross-over demo on at least one applied target (EEG or Josephson). Paper note added to the v1.0 release cycle.

Falsification

  • New entry C15 in docs/falsification.md: "QFI-based sync-order-parameter sensing beats classical Fisher information on a pre-registered perturbation benchmark." Falsifier — ratio of Fisher informations below 1 on the benchmark mean.

S12 — Automated quantum exploration of the full synchronisation phase diagram

Motivation

The sync phase diagram (K, \(\omega\) distribution, coupling topology) is vast. Classical explorations are either exhaustive on tiny N or mean-field on large N. A QPU-in-the-loop Bayesian optimiser, driven by signal-rich observables already in the repo (persistent homology \(p_{h1}\), Krylov complexity, OTOC scrambling speed), can prioritise "interesting" regions — chimera states, explosive-sync precursors, metastable basins — and only spend hardware shots where the classical reference has lost confidence.

This is the step from "simulator" to "discovery engine".

Deliverables

  1. discovery/ subpackage (new):
  2. bayes_explorer.py — Gaussian-process / scikit-optimize Bayesian optimiser over (K_scale, \(\omega\)-spread, topology-parameter) space.
  3. phase_scan.py — orchestrator that calls the Rust Hamiltonian builder for classical pre-screening, promotes high-interest points to the IBM queue, and streams results back to update the GP surrogate.
  4. interest_metrics.py — weighted combination of \(p_{h1}\), Krylov complexity, OTOC, spectral form factor, chimera index. Each contributor already exists.
  5. Hardware campaign: a 100-point phase-diagram scan on ibm_kingston (N = 4) prioritised by the Bayesian loop. Phase 2 IBM credits scope.
  6. Scientific deliverable: a published phase-diagram figure with at least one labelled "discovered" feature (a chimera, a metastable basin, an explosive-sync edge) not previously characterised on hardware for this coupling class.
  7. docs/discovery_engine.md — operator manual + reproducibility hooks.

Risks

  • GP surrogates scale poorly with dimensionality. Keep the search space low-D (≤ 4 free parameters) or use sparse GP approximations.
  • The Bayesian optimiser can collapse into an exploitation mode that never visits genuinely new regions; explicit diversity constraints needed.
  • IBM credits for a 100-point scan are substantial; budget confirmed before activation.

Prerequisites

  • Phase 2 IBM credits.
  • Persistent-homology module, Krylov complexity, OTOC, spectral form factor — all already in analysis/ (v0.9.1).
  • [rl] or [bayes] new extra with scikit-optimize or botorch.

Acceptance

At least one novel feature of the hardware-measured phase diagram (confirmed against the classical reference as a "QPU-first detection") is documented in the paper. Reproducer script runs end-to-end under ≤ 30 minutes of QPU time plus a classical budget ceiling.

Falsification

  • New entry C16 in docs/falsification.md: "The Bayesian discovery loop finds a feature not visible in the classical pre-screen at the same compute budget." Falsifier — every hardware-flagged feature is already present in the classical pre-screen.

S13 — Bosonic / continuous-variable quantum Kuramoto

Motivation

Companion to S10 but on the software-layer side. Every physical oscillator is natively a harmonic (or anharmonic) CV mode. Mapping Kuramoto directly to qumodes — without the qubit-encoding overhead — is the natural compilation for CV hardware (Xanadu photonic, IonQ's planned CV, trapped-ion motional modes). This is the digital/analog-bridge complement to S10: instead of picking a specific vendor, pick a mode-centric abstraction and compile into whichever CV backend is available.

Deliverables

  1. phase/cv_kuramoto.py — qumode-level solver that accepts the same K_nm + \(\omega\) API as QuantumKuramotoSolver but compiles to a CV-gate sequence (beam-splitter + squeezing + displacement) rather than RZZ / RX / CX.
  2. hardware/photonic.py (extends S10 if S10 lands first) — bridge to Strawberry Fields / Bosonic Qiskit for simulator execution.
  3. Rust-side CV pulse shaper: extend the hypergeometric engine to parametric-squeezing envelopes appropriate for CV drives.
  4. Conversion layer: map a measured qumode state back to a "standard" sync order parameter R so CV and qubit results can be compared apples-to-apples.
  5. Demo: sync transition at three heterogeneous-frequency qumodes, reproduced on a CV simulator with a fidelity target documented in the acceptance criterion.
  6. docs/cv_kuramoto.md — theory note explaining the qumode encoding, the mode-to-sync-observable conversion, and the trade-offs vs. digital qubit encoding.

Risks

  • CV hardware access is harder than superconducting QPU access; the demo may live on a simulator for the first release.
  • The CV state space is infinite-dimensional; truncating cleanly (Fock cutoff) without distorting the physics is a non-trivial parameter choice.
  • Bosonic Qiskit is a third-party fork with slower release cadence; upstream dependency on a potentially unmaintained package.

Prerequisites

  • S10 (analog backends) is a natural parent — do S10 first or in parallel.
  • Rust hypergeometric pulse engine — already shipped in v0.9.5.

Acceptance

A reproducible CV-simulator demo at N = 3 qumodes where the CV-computed order parameter agrees with the qubit-computed reference within 5 % over a K-sweep. Theory note published.

Falsification

  • New entry C17 in docs/falsification.md: "CV-encoded Kuramoto reproduces the qubit-encoded sync transition to within 5 %." Falsifier — mean absolute deviation > 5 % on the pre-registered K-sweep.

S14 — Hybrid quantum-classical forecasting engine

Motivation

The chronic pain point of classical Kuramoto is exponential cost in chaotic or high-dimensional regimes (brain connectomes, grid cascades, tokamak disruption dynamics). QPU-computed signals — OTOC scrambling rate, DLA invariants, partial sync snapshots — are exactly the quantities classical solvers cannot cheaply access. Feeding those as correction terms into a large-N classical Kuramoto solver (scpn-fusion-core, sc-neurocore) closes the prediction loop in the regime where pure classical solvers saturate.

The SNN / SSGF / ITER / EEG cross-repo bridges already exist in this codebase; S14 closes the prediction loop that those bridges have been waiting for.

Deliverables

  1. forecasting/ subpackage (new):
  2. quantum_corrections.py — extract OTOC + DLA invariants + partial R snapshots from a QPU run, packed into a CorrectionBundle dataclass.
  3. hybrid_solver.py — wrapper around the existing classical Kuramoto solver (scpn_quantum_control.hardware.classical. classical_kuramoto_reference) that injects the CorrectionBundle as additive forcing on the right-hand side. Coupling strength of the injection is a hyperparameter.
  4. forecast_validator.py — compares a hybrid trajectory against a held-out "ground truth" (a long classical run or a held-out measurement).
  5. Three applied demos:
  6. Brain-connectome: use the EEG PLV adapter already in applications/eeg_benchmark.py; show the hybrid forecast beats pure classical on a held-out trajectory from the available EEG dataset.
  7. ITER: use the applications/iter_benchmark.py stub; compare hybrid forecast on an 8-mode tokamak proxy.
  8. Power grid: applications/power_grid.py IEEE-5-bus with a contrived chaotic regime.
  9. docs/hybrid_forecasting.md — theory note on where quantum corrections help (chaotic / high-dim) vs. where they do not (near-integrable / small-N).

Risks

  • "Hybrid beats classical" is a non-trivial claim and needs honest falsification: classical can be made to win by tuning the correction weight to zero. The benchmark must fix the hyperparameter across all runs and not post-hoc optimise.
  • The three applied targets each carry their own data quality risk (EEG ground-truth is noisy; IEEE-5-bus is a toy; ITER data is partially synthetic).

Prerequisites

  • OTOC + DLA modules already in analysis/.
  • hardware/classical.py Kuramoto reference — already in repo.
  • Cross-repo bridges (sc-neurocore, scpn-fusion-core, scpn-phase-orchestrator) already exist in src/scpn_quantum_control/bridge/.

Acceptance

On a pre-registered benchmark set of chaotic Kuramoto trajectories, the hybrid forecast achieves ≥ 15 % lower mean-squared-error over a held-out window than the pure classical forecast, at matched compute budget, on ≥ 2 of the 3 applied targets. Zenodo deposit of the benchmark.

Falsification

  • New entry C18 in docs/falsification.md: "Hybrid quantum-classical forecast beats pure classical on chaotic Kuramoto trajectories at matched compute budget." Falsifier — hybrid underperforms pure classical on ≥ 2 of the 3 pre- registered benchmarks.

S15 — DLA-protected many-body scars for long-lived synchronisation

Motivation

Quantum many-body scars — non-thermalising eigenstates embedded in an otherwise chaotic spectrum — have been studied on Rydberg arrays and spin chains but never tied to heterogeneous Kuramoto synchronisation. The DLA parity structure of the XY Hamiltonian is a natural candidate for scar-supporting symmetry: the two sectors decouple under unitary evolution, and any eigenstate supported entirely on one sector is protected from thermalising into the other. Using the Rust engine to pre-compute scar-preserving drives and inject them as mid-circuit corrections is the obvious implementation path.

Deliverables

  1. analysis/many_body_scars.py — numerical identification of DLA-sector-supported eigenstates for N ≤ 8 via the existing build_xy_generators output; classification by overlap with thermal ensemble.
  2. Scar-preserving drive library: scpn_quantum_engine helper that, given a target scar state, computes a sequence of mid-circuit rotations that project the instantaneous state back onto the scar subspace.
  3. Hardware demo on ibm_kingston at N = 4: show that the scar-preserved trajectory maintains \(R \geq R_*\) for ≥ 2× the depth at which the open-loop Trotter crashes into the coherence wall.
  4. Cross-check against thermal ETH prediction — scar state eigenvalue statistics should be Poisson while the rest of the spectrum is Wigner-Dyson.
  5. docs/scars_sync.md — theory note plus operator manual.

Risks

  • Scar construction from a partial DLA (when the DLA is not a full representation of a simple Lie algebra) may not admit clean analytical scars — the numerical search returns approximate scars with finite lifetime.
  • Heterogeneous \(\omega_i\) breaks the symmetries that typically protect scars in homogeneous spin chains; DLA-based protection must be proven (not assumed) to survive the heterogeneity.

Prerequisites

  • DLA machinery in analysis/dynamical_lie_algebra.py — already in repo.
  • Rust drive-shaping in pulse_shaping.rs — already in repo.
  • Theorist pass on the DLA-partial-scar construction (1 week analytical work before engineering starts).

Acceptance

Scar-preserved sync trajectory on hardware demonstrates a documented coherence-lifetime extension over the open-loop baseline on a pre-registered N = 4 benchmark. Paper note + raw data to Zenodo.

Falsification

  • New entry C19 in docs/falsification.md: "A DLA-sector- supported scar subspace exhibits longer sync lifetime than generic eigenstates at matched fidelity." Falsifier — no statistically significant lifetime advantage over a dimension-matched random eigenstate on the benchmark.

S16 — Quantum network tomography (reconstruct hidden K_nm from observables)

Motivation

Classical network reconstruction — inferring a coupling matrix from time-series data of oscillator phases — is mature. Its quantum-enhanced analogue exists only as tiny-N theory. The project's witnesses + OTOC + DLA structure provide a richer observable set than classical phase-only data; feeding this into a differentiable Rust forward model enables end-to-end inverse inference of an unknown K_nm matrix and \(\omega\) vector from hardware-measured observations of the oscillator network.

Deliverables

  1. analysis/network_tomography.py:
  2. reconstruct_knm(witnesses, otocs, order_params, n_osc) — inverse-problem solver over the coupling matrix.
  3. reconstruct_frequencies(spectra, witnesses) — recovery of \(\omega\) from the measured observables.
  4. Differentiable Rust forward model — scpn_quantum_engine extension that backpropagates a loss from the observable space through the Trotter dynamics to K_nm parameters.
  5. Applied demos:
  6. EEG PLV matrix → inferred K_nm, compared against the published connectivity prior.
  7. IEEE 5-bus power grid → inferred K_nm from sync observables at the three grid buses.
  8. Regularisation study: L1 sparsity, low-rank, and topology-informed priors.
  9. docs/quantum_tomography.md — theory note + operator manual.

Risks

  • Identifiability: many K matrices produce the same macroscopic sync observables. Regularisation is not optional.
  • Classical network reconstruction is a well-understood hard problem; the quantum advantage must be measurable (better reconstruction error, lower data requirements, or broader applicability) — not assumed.

Prerequisites

  • Witnesses, OTOC, order-param machinery — already in repo.
  • scpn_quantum_engine differentiable extension (new work ~2 weeks inside the Rust crate).
  • Benchmark ground-truth datasets (EEG, IEEE-5, a synthetic graph corpus).

Acceptance

On a pre-registered benchmark of 50 synthetic graphs (N = 8, varying sparsity), quantum-assisted tomography recovers K with < 10 % mean absolute error at shot budgets where the classical baseline exceeds 20 %. One applied demo (EEG or IEEE-5) documented with the reconstruction error vs. the published reference.

Falsification

  • New entry C20 in docs/falsification.md: "Quantum-assisted tomography recovers K_nm to below 10 % MAE vs. classical baseline at matched data / shot budget." Falsifier — ≥ 10 % MAE gap in favour of the classical baseline on the benchmark.

S17 — Higher-order (simplicial / hypergraph) quantum Kuramoto

Motivation

Classical Kuramoto has been generalised to include explicit triplet, quadruplet, and higher-order couplings (2024–2025 literature on simplicial Kuramoto; Lucas et al., Battiston et al.). No quantum hardware realisation has been reported. Extending the K_nm mapper to ingest a hypergraph (or simplicial complex) and compile triplet interactions to multi-qubit Trotter gates — plus pulse-shaped multi-qubit drives on future Heron / Loon chips — opens access to systems with genuine multi-way interactions: social contagion, chemical reaction networks, multi-body plasma modes.

Deliverables

  1. bridge/higher_order_mapper.py — hypergraph / simplicial-tensor ingestion producing a Qiskit circuit with explicit three- and four-body Trotter terms.
  2. Native multi-qubit gate exploration — for backends that expose them (future Heron / Loon), use the native gate instead of Trotter-decomposed CXs.
  3. Rust-side hypergraph coupling tensor: efficient storage + Trotter-term enumeration.
  4. Hardware demo at N = 6 with two triplet couplings: confirm the sync transition occurs at a shifted \(K_c^{(3)} \neq K_c^{(2)}\) predicted by classical higher-order Kuramoto.
  5. docs/higher_order_kuramoto.md — theory + operator manual.

Risks

  • Multi-qubit gate decomposition cost grows combinatorially; a dense triplet coupling on 6 qubits may exceed the coherence budget for Trotter-depth ≥ 4.
  • Hypergraph-native gates are hardware-specific; portability across vendors is limited.

Prerequisites

  • Classical higher-order Kuramoto mapper (extension of knm_hamiltonian.py — roughly 2 weeks).
  • Hardware availability of multi-qubit gates, or acceptance of Trotter decomposition cost on current Heron r2.

Acceptance

Measurable \(K_c\) shift from pairwise to three-body couplings on hardware at N = 6, matching the classical higher-order prediction within 15 % on a pre-registered benchmark.

Falsification

  • New entry C21 in docs/falsification.md: "Higher-order sync transition distinguishable from pairwise baseline on hardware at N = 6." Falsifier — measured \(K_c\) shift within statistical uncertainty of zero.

S18 — Synchronisation-protected quantum memories and repeaters

Motivation

A globally synchronised phase subspace is approximately eigen-decoupled from the rest of the Hilbert space under the sync-protected dynamics — a natural error-suppressing subspace. Encoding logical qubits into this manifold and using DLA parity witnesses as syndrome measurements would extract bit-flip / phase-flip errors without breaking the sync. The sync-protected logical qubit is a candidate primitive for distributed clock networks, quantum internet repeater nodes, and fault-tolerant sensor arrays.

Deliverables

  1. qec/sync_memory.py:
  2. SyncLogicalQubit dataclass and constructor that encodes a target logical state into the sync manifold.
  3. Syndrome measurement primitive using sync_witness.py observables as the parity check.
  4. Error-correction cycle: detect → classical decision → apply corrective drive.
  5. Hardware demo at N = 4: logical qubit encoded in the sync manifold shows documented coherence-time extension vs. a single-qubit reference stored in the same hardware class.
  6. Theoretical analysis: proof (or refutation) that the sync manifold satisfies the approximate stabiliser-code conditions.
  7. docs/sync_memory.md — theory + protocol.

Risks

  • The sync manifold is a continuous subspace; mapping discrete error syndromes onto it requires care. A formal analysis may conclude that the error suppression does not scale — still a publishable negative result.
  • Coherence-time gain on hardware may be dominated by the drive overhead, not the manifold protection. Need matched-budget comparison.

Prerequisites

  • Witnesses + DLA parity framework — already in repo.
  • qec/ scaffolding — already in repo.
  • Theorist pass on the "is-the-sync-manifold-a-stabiliser-code" question.

Acceptance

Logical qubit encoded in the sync manifold demonstrates coherence extension on a pre-registered benchmark (ratio of logical lifetime to unprotected lifetime ≥ documented threshold, e.g. 1.5× at N = 4, Heron r2). Clean positive or clean negative result publishable.

Falsification

  • New entry C22 in docs/falsification.md: "Sync-manifold logical qubit outlives a dimension-matched unprotected qubit in hardware." Falsifier — coherence-lifetime ratio ≤ 1.0 on the benchmark.

S19 — Entanglement phase diagram + magic + Krylov complexity

Motivation

The project already ships magic_sre.py (stabiliser Rényi entropy), krylov_complexity.py, entanglement_entropy.py, entanglement_spectrum.py, and the OTOC machinery. What is missing is the combined phase diagram: a single scan of these measures across (K, \(\omega\)-spread, topology) producing a publishable reference dataset for the quantum-chaos / collective-phenomena community. This is a modest engineering lift with outsized documentation value.

Deliverables

  1. analysis/entanglement_phase_diagram.py — scan orchestrator that, given a parameter grid, computes:
  2. Multipartite entanglement (negativity, fidelity-based).
  3. Stabiliser Rényi entropy (magic).
  4. Krylov complexity.
  5. OTOC scrambling rate.
  6. Spectral form factor. For each (K, \(\omega\)-spread, topology) point.
  7. Published dataset: hardware-measured values at N = 4 across a 10 × 10 parameter grid, Zenodo DOI.
  8. Reference figure: four-panel phase diagram suitable for a publication.
  9. docs/entanglement_phase_diagram.md + paper note.

Risks

  • Multipartite entanglement estimators on hardware are shot-hungry; the 10 × 10 grid at N = 4 needs careful shot budgeting.
  • The "reference dataset" framing only works if the dataset is published in a citable form (Zenodo + paper note).

Prerequisites

  • All five component modules — already in repo.
  • Phase 2 IBM credits for the hardware column at usable statistics.

Acceptance

Published figure + Zenodo deposit of the four-panel phase diagram. Paper note fits into the v1.0 release cycle.

Falsification

  • New entry C23 in docs/falsification.md: "Entanglement + magic + Krylov complexity show a coherent transition signature at \(K_c\) consistent across all four measures." Falsifier — transition signatures diverge in location by > 20 % of the measurement range across measures.

S20 — Quantum Kuramoto universal control-benchmark suite (MLPerf-style)

Motivation

Optimal quantum-control libraries exist (Qutip's qtrl, GrapeQuantum, etc.) but none define a standardised, hardware- validated complex-systems benchmark. Shipping a "control challenge" harness where users submit arbitrary pulse / ansatz / feedback strategies and the Rust-accelerated simulator + IBM hardware runner scores them on sync quality, resource cost, noise robustness, and DLA expressivity — with a public leaderboard and reproducible submission manifest — creates a MLPerf-style community asset.

Deliverables

  1. benchmark_suite/ subpackage:
  2. submission.py — schema for user submissions (JSON manifest specifying pulse / ansatz / feedback strategy).
  3. scorer.py — five-axis scoring: sync fidelity, resource count, noise robustness, DLA sector expressivity, wall time.
  4. leaderboard.py — CSV / JSON leaderboard with SHA-256 submission IDs.
  5. Public submission UI: GitHub Actions workflow that accepts a PR opening a new submission, scores it on a fixed classical simulator, and — optionally — promotes it to a scheduled hardware run when the CEO approves.
  6. Reference submissions: Trotter baseline, ADAPT-VQE, GUESS-mitigated Trotter, adaptive-branching (S8). Each scored on every axis.
  7. docs/benchmark_challenge.md — operator manual for submitters.
  8. Kickoff visibility: announcement on the @qiskit Slack / Unitary Foundation Discord / r/QuantumComputing (copy already drafted in .coordination/launch_copy/).

Risks

  • Community adoption is not automatic. The MLPerf comparison is aspirational — MLPerf has consortium backing. A small-scale version is achievable; consortium scale is not.
  • Hardware cost for promoting submissions to real QPUs needs a defined budget cap per submitter.

Prerequisites

  • scpn_quantum_engine — already in repo.
  • HardwareRunner — already in repo.
  • S5 harness (open-data + validation) is a natural predecessor — activate S5 first so S20 can reuse the data-loading APIs.

Acceptance

Leaderboard live, ≥ 4 reference submissions scored, first three external submissions merged within 6 months of kickoff. Note: infrastructure track — no scientific claim, therefore no falsifier.

S21 — Multi-scale quantum → classical bridging layer

Motivation

The macroscopic dynamics of a large-N Kuramoto system are classical (fluid-limit or mean-field); the microscopic dynamics of an N = 4…20 quantum system are exactly computed. A QPU-computed "effective K_{ij}" and "effective \(\omega\) distribution" — derived from DLA invariants and hardware-measured fluctuation spectra — can inject quantum corrections into the classical large-N solver at the coarse-grained scale where classical solvers saturate. This is the formal version of the hybrid forecasting engine in S14, generalised to multi-scale systems (brain connectome → neuron dynamics; power grid → per-bus oscillator; tokamak → MHD mode spectrum).

Deliverables

  1. bridge/coarse_graining.py:
  2. effective_K_from_quantum(quantum_observables) — extract renormalised couplings from DLA invariants + fluctuation spectra.
  3. effective_omega_from_quantum(spectra) — recover the effective frequency distribution.
  4. classical_large_N_hybrid(quantum_effective, classical_solver) — inject the quantum-derived effective parameters into the classical solver.
  5. Integration with sc-neurocore and scpn-fusion-core (bridges already exist).
  6. Three applied demos:
  7. Brain-scale (100+ node EEG network) with quantum corrections at the N = 4 microscale.
  8. Grid-scale (IEEE-118 or larger) with quantum corrections at bus-cluster level.
  9. Tokamak-scale MHD mode spectrum (ITER benchmark stub).
  10. docs/multi_scale_bridging.md — theory + protocol.

Risks

  • The coarse-graining operator is not unique; the choice must be benchmarked against analytical mean-field predictions to avoid post-hoc fitting.
  • "Everyone does either pure quantum or pure classical; zero hybrid" is an over-claim. Hybrid RG methods exist (classical); the novelty is injecting real-hardware quantum corrections, not the concept of multi-scale hybrid simulation itself.

Prerequisites

  • DLA invariants, witness machinery, bridges — all in repo.
  • Large-N classical Kuramoto solver — available via scpn-fusion-core.

Acceptance

On a pre-registered benchmark of brain-scale or grid-scale Kuramoto, the multi-scale hybrid beats the pure-classical solver at matched compute budget by ≥ 10 % on a forecasting mean-squared-error metric.

Falsification

  • New entry C24 in docs/falsification.md: "Quantum-corrected multi-scale solver beats pure classical at matched budget on brain-scale or grid-scale Kuramoto." Falsifier — pure classical ties or wins on the benchmark.

S22 — Non-Hermitian / PT-symmetric quantum Kuramoto + exceptional points

Motivation

PT-symmetric quantum sync exists in toy theoretical models (2025–2026 on spin oscillators). No hardware realisation is DLA-protected. Extending LindbladSyncEngine with balanced gain-loss jumps — or auxiliary-qubit dilation of a non-Hermitian Hamiltonian onto a unitary circuit — opens access to exceptional-point phenomena on superconducting hardware. Near an exceptional point, small perturbations produce disproportionately large response — the basis for exceptional-point-enhanced sensing.

Deliverables

  1. phase/non_hermitian_kuramoto.py:
  2. Balanced-gain-loss extension of the XY Hamiltonian.
  3. EP-locator: sweeps the gain / loss parameter and detects eigenvalue coalescence.
  4. Drive scheduler: Rust hypergeometric pulse envelope that steers the system across an EP.
  5. Auxiliary-qubit dilation primitive: convert a non-Hermitian evolution to a unitary extended-Hilbert-space evolution for execution on a standard QPU.
  6. Hardware demo at N = 4 + 2 ancillae: measure the sync order parameter across an EP, compare against the Hermitian baseline.
  7. Sensing demo: EP-enhanced detection of a weak applied signal.
  8. docs/non_hermitian_kuramoto.md — theory + protocol.

Risks

  • Dilation doubles the required qubit count; N = 4 physics needs 6 hardware qubits.
  • EP sensitivity amplifies noise along with signal — net metrological gain is not automatic.

Prerequisites

  • LindbladSyncEngine — already in repo.
  • Rust pulse engine — already in repo.
  • Dilation primitive (new ~2 weeks).

Acceptance

EP-enhanced signal-to-noise on a pre-registered weak-signal benchmark exceeds the Hermitian baseline by a documented factor.

Falsification

  • New entry C25 in docs/falsification.md: "Sensitivity enhancement near an engineered exceptional point exceeds the Hermitian baseline on the pre-registered benchmark." Falsifier — SNR ratio ≤ 1.0 on the benchmark.

S23 — Quantum reservoir computing powered by Kuramoto transients

Motivation

Quantum reservoir computing (QRC) is emerging. The transient dynamics of a quantum Kuramoto system (pre-sync evolution, chimera states, OTOC scrambling) are natively high-dimensional and nonlinear — the criteria for a useful reservoir. Reading out DLA parity + sync witnesses on hardware and training a classical linear layer on top is a minimal-engineering addition that positions the project as a hardware-evidence-gated quantum reservoir for oscillator-based forecasting.

Deliverables

  1. qrc/kuramoto_reservoir.py (new):
  2. KuramotoReservoir class that runs a pre-configured transient evolution and emits a feature vector of observables.
  3. Training loop: ridge regression / linear classifier on top of the feature vectors.
  4. Standard QRC benchmarks:
  5. NARMA-10 nonlinear time-series prediction.
  6. Mackey-Glass chaotic prediction.
  7. MNIST-like pattern classification (scaled-down).
  8. Hardware demo on ibm_kingston at N = 4.
  9. Comparison vs. classical echo state network baseline at matched feature dimension.
  10. docs/quantum_reservoir.md — protocol + results.

Risks

  • Reservoir performance depends sensitively on hardware coherence; a reservoir that works on the simulator may fail on noisy hardware.
  • Classical echo state networks are extremely efficient; beating them on the same task is a high bar.

Prerequisites

  • qrc_phase_detector.py — already in repo (v0.9.1).
  • OTOC + witnesses — already in repo.
  • Benchmark harness (S5 is a natural prerequisite).

Acceptance

Kuramoto reservoir matches or exceeds the classical echo state network on at least one pre-registered benchmark at matched feature dimension.

Falsification

  • New entry C26 in docs/falsification.md: "Quantum Kuramoto reservoir beats classical echo state network on a pre-registered time-series benchmark." Falsifier — reservoir underperforms by ≥ 10 % in MSE or accuracy on the benchmark.

S24 — Quantum speed limits for collective synchronisation

Motivation

Quantum speed limits (QSL) — Mandelstam–Tamm, Margolus–Levitin — are well-characterised for single-qubit gates. The collective-sync extension combines: DLA dimension as the effective Hilbert-space dimension, OTOC growth rate as the proxy for the Hamiltonian norm entering the QSL, and the hardware-measurable sync observable as the target state. The project already has analysis/quantum_speed_limit.py (v0.9.1); extending it to collective observables and measuring the saturation on hardware provides the first experimental QSL certificate for a many-body-collective-phenomenon target.

Deliverables

  1. Extension of analysis/quantum_speed_limit.py:
  2. collective_qsl(K, omega, target_R) — compute the theoretical Mandelstam–Tamm and Margolus–Levitin bounds for reaching a target global sync R.
  3. DLA-constrained tightening: use the DLA dimension to constrain the effective evolution space.
  4. Hardware measurement: sweep K values; record actual time to reach target \(R_*\); compare against the theoretical bound.
  5. Published figure: theoretical QSL curve vs. measured time across K.
  6. docs/collective_qsl.md — theory + protocol.

Risks

  • The QSL bound loosens when the observable is global rather than single-qubit; the tightest bound for collective R may be hard to achieve on hardware within the coherence budget.
  • OTOC-based norm proxy may not be tight for the particular Hamiltonian class; alternative Hamiltonian-norm estimators may be needed.

Prerequisites

  • quantum_speed_limit.py — already in repo.
  • DLA dimension calculator — already in repo.
  • OTOC — already in repo.

Acceptance

Published figure showing the hardware-measured time-to-sync saturating the DLA-constrained QSL within a pre-registered fraction (e.g. within 20 % of the theoretical bound).

Falsification

  • New entry C27 in docs/falsification.md: "Hardware-measured time-to-sync saturates the DLA-constrained QSL within 20 %." Falsifier — consistent gap > 20 % on the pre-registered benchmark, implying either a loose bound or an over-cautious hardware drive schedule.

S25 — Topological defects + vortex dynamics on 2D quantum oscillator lattices

Motivation

Classical Kuramoto on a 2D lattice supports phase vortices; their creation, annihilation, and motion underpin defect-mediated phase transitions and the Kosterlitz–Thouless universality class. The project's gauge/vortex_detector.py and gauge/wilson_loop.py modules implement the detection primitives. What is missing: extend the mapper to a 2D lattice topology, engineer vortex creation via targeted drives, track their motion, and read out the winding number on hardware.

Deliverables

  1. Extension of bridge/knm_hamiltonian.py — 2D lattice topology ingestion with explicit nearest-neighbour K_nm.
  2. phase/vortex_dynamics.py:
  3. create_vortex_pair(position_a, position_b, strength) — compile a drive that nucleates a ± vortex pair at the specified positions.
  4. annihilate_vortex(position) — corresponding annihilation primitive.
  5. track_vortex_motion(readout_series) — extract vortex trajectories from spatially resolved sync witnesses.
  6. Hardware demo on a 4 × 4 patch of ibm_kingston (16 qubits, within the connectivity envelope of Heron r2): create a vortex pair, observe its motion under Kuramoto dynamics, annihilate.
  7. docs/quantum_vortex_dynamics.md — theory + protocol.

Risks

  • 16-qubit 2D-lattice dynamics exceed the coherence budget on Heron r2 for non-trivial Trotter depths. A scaled-down 3 × 3 patch may be the realistic target.
  • Spatial resolution of the vortex core requires partial-state tomography of each local region; shot budget is substantial.

Prerequisites

  • vortex_detector.py, wilson_loop.py, universality.py — already in repo.
  • 2D-lattice-topology K_nm builder (extension).

Acceptance

Vortex pair creation and annihilation reproduced on hardware at matched topological charge. Winding-number measurement on a hardware-generated vortex agrees with the theoretical prediction within the measurement uncertainty.

Falsification

  • New entry C28 in docs/falsification.md: "Vortex pair creation and annihilation reproducible on hardware at matched topological charge." Falsifier — winding-number measurement inconsistent with the theoretical charge by more than 1 σ on the benchmark.

S26 — Entanglement-mediated long-range synchronisation

Motivation

Entanglement (Bell pairs, GHZ states, virtual couplings) as a resource for distributing information across a quantum processor is well-characterised. Its use as a sync-enhancement resource on heterogeneous Kuramoto networks is not. Pre-sharing Bell pairs between distant oscillator subsets and quantifying the boost in \(R_{global}\) vs. the unentangled baseline closes a gap between the quantum-networks and the quantum-sync literatures.

Deliverables

  1. phase/entanglement_mediated_sync.py:
  2. prepare_entangled_subsets(subset_pairs) — Bell / GHZ preparation across the specified qubit pairs or groups.
  3. evolve_with_entanglement(K, omega, entanglement_config) — evolve the full system with the entangled subsets in place.
  4. Topology-constrained hardware demo: Bell pairs across the diagonal of a heavy-hex patch, then Kuramoto evolution.
  5. Quantitative metric: entanglement-boost factor \(\Delta R / R_*\) vs. the classically coupled baseline.
  6. docs/entanglement_mediated_sync.md — protocol + results.

Risks

  • Superconducting topology limits where Bell pairs can be placed (all-to-all entanglement across distant qubits requires SWAP overhead that erodes the measured boost).
  • Bell-pair infidelity on hardware may dominate the entanglement-mediated boost.

Prerequisites

  • Bell-pair preparation primitive — already in repo (crypto/bell_test).
  • Heron r2 topology map (documented).

Acceptance

Entanglement-mediated sync shows documented gain over the unentangled classical baseline on a pre-registered hardware topology.

Falsification

  • New entry C29 in docs/falsification.md: "Entanglement- mediated sync exceeds the unentangled-classical baseline on the pre-registered hardware topology." Falsifier — gain within statistical uncertainty of zero.

S27 — Hardware-in-the-loop inverse design of oscillator networks

Motivation

The forward compilation "K_nm → circuit → hardware → observables" is common. The inverse — "target sync pattern → discover K_nm and \(\omega\) that realise it on hardware" — requires a closed hardware-in-the-loop optimisation. VQE + Rust-accelerated forward mapper + QPU feedback is the natural architecture. Practical targets: maximal chimera stability, robustness against a specific noise model, reproduction of a biological sync pattern observed in EEG.

Deliverables

  1. control/inverse_design.py:
  2. inverse_design_knm(target_pattern, n_osc, objective) — closed-loop optimiser. Accepts a target sync pattern and an objective function; returns optimised K_nm and \(\omega\).
  3. Uses scpn_quantum_engine for fast classical pre-screening; promotes only the top-K candidates to hardware.
  4. Three applied demos:
  5. Chimera-target: discover K_nm that stably hosts a pre-specified chimera configuration at N = 4.
  6. EEG-target: reproduce a sync pattern observed in an EEG recording on the hardware.
  7. Noise-robust target: maximise \(R_{global}\) stability under a pre-specified Pauli noise model.
  8. docs/inverse_design.md — protocol + results.

Risks

  • Hardware-in-the-loop optimisation is expensive in QPU time; the classical pre-screening must aggressively prune candidates.
  • The objective landscape may be non-convex; expect many local optima and document convergence statistics.

Prerequisites

  • S1 (feedback loop plumbing) — activate first; S27 reuses the same observer architecture.
  • scpn_quantum_engine — already in repo.
  • VQE — already in repo.

Acceptance

Inverse-designed K_nm reproduces the target sync pattern on hardware within a pre-registered tolerance on at least two of the three applied targets.

Falsification

  • New entry C30 in docs/falsification.md: "Inverse design reproduces a pre-registered target sync pattern on hardware within documented tolerance." Falsifier — fails to converge on ≥ 2 of 3 targets within the QPU budget.

S28 — Synchronisation-enhanced distributed quantum metrology

Motivation

Quantum metrology achieves Heisenberg-limited sensing by using entangled probe states. The synchronisation transition itself generates entanglement — a finding already in the repo's analysis/qfi_criticality.py + entanglement_sync.py. Deploying multiple synchronised oscillator subsets as a quantum sensor array, with DLA-parity-protected readout, converts the sync transition from a physics demo into a distributed sensing primitive for applications where the target signal perturbs the coupling matrix (global magnetic-field gradients, climate-scale oscillator networks, biological rhythms).

Deliverables

  1. sensing/distributed_sync_sensor.py:
  2. SensorArray dataclass — M synchronised subsets each of size n_sub = N / M; readout observables DLA-protected.
  3. estimate_parameter(measurements, prior) — maximum- likelihood estimator over the hypothesis.
  4. Hardware demo at N = 8 with M = 2 subsets: detect an applied single-qubit phase perturbation below the single-subset classical Fisher limit.
  5. Scaling analysis: simulate the expected Heisenberg-limited scaling vs. M and compare against the single-subset limit.
  6. docs/distributed_sync_sensing.md — theory + protocol.

Risks

  • Heisenberg scaling requires entanglement coherence time longer than the sensing integration time. Heron r2 coherence budget caps the usable integration window; the hardware demo may show a fraction of the theoretical scaling.
  • "Heisenberg-limited on global magnetic fields / biological rhythms" is an applied claim that needs a specific application-target to be published.

Prerequisites

  • QFI + entanglement-sync modules — already in repo.
  • Multi-subset array topology design on Heron r2.

Acceptance

Distributed sync sensor achieves super-classical Fisher information on a pre-registered sensing target.

Falsification

  • New entry C31 in docs/falsification.md: "Distributed sync sensor achieves super-classical Fisher information on the pre-registered target." Falsifier — Fisher-information ratio ≤ 1.0 on the benchmark.

S29 — Floquet quantum Kuramoto for discrete time-crystalline order

Motivation

Floquet time crystals — subharmonic response under periodic drive — have been realised on homogeneous spin chains. Heterogeneous Kuramoto oscillators with DLA parity have not been tested as a time-crystalline platform. The project already ships phase/floquet_kuramoto.py (v0.9.1); the differentiation is explicit tracking of how the DLA parity protects subharmonic response across the sync transition on hardware, and how drive shaping via the Rust hypergeometric engine extends the time- crystalline lifetime.

Deliverables

  1. Extension of phase/floquet_kuramoto.py:
  2. subharmonic_response(drive_period, observable) — measure the expected period-2T response signature.
  3. dla_protected_drive(K, target_subharmonic) — Rust- engineered drive schedule that preserves the DLA sector.
  4. Hardware demo at N = 4: measure the subharmonic response vs. drive frequency across the sync transition.
  5. Lifetime benchmark: compare DLA-protected drive schedule vs. naive drive on time-crystalline stability.
  6. docs/floquet_kuramoto.md — theory + protocol (extends existing documentation).

Risks

  • Heterogeneity breaks the symmetry that typically protects Floquet time crystals; the DLA protection must be proven to survive.
  • Hardware coherence on Heron r2 may be insufficient to distinguish a short-lived time crystal from a trivial subharmonic echo.

Prerequisites

  • floquet_kuramoto.py — already in repo.
  • Rust hypergeometric pulse engine — already in repo.

Acceptance

Subharmonic response survives the DLA-protected drive schedule at a pre-registered heterogeneity threshold, on hardware.

Falsification

  • New entry C32 in docs/falsification.md: "Subharmonic response survives DLA-protected drive schedule at heterogeneity beyond a pre-registered threshold." Falsifier — response decays on the same timescale as the naive-drive baseline.

S30 — Quantum Kuramoto for community detection and modularity optimisation

Motivation

Classical community detection (Louvain, Infomap, spectral methods) is mature. Mapping network modularity into the quantum sync landscape — where each community corresponds to a locally synchronised cluster — allows the QPU to discover partitions that classical algorithms miss in chaotic or high-dimensional graphs. The DLA-invariant structure of the XY Hamiltonian provides a natural regulariser.

Deliverables

  1. applications/community_detection.py:
  2. partition_via_sync(graph, n_quantum_qubits) — quantum community detection using a VQE-minimised modularity objective over a hardware-compatible sub-graph.
  3. Rust-accelerated modularity evaluation for large classical graphs.
  4. Benchmarks on standard graph corpora:
  5. Zachary's Karate Club.
  6. LFR (Lancichinetti-Fortunato-Radicchi) benchmark at sizes compatible with hardware limits.
  7. Random geometric graphs.
  8. Comparison vs. Louvain and Leiden at matched graph size.
  9. docs/quantum_community_detection.md — protocol + results.

Risks

  • Quantum hardware size (N ≤ 20) limits community-detection problems to toy graphs; the "at scale" framing overclaims unless restricted to small hard instances.
  • Modularity landscape on the QPU may not be meaningfully different from the classical one for the graph sizes accessible today.

Prerequisites

  • Witnesses + DLA invariants — already in repo.
  • Graph-benchmark corpus (open-source datasets).

Acceptance

Quantum-discovered community partition matches or exceeds Louvain on a pre-registered hard instance (low signal-to-noise LFR benchmark).

Falsification

  • New entry C33 in docs/falsification.md: "Quantum community detection beats Louvain on a pre-registered hard LFR instance." Falsifier — Louvain wins on the hard instance at matched compute budget.

S31 — DLA-protected many-body localisation / delocalisation transitions

Motivation

Many-body localisation (MBL) is a mature quantum-chaos research area; no connection has been made to heterogeneous Kuramoto sync or DLA-protected collective phenomena. Engineering disorder in \(\omega\) and coupling topology drives a localisation transition; mapping the mobility edge via DLA parity + OTOC tools and quantifying how global sync survives localisation is the deliverable.

Deliverables

  1. analysis/mbl_sync.py:
  2. disorder_sweep(omega_std, K_grid) — disorder-driven localisation sweep.
  3. mobility_edge_detector(spectra, otoc) — locate the localisation-delocalisation transition.
  4. sync_survival_under_localisation(disorder, K) — quantify how \(R_{global}\) survives below and above the mobility edge.
  5. Hardware demo at N = 4 — 6: map a coarse mobility-edge phase diagram on ibm_kingston.
  6. Classical reference: compare against exact-diagonalisation of the same disorder realisations at N = 4 — 6.
  7. docs/mbl_sync.md — theory + protocol.

Risks

  • MBL classification is statistically demanding; hundreds of disorder realisations per point on the phase diagram may be needed. The QPU budget constrains what is achievable.
  • Whether DLA parity really protects collective sync across the mobility edge is an open question; the result may be a publishable negative.

Prerequisites

  • DLA + OTOC — already in repo.
  • Disorder-sweep harness (extension).

Acceptance

Mobility edge detectable via DLA parity + OTOC on a pre-registered disorder model; phase diagram published.

Falsification

  • New entry C34 in docs/falsification.md: "Mobility edge detectable on hardware via DLA parity + OTOC on a pre-registered disorder model." Falsifier — no mobility edge signature above statistical noise on the phase diagram.

S32 — Monitored quantum Kuramoto (measurement-induced transitions)

Motivation

Measurement-induced phase transitions (MIPT) are an emerging sub-field of quantum dynamics. Weak or projective measurement on subsets of the system, combined with unitary evolution, gives rise to entanglement phase transitions (volume-law to area-law) as the measurement rate varies. Applying this to oscillator networks with DLA witnesses and heterogeneous Kuramoto dynamics has not been attempted on hardware. IBM Dynamic Circuits provide the mid-circuit measurement primitive.

Deliverables

  1. phase/monitored_kuramoto.py:
  2. MonitoredKuramotoCircuit(measurement_rate, subset) — insert mid-circuit measurements on a specified subset at a controlled rate.
  3. Entanglement-entropy estimator compatible with measurement-induced collapses.
  4. Phase diagram: entanglement vs. measurement rate at fixed K; locate the volume-law-to-area-law transition on hardware.
  5. Cross-check against sync order parameter: does the MIPT track a transition in \(R_{global}\)?
  6. docs/monitored_kuramoto.md — theory + protocol.

Risks

  • Dynamic Circuits mid-circuit measurement rates are backend-bounded; scanning measurement rate finely may exceed the timing budget.
  • Entanglement estimation under measurement requires classical shadow tomography or ancilla-based methods; shot budget is substantial.

Prerequisites

  • Dynamic Circuits support — depends on S1 or S8 landing first.
  • Witnesses + shadow tomography — already in repo.

Acceptance

Measurement-induced transition detectable in the entanglement vs. measurement-rate plot on hardware at N = 4.

Falsification

  • New entry C35 in docs/falsification.md: "MIPT detectable in entanglement vs. measurement-rate plot on hardware." Falsifier — no transition signature above statistical noise on the pre-registered benchmark.

S33 — Quantum-enhanced Lyapunov spectra for chaotic Kuramoto

Motivation

Classical Lyapunov-spectrum computation for large-N chaotic Kuramoto scales poorly. The QPU-computed OTOC scrambling rate is a natural proxy for the maximum Lyapunov exponent, and DLA-constrained trajectories give access to collective Lyapunov modes that pure classical long-time integration cannot reach within budget. Injecting these into a classical large-N solver as "quantum corrections" is the specific payoff.

Deliverables

  1. analysis/lyapunov_spectrum.py:
  2. collective_lyapunov_from_otoc(otoc_timeseries) — OTOC growth-rate → Lyapunov-exponent extraction.
  3. dla_constrained_lyapunov_spectrum(K, omega) — DLA-sector-resolved Lyapunov spectrum.
  4. Classical feedback: injected into the large-N Kuramoto solver in scpn-fusion-core as correction terms (extension of S14).
  5. Applied demos: tipping-point prediction on a chaotic IEEE grid model; cascade-risk quantification on a brain- connectome stability question.
  6. docs/quantum_lyapunov.md — theory + protocol.

Risks

  • OTOC → Lyapunov conversion is approximate; the proxy may not be tight for heterogeneous Kuramoto.
  • Tipping-point prediction is a statistically demanding claim that needs held-out validation.

Prerequisites

  • OTOC — already in repo.
  • DLA — already in repo.
  • Classical large-N solver — scpn-fusion-core.

Acceptance

Quantum-extracted Lyapunov spectrum agrees with the classical truth on a pre-registered small-N benchmark within a documented tolerance.

Falsification

  • New entry C36 in docs/falsification.md: "Quantum-extracted Lyapunov spectrum agrees with classical truth to within pre-registered tolerance on the benchmark." Falsifier — gap beyond tolerance on ≥ 50 % of benchmark instances.

S34 — Self-organising Kuramoto (autonomous drive engineering)

Motivation

Every quantum-control protocol in the repo today is externally driven: a classical controller computes the next drive and submits it. S34 closes the loop inside the circuit itself — the measured sync order parameter generates the next drive via classical feed-forward from the previous shot's results, with no external parameter tuning. This is the autonomous variant of S1 and S8; the differentiation is explicitly "no external controller in the loop at steady state".

Deliverables

  1. control/autonomous_drive.py:
  2. AutonomousDriveLoop — closed-loop driver that reads the previous shot's observables, computes the next drive via a deterministic (classical) rule, and submits without human input.
  3. Convergence criterion: the loop terminates when the measured R saturates within a pre-registered tolerance.
  4. Hardware demo at N = 4: show autonomous convergence to a target R on an adversarially disturbed Kuramoto trajectory.
  5. Comparison against externally tuned baseline (S1 with manually specified drives).
  6. docs/autonomous_kuramoto.md — protocol + results.

Risks

  • Autonomous loops can oscillate or diverge; the deterministic rule must have a convergence proof or empirical convergence guarantees.
  • Overlaps with S1 (hybrid feedback loop) and S8 (adaptive branching); positioning needs to be "autonomous variant", not "different approach".

Prerequisites

  • S1 + S8 (feedback plumbing).
  • Convergence analysis for the deterministic rule (theorist pass).

Acceptance

Autonomous loop converges to target R within a pre-registered tolerance on hardware without external parameter tuning.

Falsification

  • New entry C37 in docs/falsification.md: "Autonomous drive loop converges to target R without external tuning on the pre-registered benchmark." Falsifier — loop fails to converge or diverges on ≥ 30 % of runs.

S35 — Quantum Kuramoto as native simulator for active matter (non-reciprocal)

Motivation

Active matter — flocking, swarming, non-reciprocal interactions — is almost exclusively classical / mean-field in current literature. A quantum hardware realisation with DLA analysis of non-reciprocal K_nm (directed couplings) positions the project as the reference quantum-active-matter platform. Non-reciprocal K_{ij} ≠ K_{ji} violates Hermiticity; execution requires the auxiliary-qubit dilation primitive from S22.

Deliverables

  1. phase/active_matter.py:
  2. Non-reciprocal K_nm ingestion.
  3. Dilation compilation (shared with S22).
  4. Active-matter-specific observables: flocking order parameter, swarming correlation length.
  5. Hardware demo at N = 4 on the dilated space (N = 4 + 4 ancillae): show a sync transition characteristic of non-reciprocal dynamics, distinguishable from the Hermitian baseline.
  6. docs/quantum_active_matter.md — theory + protocol.

Risks

  • Dilation doubles the qubit requirement; N = 4 active matter demands 8 physical qubits on Heron r2.
  • Active-matter signatures (flocking transition) may be indistinguishable from trivial asymmetry effects at the accessible N; benchmark against classical prediction carefully.

Prerequisites

  • S22 (dilation primitive).
  • Non-reciprocal K_nm extension to the mapper.

Acceptance

Non-reciprocal sync transition distinguishable from the Hermitian baseline on hardware at N = 4 on a pre-registered benchmark.

Falsification

  • New entry C38 in docs/falsification.md: "Non-reciprocal sync transition distinguishable from Hermitian baseline on hardware at matched compute budget." Falsifier — indistinct transition signature on the pre-registered benchmark.

Foundational tracks (S36–S53) — compact format

The tracks below are scoped in a compact-but-rigorous format (motivation, deliverables, risks, prerequisites, acceptance, falsifier — no long-form narrative). Each still demands the same activation-gate rigour as S1–S35. On activation, the responsible session expands the compact entry into the full S1–S35-style form before execution starts.

Source archive. The original full-length source text for every track below is preserved in .coordination/strategic_roadmap_sources/2026-04-18_differentiation_tracks_s36_plus_RAW.md (gitignored). Deduplication collapsed seven proposal rounds from 2026-04-18 into this block; tracks that appeared in multiple rounds are merged with cross-references.

S36 — Information geometry on quantum sync manifolds

Motivation. The manifold of reachable sync states, parameterised by (K_nm, ω, DLA generators), is a Riemannian manifold with the quantum Fisher information tensor as natural metric. Geodesics, sectional curvature, and natural-gradient flows give provably optimal control paths across the sync transition. Information geometry exists for single-qubit and simple VQE landscapes; no application to collective Kuramoto order parameters on hardware has surfaced in the literature surveyed through 2026-04.

Deliverables. analysis/sync_information_geometry.py with Fisher-tensor computation from observables; Rust-side geodesic integrator; natural-gradient-flow optimal-control demo on N = 4.

Risks. Fisher-tensor estimation is shot-hungry; natural-gradient directions can diverge near singular points.

Prerequisites. analysis/qfi_criticality.py (done), Rust accel (done).

Acceptance. Natural-gradient path from incoherent to full sync on hardware beats straight-line Trotter on final R at matched depth on a pre-registered benchmark.

Falsification. C39: natural-gradient path beats straight-line Trotter at matched depth. Falsifier — no measurable R advantage on the benchmark.

S37 — Categorical / compositional quantum Kuramoto

Motivation. Oscillator networks can be formalised as objects in a symmetric monoidal category, with sync-preserving DLA-invariant morphisms as arrows. Compositional composition of sub-networks — hierarchical SCPN layers — enables modular circuit construction without exponential growth. Categorical QM is mature but has not been applied to synchronisation phenomena.

Deliverables. bridge/category_theory.py encoding network objects + morphisms; compositional K_nm builder; demo of a 2-layer hierarchical SCPN network compiled through the category.

Risks. Category-theoretic formalism has steep onboarding cost; practical payoff only at ≥ 3 hierarchical layers (where the hardware budget constrains the demo).

Prerequisites. mapper refactor, theorist pass on the category definition.

Acceptance. 2-layer hierarchical SCPN network compiles to a circuit of depth ≤ the flat-compilation depth by a documented fraction.

Falsification. Infrastructure track — no scientific claim; no falsifier.

S38 — Quantum Kuramoto field theory continuum limit + RG flows

Motivation. Large-N limit of the lattice Kuramoto-XY mapping yields an effective scalar QFT (φ⁴-like with DLA-protected symmetries). Tensor-network + DLA truncation compresses it. Running low-energy dynamics on hardware and extracting RG flows of the order parameter provides the first experimental bridge between many-body oscillators and genuine QFT phenomenology.

Deliverables. phase/qkft_continuum.py with tensor-network compression; RG-flow extractor using coarse-graining from DLA invariants; hardware demo at N = 4 — 6 measuring effective coupling renormalisation.

Risks. The φ⁴-effective-theory derivation is analytically demanding; a loose identification of the effective-field parameters invalidates the RG readout.

Prerequisites. quimb tensor-network tier (done), DLA (done), QuTiP baseline (done).

Acceptance. Published RG-flow diagram with a hardware-measured critical exponent agreeing with the classical Kuramoto mean-field prediction within a pre-registered tolerance.

Falsification. C40: hardware-measured RG flow matches mean-field critical exponent to pre-registered tolerance. Falsifier — exponent off by > tolerance.

S39 — Autopoietic / self-referential oscillator networks

Motivation. Sync order parameter dynamically rewrites K_nm without external controller. Extension of S34 (autonomous drive) where the coupling matrix itself is the feedback target rather than just the drive amplitude. Closed self-maintaining loops directly model origins-of-life, synthetic biology, and consciousness patterns as physical realisations inside quantum hardware.

Deliverables. control/autopoietic_loop.py — closed loop where measurement at shot n computes the K_nm to use at shot n+1; demo at N = 4 showing maintained non-trivial sync pattern without external input.

Risks. Autopoietic loops can collapse to trivial fixed points (R = 0 or R = 1) instead of sustaining a non-trivial pattern; parameter-regime search needed.

Prerequisites. S34 (autonomous drive) + S1 (feedback plumbing).

Acceptance. Autopoietic loop sustains a non-trivial sync pattern (0 < R < 1, chimera-type) for ≥ 20 feedback cycles without external input.

Falsification. C41: autopoietic loop sustains non-trivial pattern for ≥ 20 cycles. Falsifier — collapse to trivial R on ≥ 50 % of runs on the pre-registered benchmark.

S40 — Holographic duals via quantum synchronisation

Motivation. Boundary oscillator network sync mapped to a bulk gravitational-like degree of freedom, with DLA invariants as the holographic dictionary. Measure boundary order parameters on hardware, extract bulk geometry proxies. AdS/CFT in many-body quantum sync has not surfaced in the literature surveyed.

Deliverables. analysis/holographic_dual.py — boundary-to-bulk map using DLA invariants; hardware demo at N = 4 extracting a bulk-metric proxy from boundary observables.

Risks. Holographic interpretation is ambitious. The result may be unfalsifiable without a consensus holographic dictionary for heterogeneous Kuramoto-XY; clearly mark any "bulk metric" extracted as proxy, not derived.

Prerequisites. DLA machinery (done), theorist pass on the dual map construction.

Acceptance. Published theory note + hardware-measured bulk-metric proxy, with the mapping clearly framed as conjectural pending community validation.

Falsification. C42: self-consistency of the boundary ↔ bulk mapping under RG flow (tested in S38 + S40 together). Falsifier — inconsistency in the RG-flow fixed points between boundary and bulk at the pre-registered precision.

S41 — Quantum causal discovery with intervention

Motivation. OTOC growth + DLA parity asymmetry + targeted mid-circuit interventions (conditional drives, projective measurements) infer causal directionality and hidden couplings in unknown networks. Extends S16 (network tomography) from passive observation to active intervention — a genuine do-calculus over quantum oscillator networks.

Deliverables. analysis/causal_discovery.py with intervention scheduler; integrates with Dynamic Circuits (S8 prereq); applied demo: infer directed EEG connectivity from passive + active measurements.

Risks. Causal discovery is data-hungry; the quantum advantage over classical do-calculus requires a demonstration on a pre-registered hard instance.

Prerequisites. S16 (observational tomography), Dynamic Circuits (S8), witnesses (done).

Acceptance. Directed connectivity on a pre-registered synthetic graph recovered within a documented tolerance, beating the best classical observational-only baseline.

Falsification. C43: quantum-assisted do-calculus beats classical observational baseline on pre-registered benchmark. Falsifier — classical ties or wins.

S42 — Symplectic structure-preserving Trotterisation

Motivation. Almost every quantum mapping of classical dynamics destroys the symplectic structure of the phase space. Reformulating Trotter + pulse shaping to exactly preserve symplecticity (geometric integrator analogue in the quantum domain) enables faithful long-time simulation of Hamiltonian chaos without artificial dissipation. No open-source or hardware Kuramoto pipeline enforces this.

Deliverables. phase/symplectic_trotter.py — geometric-integrator variant of the Trotter decomposition; Rust-side implementation that guarantees symplectic norm preservation; long-time chaos-demo comparison vs. standard Trotter on a pre-registered chaotic Kuramoto benchmark.

Risks. Symplectic Trotter adds gate count; coherence budget may not permit the "long-time" demo on current hardware.

Prerequisites. Rust pulse engine (done), geometric-integrator theory pass.

Acceptance. Long-time energy / norm drift on the chaotic benchmark bounded below a pre-registered fraction of the standard- Trotter drift at matched depth.

Falsification. C44: symplectic Trotter bounds long-time drift below standard Trotter at matched depth. Falsifier — drift exceeds standard Trotter on ≥ 50 % of benchmark instances.

S43 — Full resource theory of quantum synchronisation

Motivation. Formalise synchronisation (sharpness of R + DLA subspace dimension + witness robustness) as a quantum resource. Define sync-distillable entanglement, sync cost of gates, conversion rates between sync and entanglement / magic. Resource theories exist for entanglement, coherence, magic — not for collective synchronisation.

Deliverables. analysis/sync_resource_theory.py formalising sync as resource; conversion-rate measurement protocol; hardware demo at N = 4 showing conversion of entanglement → sync and back.

Risks. Resource theory framework must be formally sound (free operations, monotones) before experimental measurement means anything.

Prerequisites. witnesses (done), OTOC (done), DLA (done), theorist pass on the resource-theory axiomatisation.

Acceptance. Theory note + hardware-measured conversion rate with error bars; paper note fits the v1.0 release cycle.

Falsification. C45: sync-to-entanglement conversion rate is non-zero (i.e. sync is a distinct resource from existing ones). Falsifier — conversion rate consistent with zero on the benchmark.

S44 — Objective-collapse / macroscopic-foundations testbed

Motivation. Merges three related proposals: objective-collapse models (GRW, Penrose OR, CSL) stress-tested at mesoscopic scales; Quantum Darwinism — sync manifold as redundant encoding of "classical" information into environmental degrees; macroscopic measurement as the quantum-to-classical transition witness. All three use the same instrument: DLA-parity asymmetry as a smoking-gun observable for collapse-induced desynchronisation or redundant classical imprinting.

Deliverables. phase/foundations_testbed.py with collapse-model simulator + Darwinism redundancy estimator; scaled-hardware campaign at N = 4 → 8 measuring DLA asymmetry decay; paper note on bounds derived for GRW / CSL parameters.

Risks. Collapse signals are exponentially small at accessible N. Darwinism redundancy estimator is shot-hungry. Setting meaningful bounds may require hardware access far beyond Phase 2 budget.

Prerequisites. Large-N hardware time, DLA parity asymmetry (hardware-evidence gate — done only when the hardware ledger promotes it).

Acceptance. Published paper with a documented bound on CSL rate (or GRW parameters) from mesoscopic-scale sync stability on hardware.

Falsification. C46: sync stability on hardware places a bound on CSL collapse rate tighter than the pre-registered reference benchmark. Falsifier — no tightening beyond reference within the campaign budget.

S45 — Biologically faithful Kuramoto simulator + IIT consciousness angle

Motivation. Ingest real structural-biology data (protein interaction graphs, microtubule lattices, photosynthetic antenna complexes, C. elegans / human connectomes) as K_nm + ω inputs. Compute Φ (integrated information, IIT) and cause-effect structures directly from DLA-protected sync manifolds on hardware; compare against classical baselines + experimental bio-data (2D spectroscopy, magnetoreception, EEG). Merges the biology-data ingestion and the IIT-testbed proposals from multiple rounds.

Deliverables. applications/bio_kuramoto.py with connectome/microtubule ingestion; IIT Φ estimator on DLA-protected manifold; applied comparison against 2D photosynthesis spectroscopy or an EEG integrated-information dataset.

Risks. "Quantum biology" is a contentious field. Over-claims ("quantum consciousness", "quantum coherence in protein folding") must not appear in the commit messages, paper, or documentation. The clean deliverable is a hardware-evidence-gated quantum-simulator readout of a bio-sourced coupling matrix — no metaphysical claims beyond that.

Prerequisites. applications/eeg_benchmark.py (done), applications/fmo_benchmark.py (done), bio-data licences.

Acceptance. Hardware-measured sync signature on a published connectome (or microtubule / FMO graph) within pre-registered agreement with classical baseline; IIT Φ estimator returns documented values with error bars.

Falsification. C47: hardware-measured sync signature on a bio-sourced K_nm agrees with classical mean-field within tolerance. Falsifier — significant disagreement on ≥ 2 of 3 bio-benchmarks.

S46 — Phase-transition / attractor-landscape quantum programming

Motivation. Encode computation directly into the attractor landscape: incoherent → chimera → partial → full sync phases each implement different logic or signal-processing primitives, without explicit gates. All current quantum computing is gate / annealing; this is "thermodynamic quantum software" where computation emerges from the physics of sync itself.

Deliverables. control/attractor_programming.py — target-pattern → drive schedule compiler; demo: 2-bit AND / OR implemented as attractor-selection on N = 4; scaling-of-capacity characterisation.

Risks. Limited computational expressiveness at small N; demonstration of any non-trivial computation beyond what a classical Kuramoto attractor already provides is required to be useful.

Prerequisites. witnesses (done), floquet_kuramoto (done).

Acceptance. A pre-registered non-trivial classical task (e.g. simple classification) solved via attractor-selection on hardware at matched or better accuracy than a classical Kuramoto attractor solver.

Falsification. C48: attractor-programming beats classical Kuramoto attractor solver on a pre-registered classification task. Falsifier — parity or worse performance on the benchmark.

S47 — Analogue gravity on synchronised oscillator arrays

Motivation. Merges relativistic / curved-spacetime metrics, cosmological phase transitions + baryogenesis + defect formation, and emergent spacetime from sync. Position-dependent couplings and drives simulate quantum fields on curved backgrounds (analogue black-hole horizons, expanding universes) on flat superconducting hardware. Analogue gravity is mature in optics / BECs — not on Kuramoto-XY with DLA protection.

Deliverables. phase/analogue_gravity.py with curved-metric compiler; baryogenesis-analogue simulation on N = 4 — 6; table-top Kibble–Zurek defect-density measurement on hardware.

Risks. The analogy is qualitative unless a specific curved-background QFT claim is pre-registered. Resist over-interpreting hardware results as "quantum cosmology".

Prerequisites. S38 (QKFT), gauge/vortex_detector.py (done).

Acceptance. Published Kibble–Zurek defect-density scaling on hardware, matching the theoretical prediction for the chosen analogue-gravity mapping within a pre-registered tolerance.

Falsification. C49: Kibble–Zurek scaling exponent on hardware matches theory within tolerance. Falsifier — exponent off by > tolerance on the pre-registered benchmark.

S48 — Self-healing qubit fabrics + continuous sync QEC

Motivation. Merges two closely related proposals: self-healing qubit fabrics via engineered Kuramoto sync, and continuous analog QEC via the sync manifold. Local defects / errors trigger desynchronisation signals that propagate as corrective feedback through the network, restoring global sync and coherence without external classical control. Complements S18 (sync-as-memory) by treating sync as an error-correction process rather than a stored state.

Deliverables. qec/self_healing_fabric.py — always-on sync drive with built-in error-response feedback; hardware demo showing recovery from a simulated defect on N = 4 — 8.

Risks. Continuous feedback loops on hardware face latency bounds; the "healing time" must be less than the coherence time of the unhealed qubit fabric.

Prerequisites. S1 / S8 feedback plumbing, qec/ (done), S18 (sync-memory precursor).

Acceptance. Measured coherence-extension on a hardware fabric with injected defects vs. an unhealed baseline, exceeding a pre-registered factor.

Falsification. C50: self-healing fabric extends coherence over unhealed baseline on the pre-registered benchmark. Falsifier — no documented extension beyond statistical noise.

S49 — Quantum fluctuation theorems across sync transitions

Motivation. Experimentally test the quantum Jarzynski equality, Crooks fluctuation theorem, and thermodynamic uncertainty relations by driving across the Kuramoto sync transition and measuring work/heat distributions via DLA parity witnesses + OTOCs. Refines S9 (quantum thermodynamics) with the specific fluctuation-theorem observables.

Deliverables. thermodynamics/fluctuation_theorems.py — Jarzynski / Crooks estimators; hardware demo at N = 4 across a K-sweep spanning the sync transition.

Risks. Fluctuation-theorem tails are heavy-tailed; shot-budget for convergence is substantial.

Prerequisites. S9 (thermodynamics framework — prereq), GUESS ✓, OTOC ✓.

Acceptance. Published experimental confirmation of Jarzynski equality on the Kuramoto transition within a pre-registered statistical tolerance; work-distribution tails within predicted bounds.

Falsification. C51: measured Jarzynski average agrees with the free-energy-difference prediction within tolerance. Falsifier — significant deviation on the benchmark.

S50 — Quantum kernels from sync manifolds (ML)

Motivation. Define quantum kernels directly from the inner product structure of DLA-generated sync states; evaluate on hardware for classification / regression on real-world complex time-series. Quantum kernels exist for simple feature maps; none exploit the geometric structure of heterogeneous Kuramoto sync manifolds.

Deliverables. ml/sync_kernel.py with hardware kernel evaluator; plasma / brain / power-grid time-series classification benchmark.

Risks. Kernel methods are a crowded space; demonstrable quantum advantage on a pre-registered benchmark (not post-hoc selected) is required.

Prerequisites. DLA (done), Rust forward mapper (done), ML dataset access.

Acceptance. Kernel SVM using the hardware-measured sync kernel beats a classical Gaussian kernel baseline on a pre-registered time-series benchmark.

Falsification. C52: sync-manifold quantum kernel beats classical kernel on pre-registered benchmark. Falsifier — parity or worse on the benchmark.

S51 — Hayden–Preskill scrambling / black-hole information simulator

Motivation. OTOC growth rate + DLA-protected scrambling in synchronised oscillator arrays to model Hayden–Preskill information recovery protocols. First table-top Kuramoto-based simulator of black-hole information dynamics.

Deliverables. analysis/hayden_preskill.py — recovery-protocol simulation + hardware observable extraction; demo at N = 4 — 6 measuring a recovery fidelity consistent with Hayden–Preskill prediction.

Risks. Small-N black-hole analogues capture information scrambling but not full quantum-gravity dynamics; do not overclaim.

Prerequisites. OTOC (done), DLA (done).

Acceptance. Measured information recovery fidelity on hardware agrees with Hayden–Preskill prediction within a pre-registered tolerance for the scrambling time.

Falsification. C53: recovery fidelity agrees with Hayden–Preskill within tolerance. Falsifier — significant deviation from the predicted curve on the pre-registered benchmark.

S52 — Distributed quantum consensus via global sync (quantum internet)

Motivation. Use sharp global order-parameter transition as a consensus primitive across modular QPUs or quantum-internet nodes. Distant oscillator subsets synchronise via shared entanglement or mediated couplings; DLA witnesses certify consensus. Merges the multiple "quantum internet sync layer" proposals.

Deliverables. hardware/distributed_sync.py — multi-runner orchestrator using the existing AsyncHardwareRunner; Bell-pair- seeded distant oscillator demo on two Heron r2 regions; documented consensus primitive.

Risks. True "quantum internet" requires networking infrastructure not yet accessible on today's QPUs; the demo can only use multi-region of a single QPU or two QPUs with manual entanglement distribution.

Prerequisites. S1 async runner (done), Bell-pair preparation (done in crypto/).

Acceptance. Consensus primitive demonstrated across two independent Heron-r2 regions at a pre-registered consensus-fidelity threshold.

Falsification. C54: distant-region consensus fidelity exceeds classical clock-sync baseline on the pre-registered benchmark. Falsifier — consensus fidelity ≤ classical baseline.

S53 — Engineered self-organised criticality

Motivation. Tune (heterogeneity, topology, drive) so the system sits at the critical point of a non-equilibrium phase transition; measure avalanche statistics, power-law distributions, and information-processing capacity. SOC is classical / mean-field; no quantum hardware pipeline engineers or quantifies it in heterogeneous oscillator arrays.

Deliverables. analysis/self_organised_criticality.py — SOC detector + avalanche statistics; tuned-criticality demo on N = 6; information-processing capacity measurement at criticality.

Risks. SOC requires a separation of timescales that small-N hardware cannot provide unambiguously; the demo may show only SOC precursors, not full SOC.

Prerequisites. witnesses (done), OTOC (done), SOC-literature theorist pass.

Acceptance. Documented power-law avalanche-size distribution on hardware over at least two decades of scale.

Falsification. C55: avalanche distribution on tuned hardware follows a power law over ≥ 2 decades. Falsifier — cut-off at ≤ 1 decade on the pre-registered benchmark.

Applied verticals (cross-cutting over S1–S53)

Rounds 9 and 10 of the 2026-04-18 proposal sitting named five "applied verticals" that do not define new physics tracks but rather specific application targets any of S1–S53 can be directed at. These are cross-cutting; they do not get their own Sxx number but are documented here for the activation session to target.

Applied vertical Most relevant physics tracks
Fusion plasma stabilisation (ITER disruption forecasting + real-time control) S1 + S8 + S27 (feedback + branching + inverse design), S41 (causal discovery of plasma mode coupling), S48 (self-healing qubit fabric for control-loop latency)
Tipping-point early-warning (power grids, climate, neural seizures) S14 (hybrid forecasting), S24 (quantum speed limits for early warning), S31 (MBL / tipping precursor), S53 (SOC + avalanche statistics)
IIT consciousness testbed (connectomes, microtubules) S45 (direct) + S21 (multi-scale) + S50 (kernels on connectome sync data)
Quantum biology engineering (photosynthesis, protein folding, collective cell) S45 + S43 (sync-as-resource for bio-simulation) + S10 / S13 (analog + CV platforms)
Quantum internet infrastructure S4 (multi-vendor) + S26 (entanglement-mediated sync) + S52 (distributed consensus)
Autonomous AI physicist (discovery engine) S12 (Bayesian phase-diagram) + S39 (autopoietic) + S58-class concepts from S34 / S53 + S50 ML kernel

An applied vertical is not a separate track; activating an applied vertical means activating one or more of the physics tracks listed, with the applied-vertical dataset as the target and the applied-vertical metric as the acceptance criterion.

Cross-cutting dependencies

Several tracks share prerequisites. If any of these prerequisites slip, the dependent tracks slip with them.

Prerequisite Blocks
Phase 2 IBM credits S1, S2, S4, S8, S9, S11, S12, S15, S16, S17, S18, S22, S23, S24, S25, S26, S27, S28, S29, S30, S31, S32, S33, S34, S35 — essentially every track with a hardware deliverable
JAX tier ([jax] extra) S3 (diff-pulse) — DONE
QuTiP + Dynamiqs wired S5 (classical baselines) — DONE
qec/ benchmarks S7 (logical-level resources)
Visibility campaign (launch copy drafts) S5 (community adoption of harness)
S1 (hybrid feedback loop) S8 (adaptive branching is a follow-up of S1)
LindbladSyncEngine + GUESS + OTOC S9 — DONE
Julia tier + Rust hypergeometric pulse S10 (Rydberg SDK bridge); S13 (CV pulse shaping) — DONE
analysis/qfi_criticality.py + shadow tomography S11 — DONE
Persistent homology + Krylov complexity + SFF S12 — DONE
Cross-repo bridges (sc-neurocore / fusion-core / phase-orchestrator) S14 — DONE
Vendor SDK access (QuEra Bloqade, Xanadu Strawberry Fields, Bosonic Qiskit) S10 / S13
[bayes] or [rl] extra (scikit-optimize / botorch) S12

Dependency graph (forward direction only):

S1 → S8 (adaptive branching reuses the S1 observer plumbing)
S5 ⟂ S2 (independent, but S5's harness benefits from S2's scaling data)
S10 ⟂ S13 (parallel work on analog / CV; share SDK work but independent deliverables)
S7 ⟂ every other track (theory-bound, can run in parallel)

Funding / credit considerations

S1, S2, S4, S8, S9, S11, S12 are credit-intensive. A realistic cost estimate (Phase 2 scope) for a single hardware backend across six quarterly runs is ≳ 100 IBM Runtime hours at current pricing. S12 (phase-diagram scan) alone is ≳ 30 hours. Before activating any credit-intensive track:

  1. Confirm the 5-hour IBM Credits grant status (applied 2026-03-29).
  2. Decide whether to pursue a paid Runtime window for the gap.
  3. Consider a Google / Microsoft / QuEra research-credits application to diversify hardware access (supports S4, S10 directly).
  4. For analog / CV tracks (S10, S13), application windows to QuEra, Xanadu, PsiQuantum research programmes are the practical path.

Relationship to docs/falsification.md

Every differentiation track that produces a scientific claim needs a falsifier pre-registered in docs/falsification.md. Summary of claim IDs to be added on track activation:

Track Falsifier ID Claim
S3 C9 Learned ansatz beats hand-crafted at N ≥ 6
S4 C10 DLA parity asymmetry reproduces on non-IBM hardware
S7 C11 DLA parity survives surface-code encoding at d ≥ 3
S8 C12 Adaptive branching improves final R over open-loop Trotter at equal depth
S9 C13 Entropy-production rate peaks at the Kuramoto transition
S10 C14 Analog compilation uses fewer primitives than Trotter at matched fidelity
S11 C15 QFI-based sensing beats classical Fisher information on a pre-registered benchmark
S12 C16 Bayesian discovery loop finds a feature invisible in the classical pre-screen
S13 C17 CV-encoded Kuramoto reproduces qubit-encoded sync transition to ≤ 5 %
S14 C18 Hybrid quantum-classical forecast beats pure classical on chaotic Kuramoto
S15 C19 DLA-sector scar subspace exhibits longer sync lifetime than generic eigenstates
S16 C20 Quantum-assisted tomography recovers K_nm to < 10 % MAE at matched shot budget
S17 C21 Higher-order sync transition distinguishable from pairwise baseline at N = 6
S18 C22 Sync-manifold logical qubit outlives a dimension-matched unprotected qubit
S19 C23 Entanglement + magic + Krylov complexity show coherent transition signature at \(K_c\)
S21 C24 Quantum-corrected multi-scale solver beats pure classical at matched compute budget
S22 C25 Sensitivity enhancement near an engineered EP exceeds the Hermitian baseline
S23 C26 Kuramoto reservoir beats classical echo state network on pre-registered benchmark
S24 C27 Hardware-measured time-to-sync saturates the DLA-constrained QSL within 20 %
S25 C28 Vortex pair creation / annihilation reproducible on hardware at matched charge
S26 C29 Entanglement-mediated sync exceeds unentangled classical baseline
S27 C30 Inverse design reproduces target sync pattern within tolerance on ≥ 2/3 targets
S28 C31 Distributed sync sensor achieves super-classical Fisher information
S29 C32 Subharmonic response survives DLA-protected drive schedule beyond heterogeneity threshold
S30 C33 Quantum community detection beats Louvain on pre-registered hard LFR instance
S31 C34 Mobility edge detectable via DLA parity + OTOC on pre-registered disorder model
S32 C35 Measurement-induced transition detectable in entanglement vs. measurement-rate plot
S33 C36 Quantum-extracted Lyapunov spectrum agrees with classical truth within tolerance
S34 C37 Autonomous drive loop converges without external tuning on ≥ 70 % of runs
S35 C38 Non-reciprocal sync transition distinguishable from Hermitian baseline
S36 C39 Natural-gradient path beats straight-line Trotter at matched depth
S38 C40 Hardware-measured RG flow matches mean-field critical exponent within tolerance
S39 C41 Autopoietic loop sustains non-trivial sync pattern ≥ 20 cycles
S40 C42 Boundary ↔ bulk holographic mapping self-consistent under RG flow
S41 C43 Quantum-assisted do-calculus beats classical observational baseline
S42 C44 Symplectic Trotter bounds long-time drift below standard Trotter at matched depth
S43 C45 Sync-to-entanglement conversion rate non-zero (sync is a distinct resource)
S44 C46 Sync stability bounds CSL collapse rate tighter than reference
S45 C47 Hardware sync signature on bio-sourced K_nm agrees with classical mean-field within tolerance
S46 C48 Attractor-programming beats classical Kuramoto attractor solver on classification
S47 C49 Kibble–Zurek defect-density scaling exponent on hardware matches theory within tolerance
S48 C50 Self-healing fabric extends coherence over unhealed baseline
S49 C51 Measured Jarzynski average agrees with free-energy-difference prediction within tolerance
S50 C52 Sync-manifold quantum kernel beats classical kernel on time-series benchmark
S51 C53 Recovery fidelity agrees with Hayden–Preskill prediction within tolerance
S52 C54 Distant-region consensus fidelity exceeds classical clock-sync baseline
S53 C55 Avalanche size distribution on tuned hardware follows a power law over ≥ 2 decades

S1, S2, S5, S6, S20, S37 are infrastructure / engineering tracks; they have internal acceptance criteria but no scientific claim that needs falsification.

Activation checklist (for the future session that picks one up)

Before starting execution on any of S1–S53:

  1. Re-read this document top to bottom.
  2. Confirm the CEO has activated the specific track (none is auto-active).
  3. Re-check the "Risks" and "Prerequisites" sections — the landscape will have moved.
  4. Create a dedicated audit file under docs/internal/audit_<date>_<track>.md with a new gap list for the specific deliverables.
  5. Schedule a session log per CLAUDE_RULES.md / SHARED_CONTEXT.md protocol.
  6. Update ROADMAP.md "In progress" section with the track identifier.
  7. Add falsification criterion to docs/falsification.md if the track produces a scientific claim.

Cadence

This strategic roadmap is reviewed quarterly (January, April, July, October). The review:

  • Re-orders the priority matrix based on the last quarter's landscape.
  • Closes items that have been executed or superseded.
  • Adds new differentiation tracks as the field moves.

Each review produces a timestamped entry in ROADMAP.md §"Future".