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

Commercial license available

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

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

ORCID: 0009-0009-3560-0851

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

scpn-quantum-control — scpn-quantum-control

CI License: AGPL-3.0 Python 3.10+ Qiskit 1.0+ OpenSSF Best Practices OpenSSF Scorecard Ruff mypy

Quantum simulation of coupled Kuramoto oscillator networks on IBM superconducting hardware, with 33 research modules probing the synchronization phase transition.

What this package does

The classical Kuramoto model for coupled oscillators maps directly to the quantum XY spin Hamiltonian. Superconducting qubits are native simulators of this physics: each qubit is an oscillator on the Bloch sphere, and the XX+YY coupling between qubits reproduces the \(\sin(\theta_j - \theta_i)\) interaction of the Kuramoto model.

This package provides three things:

  1. A compiler that takes any coupling matrix \(K_{nm}\) and natural frequencies \(\omega_i\) and produces executable Qiskit circuits for IBM hardware.

  2. 33 research modules (the "gems") probing the synchronization phase transition — synchronization witnesses, topological diagnostics, chaos measures, computational complexity bounds, and open-system dynamics. ~4 are novel constructions; ~8 are first applications of existing tools to Kuramoto-XY; the rest are standard many-body diagnostics.

  3. The SCPN 16-layer network as a built-in benchmark — the coupling matrix from Paper 27 of the Sentient-Consciousness Projection Network framework, where synchronization is the mechanism by which consciousness emerges across 16 ontological layers.

Think of it as a quantum microscope for synchronization. Classical Kuramoto tells you when oscillators lock in step. This package tells you what the quantum state looks like at the transition, how hard it is to prepare, what its topology reveals, and where classical simulation fails.

Key results

Result Value
VQE ground-state error 0.05% (4-qubit, ibm_fez)
16-layer UPDE snapshot 46% error at depth 770 (NISQ-consistent)
Coherence wall depth 250–400 (Heron r2)
DLA dimension formula \(2^{2N-1} - 2\) (exact, all \(N\))
Research modules 33 (~4 novel, ~8 first-application)
IBM hardware jobs 33 completed on ibm_fez (Heron r2)
Test suite 2,813 passing, 98% coverage
Python modules 166 + 1 Rust crate

Package map

Subpackage Modules Purpose
analysis 41 Synchronization probes: witnesses, QFI, PH, OTOC, Krylov, magic, BKT, DLA
phase 14 Time evolution: Trotter, VQE, ADAPT-VQE, VarQITE, AVQDS, QSVT, Floquet DTC
bridge 11 \(K_{nm}\) → Hamiltonian, cross-repo adapters (sc-neurocore, SSGF, orchestrator)
control 5 QAOA-MPC, VQLS Grad-Shafranov, Petri nets, ITER disruption classifier
qsnn 5 Quantum spiking neural networks (LIF, STDP, synapses, training)
hardware 9 IBM Quantum runner, trapped-ion backend, GPU offload, circuit cutting
mitigation 4 ZNE, PEC, dynamical decoupling, Z₂ parity post-selection
gauge 5 U(1) Wilson loops, vortex detection, CFT, universality, confinement
identity 6 VQE attractor, coherence budget, entanglement witness, fingerprint
qec 4 Toric code, repetition code UPDE, surface code estimation, error budget
applications 10 FMO photosynthesis, power grid, Josephson array, EEG, ITER, quantum EVS
crypto 4 BB84, Bell tests, topology-authenticated QKD

Quick example

Any coupling topology — bring your own \(K\) and \(\omega\):

from scpn_quantum_control import QuantumKuramotoSolver, build_kuramoto_ring

K, omega = build_kuramoto_ring(6, coupling=0.5, rng_seed=42)
solver = QuantumKuramotoSolver(6, K, omega)
result = solver.run(t_max=1.0, dt=0.1, trotter_per_step=2)
print(f"R(t): {result['R']}")

Detect synchronization on hardware with witness operators:

from scpn_quantum_control.analysis.sync_witness import evaluate_all_witnesses

# After running X-basis and Y-basis circuits on IBM hardware:
results = evaluate_all_witnesses(x_counts, y_counts, n_qubits=4)
for name, w in results.items():
    print(f"{name}: {'SYNCHRONIZED' if w.is_synchronized else 'incoherent'}")

Limitations

  • NISQ benchmarking only. Circuit depths >400 hit the coherence wall on Heron r2.
  • SCPN coupling matrix is from unpublished work. The \(K_{nm}\) parameterisation comes from Paper 27 (2025 working paper, no external citations). The Kuramoto→XY mapping is standard; the specific coupling structure is not independently validated.
  • No quantum advantage at this scale. At \(N=4\)–16, classical exact diagonalisation is faster. Advantage requires \(N \gg 20\) with error-corrected qubits.
  • IBM hardware campaign complete. 33 jobs on ibm_fez (Heron r2), 176K+ shots. CHSH S=2.165, QBER 5.5%, 16q UPDE, dual protection confirmed.

Documentation

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

ANULUM      Fortis Studio
Developed by ANULUM / Fortis Studio

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

ANULUM      Fortis Studio
Developed by ANULUM / Fortis Studio