scpn-quantum-control 0.5.1

Quantum-native reformulations of SCPN spiking, phase dynamics, and plasma control

scpn-quantum-control

The Self-Consistent Phenomenological Network (SCPN) models hierarchical dynamics as 16 coupled Kuramoto oscillators with a coupling matrix K_nm. The Kuramoto model is isomorphic to the XY spin Hamiltonian — superconducting qubits simulate it natively via Trotterized time evolution. This repo implements that mapping: it compiles SCPN coupling parameters into Qiskit circuits and validates them on IBM Heron r2 hardware (156 qubits), achieving 0.05% VQE ground-state error and the first hardware attempt at a full 16-layer UPDE snapshot (46% error at depth 770 — consistent with NISQ expectations).

If you work on quantum simulation of coupled oscillators, NISQ benchmarking, or Kuramoto/XY physics, this repo gives you a tested pipeline from coupling matrices to hardware results.

Background: SCPN and the Quantum Mapping

SCPN is a theoretical framework in which 16 oscillator layers — each with a natural frequency omega_n — interact through a coupling matrix K_nm:

K_nm = K_base * exp(-alpha * |n - m|)

with K_base = 0.45, alpha = 0.3, and empirical calibration anchors (K[1,2] = 0.302, K[2,3] = 0.201, K[3,4] = 0.252, K[4,5] = 0.154). Cross-hierarchy boosts link distant layers (L1-L16 = 0.05, L5-L7 = 0.15). See docs/equations.md for the full parameter set.

The classical dynamics follow the Kuramoto ODE:

d(theta_i)/dt = omega_i + sum_j K_ij sin(theta_j - theta_i)

The core isomorphism: this ODE maps to the quantum XY Hamiltonian

H = -sum_{i<j} K_ij (X_i X_j + Y_i Y_j) - sum_i omega_i Z_i

where X, Y, Z are Pauli operators. Superconducting transmon qubits implement XX+YY interactions natively through controlled-Z gates, making quantum hardware a natural simulator for Kuramoto phase dynamics. The order parameter R — a measure of global synchronization — is extracted from qubit expectations: R = (1/N)|sum_i (<X_i> + i<Y_i>)|.

Coherence R as a function of coupling strength K_base across 16 SCPN layers. Strongly-coupled layers (L3, L4, L10) synchronize first; weakly-coupled L12 lags behind, consistent with the exponential decay in K_nm.

Reference: M. Sotek, Self-Consistent Phenomenological Network: Layer Dynamics and Coupling Structure, Working Paper 27 (2025). Manuscript in preparation.

Hardware Results (ibm_fez, February 2026)

Experiment	Qubits	Depth	Hardware	Exact	Error
VQE ground state	4	12 CZ	-6.2998	-6.3030	0.05%
Kuramoto XY (1 rep)	4	85	R=0.743	R=0.802	7.3%
Qubit scaling	6	147	R=0.482	R=0.532	9.3%
UPDE-16 snapshot	16	770	R=0.332	R=0.615	46%
QAOA-MPC (p=2)	4	--	-0.514	0.250	--

Full results with all 12 decoherence data points: results/HARDWARE_RESULTS.md

Key findings:

• VQE with K_nm-informed ansatz achieves publication-quality 0.05% error
• Coherence wall at depth 250-400 on Heron r2 — shallow Trotter (1 rep) beats deep Trotter on NISQ devices

More Trotter repetitions improve mathematical accuracy but increase circuit depth. On NISQ hardware, decoherence from the extra gates outweighs the Trotter error reduction. Optimal strategy: fewest reps that capture the physics.

• 16-layer UPDE snapshot on real hardware — per-layer structure partially tracks coupling topology (L12 collapse, L3 resilience at the extremes; Spearman rho = -0.13 across all layers)

Per-layer X-basis expectations from the 16-qubit UPDE snapshot on ibm_fez. L12 (most weakly coupled) shows near-complete decoherence; strongly-coupled layers (L3, L4, L10) maintain coherence.

• 12-point decoherence curve from depth 5 to 770 with exponential decay fit

Hardware-to-exact ratio R_hw/R_exact vs circuit depth. The three regimes: near-perfect readout (depth < 25), linear decoherence (85-400), and noise-dominated (> 400).

Architecture

scpn_quantum_control/
├── qsnn/           Quantum spiking neural networks
│   ├── qlif.py         Ry-rotation LIF neuron (P(spike) = sin^2(theta/2))
│   ├── qsynapse.py     Controlled-Ry synapse (CRy weight encoding)
│   ├── qstdp.py        Parameter-shift STDP learning rule
│   └── qlayer.py       Multi-qubit entangled dense layer
├── phase/          Quantum phase dynamics
│   ├── xy_kuramoto.py  Kuramoto -> XY Hamiltonian + Trotter evolution
│   ├── trotter_upde.py 16-layer UPDE as multi-site spin chain
│   └── phase_vqe.py    VQE ground state with Knm-informed ansatz
├── control/        Quantum control algorithms
│   ├── qaoa_mpc.py     QAOA binary MPC trajectory optimization
│   ├── vqls_gs.py      VQLS for Grad-Shafranov equilibrium
│   ├── qpetri.py       Quantum Petri net (superposition tokens)
│   └── q_disruption.py Quantum kernel disruption classifier
├── bridge/         Classical <-> quantum converters
│   ├── knm_hamiltonian.py  Knm matrix -> SparsePauliOp compiler
│   ├── spn_to_qcircuit.py  SPN topology -> quantum circuit
│   └── sc_to_quantum.py    Bitstream probability <-> rotation angle
├── crypto/         Topology-authenticated quantum cryptography
│   ├── knm_key.py         K_nm → VQE ground state → key material
│   ├── entanglement_qkd.py  SCPN-QKD protocol, CHSH Bell test
│   ├── topology_auth.py   Spectral fingerprint authentication
│   ├── percolation.py     Entanglement percolation on K_nm graph
│   ├── hierarchical_keys.py  Multi-layer key derivation
│   └── noise_analysis.py  Devetak-Winter key rates, noise channels
├── qec/            Quantum error correction
│   └── control_qec.py     Toric code + MWPM decoder (Knm-weighted)
├── mitigation/     Error mitigation
│   ├── zne.py          Zero-noise extrapolation (unitary folding)
│   └── dd.py           Dynamical decoupling (XY4, X2)
└── hardware/       IBM Quantum hardware runner
    ├── runner.py       ibm_fez job submission + result parsing
    ├── experiments.py  20 pre-built experiment circuits (incl. 3 crypto)
    └── classical.py    Classical Kuramoto reference solver

Quick Start

pip install -e ".[dev]"
pytest tests/ -v

Examples

See examples/README.md for a guided walkthrough. Summary:

Example	What it does
01_qlif_demo.py	Quantum LIF neuron: maps membrane potential to Ry rotation, compares firing rates with classical Bernoulli expectation
02_kuramoto_xy_demo.py	4-oscillator Kuramoto dynamics on the XY Hamiltonian via Trotter evolution; prints R(t) trajectory
03_qaoa_mpc_demo.py	QAOA-based binary MPC: optimizes 4-step coil control sequence by mapping quadratic cost to Ising Hamiltonian
04_qpetri_demo.py	Quantum Petri net: 3 places, 2 transitions — tokens evolve in superposition via controlled rotations
05_vqe_ansatz_comparison.py	Benchmarks three VQE ansatze (K_nm-informed, hardware-efficient, EfficientSU2) on the 4-qubit Kuramoto Hamiltonian
06_zne_demo.py	Zero-noise extrapolation on a noisy simulator: unitary folding + Richardson extrapolation under synthetic Heron r2 noise

All examples run on statevector simulation (no QPU needed).

Hardware execution (requires IBM Quantum credentials)

pip install -e ".[ibm]"
python run_hardware.py --experiment kuramoto --qubits 4 --shots 10000

Modules

Quantum Spiking Neural Networks (qsnn/)

Maps stochastic LIF neurons to parameterized quantum circuits. A qubit with Ry(theta) rotation + Z-basis measurement produces spike/no-spike with probability sin^2(theta/2) — direct analog of stochastic membrane potential.

Quantum Phase Dynamics (phase/)

The Kuramoto ODE is isomorphic to the XY spin Hamiltonian (see Background). Quantum hardware simulates this natively via Trotterized time evolution. The 16-layer UPDE (Unified Phase Dynamics Equation — the master equation governing all SCPN layers) becomes a 16-qubit spin chain with K_nm coupling.

Quantum Control (control/)

• QAOA-MPC: Discretize MPC action space to binary, map quadratic cost to Ising Hamiltonian, solve via QAOA
• VQLS-GS: Solve discretized Grad-Shafranov PDE as quantum linear system
• Quantum Petri: SPN tokens as qubit amplitudes, transitions fire in superposition
• Disruption classifier: 11-D feature amplitude encoding + parameterized circuit

Bridge (bridge/)

Compiles SCPN data structures into quantum circuits:

• knm_to_hamiltonian(): 16x16 coupling matrix -> SparsePauliOp
• knm_to_ansatz(): Physics-informed entanglement topology
• probability_to_angle(): p -> 2*arcsin(sqrt(p))

QEC (qec/)

Toric surface code protecting quantum control signals. MWPM decoder uses Knm graph distance instead of lattice distance for physics-aware error correction.

Quantum Cryptography (crypto/)

Topology-authenticated QKD using K_nm as shared secret:

• Key generation: VQE ground state of H(K_nm) → correlated measurement → sifted key
• CHSH Bell test: certifies entanglement via CHSH inequality violation
• Spectral fingerprint: Laplacian spectrum of K_nm as public authentication token
• Entanglement percolation: identifies above-threshold qubit pairs for QKD channels
• Hierarchical keys: 16-layer SCPN hierarchy → key derivation tree
• Noise analysis: Devetak-Winter key rates under depolarizing/amplitude-damping channels

Error Mitigation (mitigation/)

• ZNE: Global unitary folding + Richardson extrapolation (Giurgica-Tiron et al. 2020)
• DD: Dynamical decoupling pulse insertion (XY4, X2) for idle qubits (Viola et al. 1999)

Dependencies

Package	Version	Purpose
qiskit	>= 1.0.0	Circuit construction, transpilation
qiskit-aer	>= 0.14.0	Statevector + noise simulation
numpy	>= 1.24	Array operations
scipy	>= 1.10	Sparse linear algebra, optimization
networkx	>= 3.0	Graph algorithms (QEC decoder)

Optional:

• matplotlib >= 3.5 for visualization
• qiskit-ibm-runtime >= 0.20.0 for hardware execution

Notebooks

Interactive Jupyter notebooks in notebooks/:

Notebook	Covers
01_kuramoto_xy_dynamics	Kuramoto → XY mapping, Trotter evolution, 4-osc and 8-osc
02_vqe_ground_state	VQE with Knm-informed ansatz, ansatz comparison, 4q and 8q
03_error_mitigation	ZNE (unitary folding + Richardson), noisy simulator
04_upde_16_layer	Full 16-layer SCPN, per-layer coherence analysis

All run on local AerSimulator. No IBM credentials needed.

Documentation

Full docs at anulum.github.io/scpn-quantum-control — equations, architecture, API reference, hardware guide, experiment roadmap.

Related Repositories

Repository	Description
scpn-fusion-core	Classical SCPN algorithms: Kuramoto solvers, coupling matrix calibration, transport models (v3.9.2, 1899 tests)

Citation

@software{scpn_quantum_control,
  title  = {scpn-quantum-control: Quantum-Native SCPN Phase Dynamics and Control},
  author = {Sotek, Miroslav},
  year   = {2026},
  url    = {https://github.com/anulum/scpn-quantum-control}
}

License

MIT