Benchmark: Dynamic Coupling (Quantum Hebbian Learning)

Module: scpn_quantum_control.qsnn.dynamic_coupling Class: DynamicCouplingEngine

Overview

The Dynamic Coupling Engine implements quantum-classical co-evolution where a classical coupling matrix $K_{nm}$ drives quantum XY Hamiltonian evolution, and quantum correlation measurements feed back to update $K_{nm}$ via a Hebbian rule:

$K_{nm}(t+1) = (1 - \gamma) K_{nm}(t) + \eta \langle X_n X_m + Y_n Y_m \rangle$

Each co-evolution step requires: Hamiltonian construction, sparse time evolution, correlation matrix measurement, and coupling update.

Rust Acceleration

The correlation measurement step uses correlation_matrix_xy from scpn_quantum_engine when available, providing 2.9x speedup over the pure NumPy/Qiskit path.

Operation	Python (ms)	Rust (ms)	Speedup
correlation_matrix_xy (4q)	0.29	0.10	2.9x

Co-evolution Step Timing

Each .step(dt) call performs one full loop: evolve + measure + update $K$.

System Size	Step Time	Notes
N=2	<1 ms	Trivial 4x4 Hilbert space
N=4	~2 ms	Sparse evolution dominates
N=6	~8 ms	64-dimensional Hilbert space
N=8	~35 ms	256-dimensional, correlation matrix 8x8

Multi-step Co-evolution

run_coevolution(steps, dt) runs multiple steps and returns the full trajectory.

Steps	N=4 Time	N=6 Time	N=8 Time
10	~20 ms	~80 ms	~350 ms
50	~100 ms	~400 ms	~1.8 s
100	~200 ms	~800 ms	~3.5 s

Physical Invariants (Verified by Tests)

• $K_{nm}$ remains symmetric at every step
• $K_{nm} \geq 0$ (non-negative coupling)
• Diagonal $K_{nn} = 0$ (no self-coupling)
• Statevector normalised ($\|\psi\| = 1$)
• Correlation matrix symmetric ($C = C^T$)
• Decay drives $K \to 0$ when learning rate is zero

Test Coverage

9 tests in tests/test_dynamic_coupling.py:

• test_dynamic_coupling_engine_step — single step produces valid output
• test_run_coevolution — multi-step trajectory length and structure
• test_k_symmetry_preserved — symmetry invariant across steps
• test_correlation_matrix_symmetric — $C_{nm} = C_{mn}$
• test_k_diagonal_stays_zero — no self-coupling
• test_k_non_negative — coupling positivity
• test_decay_drives_k_toward_zero — thermodynamic limit
• test_statevector_normalised — quantum state normalisation
• test_rust_python_correlation_parity — Rust and Python paths agree

Running Benchmarks

pytest tests/test_dynamic_coupling.py -v -s
pytest tests/test_rust_path_benchmarks.py -k correlation_matrix -v -s