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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

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scpn-quantum-control — Dynamic Coupling Benchmark

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