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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 — Hardware Topological Optimizer Benchmark

Benchmark: Hardware Topological Optimizer

Modules:

  • scpn_quantum_control.control.topological_optimizer — local simulation path
  • scpn_quantum_control.control.hardware_topological_optimizer — hardware-in-the-loop

Overview

The Topological Coupling Optimizer iteratively rewires the coupling matrix \(K_{nm}\) to minimise persistent 1-cycles (\(p_{h1}\)) in the quantum state's correlation topology. It bridges Topological Data Analysis (TDA) and Quantum Optimal Control: instead of minimising energy (VQE), it optimises for macroscopic coherence and absence of phase vortices.

The hardware variant (HardwareTopologicalOptimizer) replaces local sparse evolution with real IBM Quantum hardware execution.

Optimisation Step Breakdown

Each .step() call performs:

  1. Hamiltonian evolution — sparse expm on current \(K\)
  2. Correlation measurement — \(\langle X_n X_m + Y_n Y_m \rangle\)
  3. TDA computation — ripser persistent homology on correlation matrix
  4. Gradient estimation — SPSA with 2 samples per step
  5. Coupling update — gradient descent on \(p_{h1}\)

Local Simulation Benchmarks

System Size Step Time TDA (ripser) Evolution Notes
N=4 ~0.5 s <10 ms ~2 ms Fast convergence
N=6 ~2.4 s <20 ms ~8 ms SPSA overhead dominates
N=8 ~8 s <50 ms ~35 ms 256-dim Hilbert space
N=16 ~45 s <50 ms ~1.8 s Sparse engine critical

TDA Efficiency: ripser computes \(H_1\) intervals for N=16 correlation matrices in under 50 ms — negligible compared to quantum evolution.

Hardware-in-the-Loop

When using HardwareTopologicalOptimizer with IBM Quantum:

Component Time Notes
Circuit construction <5 ms Trotter circuit + XYZ measurement bases
IBM queue wait 10 s–10 min Dominates total time
Hardware execution ~2 s/shot-batch 5000 shots default
TDA + gradient update <50 ms Same as local

Total step time is dominated by IBM Quantum queue latency, not computation.

The TCBO observer (compute_tcbo_observables) provides the observables that the optimizer targets:

Operation System Time Output
compute_tcbo_observables(K, omega) 4 qubits 4.6 ms \(p_{h1}\), TEE, string order

\(p_{h1} \in [0, 1]\), TEE finite, \(|\text{string\_order}| \leq 1\), \(\beta_0 + \beta_1 \approx 1\).

Physical Invariants (Verified by Tests)

  • \(K_{nm}\) remains symmetric at every step
  • \(K_{nm} \geq 0\) (non-negative coupling)
  • \(K_{nn} = 0\) (no self-coupling)
  • Gradient norm is finite (no NaN/Inf)
  • Optimisation loop converges (\(p_{h1}\) decreases or stabilises)

Test Coverage

9 tests across 2 files:

tests/test_topological_optimizer.py (6 tests):

  • test_topological_optimizer_step — single step produces valid output
  • test_optimize_loop — multi-step convergence
  • test_k_symmetry_preserved — symmetry invariant
  • test_k_non_negative — coupling positivity
  • test_diagonal_stays_zero — no self-coupling
  • test_gradient_norm_finite — numerical stability

tests/test_hardware_topological_optimizer.py (3 tests):

  • test_hardware_optimizer_step — hardware path single step
  • test_hardware_optimizer_multi_step — multi-step with mock runner
  • test_hardware_optimizer_k_non_negative — coupling positivity on hardware path

Running Benchmarks

pytest tests/test_topological_optimizer.py -v -s
pytest tests/test_hardware_topological_optimizer.py -v -s