Incorporating resource-efficient quantum subspace diagonalization algorithms into the training of Extreme Quantum Cognition Machines will improve their robustness to noisy and contradictory decision-making data compared to classical subspace selection methods.

Training Extreme Quantum Cognition Machines (EQCMs) — extreme-learning-machine-style hybrid quantum-classical classifiers/regressors that use a fixed random quantum feature map plus a linear readout — with resource-efficient quantum subspace diagonalization (QSD, e.g. quantum Krylov subspace or sample-based quantum diagonalization methods) for selecting/compressing the effective hidden-layer subspace will yield statistically significantly lower generalization error and higher label-robustness than EQCMs trained with classical subspace selection (PCA, random projection, or ridge-regularized least squares) on datasets with injected label noise (symmetric/asymmetric flip rates 5–40%) and feature contradictions (conflicting duplicate samples with opposing labels at 5–30% prevalence). Falsifiable claim: at matched trainable-parameter count and matched classical compute budget, mean test accuracy (or RMSE) of QSD-EQCM exceeds classical-subspace-EQCM by ≥3 percentage points (classification) or ≥5% relative RMSE reduction (regression), averaged over ≥5 benchmark datasets and ≥20 random seeds per noise level, with p<0.01 (paired t-test, Holm-corrected).

Minimum viable test (MVT): 3 tabular benchmark datasets (UCI Adult, MNIST-1D projected to ≤20 features via PCA, and one synthetic contradictory-label dataset), 4 noise levels (0%, 10%, 20%, 30%), 10 seeds each, comparing QSD-EQCM (simulated via PennyLane/Qiskit statevector, 8 qubits) vs. three classical baselines (PCA-ELM, random-projection ELM, ridge-regularized ELM), all matched at N=256 hidden units equivalent. Full validation extends to 8 datasets, 6 noise levels, 30 seeds, plus one real-hardware run (IBM Quantum or IonQ, ≤8 qubits) to test the hardware-noise disproof criterion.

# Pseudocode
for dataset in [Adult, GermanCredit, Ionosphere, BreastCancer, MNIST1D, CIFAR10emb, ...]:
    X, y = load_and_preprocess(dataset, max_dim=64)
    for noise_level in [0, 5, 10, 15, 20, 25, 30, 40]:
        y_noisy = inject_label_noise(y, noise_level)  # symmetric flip + contradictory dup
        for seed in range(N_SEEDS):
            set_seed(seed)
            # Quantum feature map (fixed random, untrained)
            phi_q = quantum_feature_map(X, n_qubits=8, circuit="ZZFeatureMap")
            gram_q = compute_quantum_kernel_gram(phi_q)  # via statevector sim or QPU

            # QSD subspace selection
            basis_qsd = quantum_krylov_subspace_diagonalize(gram_q, k=K)
            readout_qsd = ridge_regression(project(phi_q, basis_qsd), y_noisy)

            # Classical baselines at matched k
            basis_pca = PCA(gram_q, k=K)
            basis_rp  = random_projection(phi_q, k=K)
            basis_ridge = ridge_subspace_select(phi_q, y_noisy, k=K)

            for method, basis in [(QSD, basis_qsd), (PCA, basis_pca),
                                    (RP, basis_rp), (RidgeSel, basis_ridge)]:
                acc, rmse, wallclock = train_and_eval(phi_q, basis, y_noisy, X_test, y_test)
                log_result(dataset, noise_level, seed, method, acc, rmse, wallclock)

# Ablation: replace quantum Gram matrix with classical-shadow-estimated Gram matrix
gram_shadow = classical_shadow_estimate(X, n_qubits=8)
basis_qsd_shadow = quantum_krylov_subspace_diagonalize(gram_shadow, k=K)
# compare basis_qsd_shadow performance vs basis_qsd (real quantum) performance

# Hardware validation subset
for backend in [ibm_qpu, ionq_qpu]:
    run_subset(datasets=[Adult, Ionosphere], noise=[0,20,30], seeds=10, backend=backend)

statistical_analysis(all_results)  # paired t-test, Holm correction, slope-difference test