Quantum resource generation in dual-use quantum hardware can be enhanced by algorithms inspired by complex matrix interpolation techniques used in multi-manifold learning.

On a specified class of dual-use quantum hardware (superconducting transmon or trapped-ion platforms exposing programmable coupling/drive Hamiltonians), a control-pulse or circuit-parameter optimizer that uses complex matrix interpolation methods borrowed from multi-manifold learning (e.g., Riemannian interpolation on Grassmann/Stiefel manifolds, geodesic barycenters of unitary/density-matrix manifolds, or manifold-regularized low-rank completion of Hamiltonian parameter grids) will produce entangled-state or quantum-battery charging protocols that reach a target entanglement measure (e.g., concurrence ≥0.95 or logarithmic negativity within 5% of theoretical max) or target quantum battery ergotropy/power in fewer optimization iterations, fewer hardware shots, and/or shorter gate-sequence depth than a matched baseline optimizer (gradient descent, Nelder-Mead, standard Bayesian optimization, or GRAPE/Krotov without manifold structure), at fixed hardware noise level and fixed compute budget. The claim is falsifiable: it requires demonstrating statistically significant (p<0.05, paired across ≥20 random seeds/hardware instances) improvement in at least one of {iterations-to-convergence, shots-to-convergence, achieved entanglement/ergotropy at fixed budget} without regression in the others beyond a pre-specified tolerance (10%).

Minimum viable test (MVT): simulate a 4-8 qubit entanglement-generation task (Bell/GHZ state preparation extended to a parameterized entangling-gate calibration problem) and a 2-4 mode quantum battery charging Hamiltonian, both represented as parameterized unitary families. Implement (a) baseline optimizers: vanilla gradient descent on pulse parameters, Nelder-Mead, and standard GP-based Bayesian optimization; (b) manifold-learning-inspired optimizer: model the objective landscape as a low-rank matrix over a discretized parameter grid, use Riemannian/Grassmann-manifold interpolation (e.g., fixed-rank matrix completion via manifold optimization, or geodesic interpolation between sampled unitaries) to propose next query points, akin to Bayesian optimization but with manifold-structured surrogate instead of GP kernel. Run both against a calibrated noisy simulator (Qiskit Aer noise model matched to a public IBM backend calibration file) for ≥20 random seeds per method per noise level (3 noise levels: ideal, low-noise, realistic NISQ). Measure entanglement/ergotropy attained vs. shots consumed and wall-clock optimizer time.

# Pseudocode: manifold-interpolation quantum control optimizer

class ManifoldSurrogateOptimizer:
    def __init__(self, param_dim, rank, manifold_type="grassmann"):
        self.manifold = pymanopt.manifolds.FixedRankEmbedded(param_dim, rank)
        self.observed_params = []
        self.observed_values = []

    def fit_surrogate(self):
        # Build partially-observed matrix M over discretized param grid
        M_partial = build_sparse_matrix(self.observed_params, self.observed_values)
        # Riemannian matrix completion: find low-rank M_hat close to M_partial on observed entries
        problem = pymanopt.Problem(manifold=self.manifold,
                                     cost=lambda X: completion_loss(X, M_partial))
        solver = pymanopt.solvers.ConjugateGradient()
        self.M_hat = solver.solve(problem)

    def propose_next_point(self):
        # Expected improvement over manifold-interpolated surrogate
        candidates = sample_grid_points(unobserved=True)
        ei_scores = [expected_improvement(self.M_hat, c) for c in candidates]
        return candidates[argmax(ei_scores)]

    def run_optimization_loop(self, objective_fn, budget_shots):
        shots_used = 0
        while shots_used < budget_shots:
            self.fit_surrogate()
            next_params = self.propose_next_point()
            value, shots = objective_fn(next_params)  # runs on simulator/hardware
            self.observed_params.append(next_params)
            self.observed_values.append(value)
            shots_used += shots
        return best(self.observed_values)

# Benchmark harness
for task in [entanglement_task, battery_charging_task]:
    for noise_level in [ideal, low_noise, nisq_realistic]:
        for optimizer in [GradDescent, NelderMead, GPBayesOpt, ManifoldSurrogateOptimizer]:
            for seed in range(20):
                result = optimizer.run_optimization_loop(task.objective, budget_shots=5000)
                log_result(task, noise_level, optimizer, seed, result)

statistically_compare(results, test="wilcoxon", correction="holm-bonferroni")