Quantum-Enhanced Weight Optimization for Neural Networks Using Grover's Algorithm

The main approach to hybrid quantum-classical neural networks (QNN) is employing quantum computing to build a neural network (NN) that has quantum features, which is then optimized classically. Here, we propose a different strategy: to use quantum computing in order to optimize the weights of a classical NN. As such, we design an instance of Grover's quantum search algorithm to accelerate the search for the optimal parameters of an NN during the training process, a task traditionally performed using the backpropagation algorithm with the gradient descent method. Indeed, gradient descent has issues such as exploding gradient, vanishing gradient, or convexity problem. Other methods tried to address such issues with strategies like genetic searches, but they carry additional problems like convergence consistency. Our original method avoids these issues -- because it does not calculate gradients -- and capitalizes on classical architectures' robustness and Grover's quadratic speedup in high-dimensional search spaces to significantly reduce test loss (58.75%) and improve test accuracy (35.25%), compared to classical NN weight optimization, on small datasets. Unlike most QNNs that are trained on small datasets only, our method is also scalable, as it allows the optimization of deep networks; for an NN with 3 hidden layers, trained on the Digits dataset from scikit-learn, we obtained a mean accuracy of 97.7%. Moreover, our method requires a much smaller number of qubits compared to other QNN approaches, making it very practical for near-future quantum computers that will still deliver a limited number of logical qubits.

Fractional dynamics foster deep learning of COPD stage prediction

Chronic obstructive pulmonary disease (COPD) is one of the leading causes of death worldwide. Current COPD diagnosis (i.e., spirometry) could be unreliable because the test depends on an adequate effort from the tester and testee. Moreover, the early diagnosis of COPD is challenging. We address COPD detection by constructing two novel physiological signals datasets (4432 records from 54 patients in the WestRo COPD dataset and 13824 medical records from 534 patients in the WestRo Porti COPD dataset). The authors demonstrate their complex coupled fractal dynamical characteristics and perform a fractional-order dynamics deep learning analysis to diagnose COPD. The authors found that the fractional-order dynamical modeling can extract distinguishing signatures from the physiological signals across patients with all COPD stages from stage 0 (healthy) to stage 4 (very severe). They use the fractional signatures to develop and train a deep neural network that predicts COPD stages based on the input features (such as thorax breathing effort, respiratory rate, or oxygen saturation). The authors show that the fractional dynamic deep learning model (FDDLM) achieves a COPD prediction accuracy of 98.66% and can serve as a robust alternative to spirometry. The FDDLM also has high accuracy when validated on a dataset with different physiological signals.