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. Since the dawn of Deep Learning (DL) in 2012, one of its most investigated topics has been the convergence of NN [1]. Traditionally, we may achieve convergence after minimizing the loss function by calculating the loss's derivative for the network's initial weights. This way, the gradient descent method determines the optimal parameter values [2]. There are several variants of gradient descent in the literature: stochastic gradient descent, batch gradient descent, and mini-batch gradient descent [3], [4].