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

arXiv: https://arxiv.org/abs/2504.14568 · HTML: https://mlsanity.com/paper/2504.14568/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 37 references that are in the map.
- First posted on arXiv 20 Apr 2025.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Dive into Deep Learning](https://mlsanity.com/paper/2106.11342/) (2021)
- [Quantum Perceptron Models](https://mlsanity.com/paper/1602.04799/) (2016)
- [A Grover-search Based Quantum Learning Scheme for Classification](https://mlsanity.com/paper/1809.06056/) (2018)
- [Simulation of a Variational Quantum Perceptron using Grover's Algorithm](https://mlsanity.com/paper/2305.11040/) (2023)
- [Quantum Neural Network for Quantum Neural Computing](https://mlsanity.com/paper/2305.08544/) (2023)
- [Gradient Descent based Optimization Algorithms for Deep Learning Models Training](https://mlsanity.com/paper/1903.03614/) (2019)
- [Quantum Neural Networks in Practice: A Comparative Study with Classical Models from Standard Data Sets to Industrial Images](https://mlsanity.com/paper/2411.19276/) (2024)
- [Developing Mathematical Oracle Functions for Grover Quantum Search Algorithm](https://mlsanity.com/paper/2109.05921/) (2021)
- [BGADAM: Boosting based Genetic-Evolutionary ADAM for Neural Network Optimization](https://mlsanity.com/paper/1908.08015/) (2019)

## Built on by (most cited first, 1 of 1)

- [Quantum Deep Learning Still Needs a Quantum Leap](https://mlsanity.com/paper/2511.01253/) (2025)

## Abstract (arXiv)

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.