Adaptive Grover-driven optimization for quantum-inspired deep learning: A gradient-free training framework

Irsa Sajjad; Huda M. Alshanbari; Mohammed M. A. Almazah; Hanen Louati; Sana Rauf; Irsa Sajjad; Huda M. Alshanbari; Mohammed M. A. Almazah; Hanen Louati; Sana Rauf

doi:10.3934/math.20251168

AIMS Mathematics

2025, Volume 10, Issue 11: 26568-26592. doi: 10.3934/math.20251168

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Research article

Adaptive Grover-driven optimization for quantum-inspired deep learning: A gradient-free training framework

1.
Department of Mathematics, National University of Modern Languages, Islamabad, Pakistan; irsa.sajjad@numl.edu.pk
2.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia; hmalshanbari@pnu.edu.sa
3.
Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil 61421, Saudi Arabia; mmalmazah@kku.edu.sa
4.
Mathematics Department, Faculty of Science, Northern Border University, Arar, KSA, Saudi Arabia; Hanen.Louati@nbu.edu.sa

Received: 16 August 2025 Revised: 10 October 2025 Accepted: 04 November 2025 Published: 17 November 2025
MSC : 91A81, 82B10

Training deep neural networks remains difficult due to vanishing gradients, non-convex loss surfaces, and hyperparameter sensitivity. These obstacles are compounded by quantum machine learning, where barren plateaus, circuit depth, and hardware noise restrict the applicability of gradient-based approaches. To overcome these drawbacks, this study presents adaptive Grover-driven parallel quantum optimization (AG-PQO), a hybrid, gradient-free scheme that leverages Grover's quadratic search speedup, along with adaptive loss-aware discretization and fidelity-based regularization. In contrast to more classical optimizers, such as Adam or evolutionary strategies (ES), which are either sensitive to the adequacy of the gradient update or exhibit poor scaling behavior, AG-PQO optimizes by performing Grover-accelerated candidate exploration across layers and reuses high-quality solutions in quantum memory caching. Testing indicates that AG-PQO yields higher accuracy, 2%–3% above Adam and ES, and faster convergence with less end-value loss than Adam, ES, and quantum feedforward-backpropagation (QFB). It is worth noting that AG-PQO remains stable at the simulated noise level of NISQ and has the potential to scale to near-term quantum processors.
Citation: Irsa Sajjad, Huda M. Alshanbari, Mohammed M. A. Almazah, Hanen Louati, Sana Rauf. Adaptive Grover-driven optimization for quantum-inspired deep learning: A gradient-free training framework[J]. AIMS Mathematics, 2025, 10(11): 26568-26592. doi: 10.3934/math.20251168

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Abstract

Training deep neural networks remains difficult due to vanishing gradients, non-convex loss surfaces, and hyperparameter sensitivity. These obstacles are compounded by quantum machine learning, where barren plateaus, circuit depth, and hardware noise restrict the applicability of gradient-based approaches. To overcome these drawbacks, this study presents adaptive Grover-driven parallel quantum optimization (AG-PQO), a hybrid, gradient-free scheme that leverages Grover's quadratic search speedup, along with adaptive loss-aware discretization and fidelity-based regularization. In contrast to more classical optimizers, such as Adam or evolutionary strategies (ES), which are either sensitive to the adequacy of the gradient update or exhibit poor scaling behavior, AG-PQO optimizes by performing Grover-accelerated candidate exploration across layers and reuses high-quality solutions in quantum memory caching. Testing indicates that AG-PQO yields higher accuracy, 2%–3% above Adam and ES, and faster convergence with less end-value loss than Adam, ES, and quantum feedforward-backpropagation (QFB). It is worth noting that AG-PQO remains stable at the simulated noise level of NISQ and has the potential to scale to near-term quantum processors.

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