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  • Open Access

Quantum-inspired weight-constrained neural network: Reducing variable numbers by 100× compared to standard neural networks

Shaozhi Li*

M Sabbir Salek and Mashrur Chowdhury

Yao Wang†

  • National Center for Transportation Cybersecurity and Resiliency (TracR), Clemson University, South Carolina 29631, USA

  • National Center for Transportation Cybersecurity and Resiliency (TracR), Clemson University, South Carolina 29631, USA and Glenn Department of Civil Engineering, Clemson University, Clemson, South Carolina 29634, USA

  • *Contact author: lishaozhi@mail.neu.edu.cn
  • †Contact author: yao.wang@emory.edu
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Phys. Rev. Research 8, 013142 – Published 9 February, 2026

DOI: https://doi.org/10.1103/wb1b-ntpc

Abstract

Although quantum machine learning has shown great promise, the practical application of quantum computers remains constrained in the noisy intermediate-scale quantum era. To take advantage of quantum machine learning, we investigate the underlying mathematical principles of these quantum models and find that the quantum neural network with amplitude encoding is equivalent to a weight-constrained neural network. Motivated by this discovery, we develop a classical weight-constrained neural network. We find that this approach can reduce the number of variables in a classical neural network by a factor of 135 while preserving its accuracy. In addition, we develop a dropout method to enhance the robustness of quantum machine learning models, which are highly susceptible to adversarial attacks. This technique can also be applied to improve the adversarial robustness of the classical weight-constrained neural network, which is essential for industry applications, such as self-driving vehicles. Our work offers an approach to reduce the complexity of large classical neural networks, addressing a critical challenge in machine learning.

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Phys. Rev. Research 8, 013142– Published 9 February, 2026
  • Received 18 May 2025
  • Accepted 12 January 2026
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