Superpositional Gradient Descent: Harnessing Quantum Principles for
  Model Training
Authors: name: Ahmet Erdem Pamuk, name: Emir Kaan Özdemir, name: Şuayp Talha Kocabay

Large language models (LLMs) are increasingly trained with classical
optimization techniques like AdamW to improve convergence and generalization.
However, the mechanisms by which quantum-inspired methods enhance classical
training remain underexplored. We introduce Superpositional Gradient Descent
(SGD), a novel optimizer linking gradient updates with quantum superposition by
injecting quantum circuit perturbations. We present a mathematical framework
and implement hybrid quantum-classical circuits in PyTorch and Qiskit. On
synthetic sequence classification and large-scale LLM fine-tuning, SGD
converges faster and yields lower final loss than AdamW. Despite promising
results, scalability and hardware constraints limit adoption. Overall, this
work provides new insights into the intersection of quantum computing and deep
learning, suggesting practical pathways for leveraging quantum principles to
control and enhance model behavior.