Superpositional Gradient Descent: Harnessing Quantum Principles for Model Training

TL;DR

This paper introduces Superpositional Gradient Descent, a quantum-inspired optimizer that improves training speed and results of large language models by integrating quantum principles into classical optimization.

Contribution

It presents a novel quantum-inspired optimizer, Superpositional Gradient Descent, with a mathematical framework and implementation that enhances model training.

Findings

SGD converges faster than AdamW on synthetic and large-scale tasks.

SGD achieves lower final loss compared to AdamW.

Scalability and hardware constraints limit practical adoption.

Abstract

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.