# Superpositional Gradient Descent: Harnessing Quantum Principles for Model Training

arXiv: https://arxiv.org/abs/2511.01918 · HTML: https://mlsanity.com/paper/2511.01918/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 34 references that are in the map.
- First posted on arXiv 1 Nov 2025.

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Escaping From Saddle Points --- Online Stochastic Gradient for Tensor Decomposition](https://mlsanity.com/paper/1503.02101/) (2015)
- [Why Can GPT Learn In-Context? Language Models Implicitly Perform Gradient Descent as Meta-Optimizers](https://mlsanity.com/paper/2212.10559/) (2022)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Beyond Convexity: Stochastic Quasi-Convex Optimization](https://mlsanity.com/paper/1507.02030/) (2015)
- [TensorFlow Quantum: A Software Framework for Quantum Machine Learning](https://mlsanity.com/paper/2003.02989/) (2020)
- [Machine learning & artificial intelligence in the quantum domain](https://mlsanity.com/paper/1709.02779/) (2017)
- [Quantum Variational Autoencoder](https://mlsanity.com/paper/1802.05779/) (2018)
- [Quantum support vector machine for big data classification](https://mlsanity.com/paper/1307.0471/) (2013)
- [Quantum Natural Language Processing](https://mlsanity.com/paper/2403.19758/) (2024)
- [Quantum Embedding with Transformer for High-dimensional Data](https://mlsanity.com/paper/2402.12704/) (2024)

## Abstract (arXiv)

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.