# Quantum Natural Stochastic Pairwise Coordinate Descent

arXiv: https://arxiv.org/abs/2407.13858 · HTML: https://mlsanity.com/paper/2407.13858/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 90 references that are in the map.
- First posted on arXiv 18 Jul 2024.

## Builds on (most cited first, 16 of 16)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms](https://mlsanity.com/paper/1901.05374/) (2019)
- [Advances in Quantum Deep Learning: An Overview](https://mlsanity.com/paper/2005.04316/) (2020)
- [Universal discriminative quantum neural networks](https://mlsanity.com/paper/1805.08654/) (2018)
- [Optimizing Quantum Federated Learning Based on Federated Quantum Natural Gradient Descent](https://mlsanity.com/paper/2303.08116/) (2023)
- [Toward Physically Realizable Quantum Neural Networks](https://mlsanity.com/paper/2203.12092/) (2022)
- [Quantum chi-squared tomography and mutual information testing](https://mlsanity.com/paper/2305.18519/) (2023)
- [Quantum Capsule Networks](https://mlsanity.com/paper/2201.01778/) (2022)
- [LAWS: Look Around and Warm-Start Natural Gradient Descent for Quantum Neural Networks](https://mlsanity.com/paper/2205.02666/) (2022)
- [Experimental quantum natural gradient optimization in photonics](https://mlsanity.com/paper/2310.07371/) (2023)

## Built on by (most cited first, 1 of 1)

- [Quantum Federated Learning: A Comprehensive Survey](https://mlsanity.com/paper/2508.15998/) (2025)

## Abstract (arXiv)

Variational quantum algorithms, optimized using gradient-based methods, often exhibit sub-optimal convergence performance due to their dependence on Euclidean geometry. Quantum natural gradient descent (QNGD) is a more efficient method that incorporates the geometry of the state space via a quantum information metric. However, QNGD is computationally intensive and suffers from high sample complexity. In this work, we formulate a novel quantum information metric and construct an unbiased estimator for this metric using single-shot measurements. We develop a quantum optimization algorithm that leverages the geometry of the state space via this estimator while avoiding full-state tomography, as in conventional techniques. We provide the convergence analysis of the algorithm under mild conditions. Furthermore, we provide experimental results that demonstrate the better sample complexity and faster convergence of our algorithm compared to the state-of-the-art approaches. Our results illustrate the algorithm's ability to avoid saddle points and local minima.