# LAWS: Look Around and Warm-Start Natural Gradient Descent for Quantum Neural Networks

arXiv: https://arxiv.org/abs/2205.02666 · HTML: https://mlsanity.com/paper/2205.02666/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 50 references that are in the map.
- First posted on arXiv 5 May 2022.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Lookahead Optimizer: k steps forward, 1 step back](https://mlsanity.com/paper/1907.08610/) (2019)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)
- [Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms](https://mlsanity.com/paper/1901.05374/) (2019)
- [Optimal training of variational quantum algorithms without barren plateaus](https://mlsanity.com/paper/2104.14543/) (2021)
- [TENGraD: Time-Efficient Natural Gradient Descent with Exact Fisher-Block Inversion](https://mlsanity.com/paper/2106.03947/) (2021)

## Built on by (most cited first, 3 of 3)

- [Scalable Quantum Neural Networks for Classification](https://mlsanity.com/paper/2208.07719/) (2022)
- [Quantum Natural Stochastic Pairwise Coordinate Descent](https://mlsanity.com/paper/2407.13858/) (2024)
- [Quantum Machine Learning via Contrastive Training](https://mlsanity.com/paper/2511.13497/) (2025)

## Abstract (arXiv)

Variational quantum algorithms (VQAs) have recently received significant attention from the research community due to their promising performance in Noisy Intermediate-Scale Quantum computers (NISQ). However, VQAs run on parameterized quantum circuits (PQC) with randomly initialized parameters are characterized by barren plateaus (BP) where the gradient vanishes exponentially in the number of qubits. In this paper, we first review quantum natural gradient (QNG), which is one of the most popular algorithms used in VQA, from the classical first-order optimization point of view. Then, we proposed a underlineLook underlineAround underlineWarm-underlineStart QNG (LAWS) algorithm to mitigate the widespread existing BP issues. LAWS is a combinatorial optimization strategy taking advantage of model parameter initialization and fast convergence of QNG. LAWS repeatedly reinitializes parameter search space for the next iteration parameter update. The reinitialized parameter search space is carefully chosen by sampling the gradient close to the current optimal. Moreover, we present a unified framework (WS-SGD) for integrating parameter initialization techniques into the optimizer. We provide the convergence proof of the proposed framework for both convex and non-convex objective functions based on Polyak-Lojasiewicz (PL) condition. Our experiment results show that the proposed algorithm could mitigate the BP and have better generalization ability in quantum classification problems.