# Ravines in quantum cost landscapes: opportunities for improved VQA predictions

arXiv: https://arxiv.org/abs/2607.01329 · HTML: https://mlsanity.com/paper/2607.01329/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 33 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [Empirical Analysis of the Hessian of Over-Parametrized Neural Networks](https://mlsanity.com/paper/1706.04454/) (2017)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Topology and Geometry of Half-Rectified Network Optimization](https://mlsanity.com/paper/1611.01540/) (2016)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)
- [Entangled Datasets for Quantum Machine Learning](https://mlsanity.com/paper/2109.03400/) (2021)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [A unifying account of warm start guarantees for patches of quantum landscapes](https://mlsanity.com/paper/2502.07889/) (2025)
- [Mode connectivity in the loss landscape of parameterized quantum circuits](https://mlsanity.com/paper/2111.05311/) (2021)

## Abstract (arXiv)

The geometric and topological structure of quantum cost landscapes (QCLs) governs the optimization and thus the predictive power of variational quantum algorithms (VQAs). We systematically analyze ravines - low-cost paths connecting local minima - using an adapted version of the nudged elastic band (NEB) algorithm, a method originating from theoretical chemistry. By training quantum neural networks (QNNs) to classify the concentratable entanglement of quantum states, we apply the NEB algorithm and numerically identify ravine structures in QCLs of hardware-efficient ansatzes. Beyond visualizing these ravines, we construct an ensemble prediction framework by averaging predictions from QNNs parameterized along the low-cost NEB path. We introduce a resource-light pre-training metric which quantifies local-prediction variability and serves as a strong performance indicator for VQAs, even beyond the scope of this study. When base classifiers are drawn from circuit and weight initializations exhibiting high local-prediction variability, the quantum-based NEB ensembles outperform both classical and naive quantum alternatives. Moreover, a complexity analysis shows that leveraging the ravine-like structure of QCLs with the QNN NEB approach substantially reduces computational costs compared to naive QNN ensembling. A depth and qubit scaling analysis indicates that ravines persist across both scalings, and that, despite the expected growth in resource requirements with the qubit scaling, the NEB approach also accelerates convergence over the naive alternative.