# Mode connectivity in the loss landscape of parameterized quantum circuits

arXiv: https://arxiv.org/abs/2111.05311 · HTML: https://mlsanity.com/paper/2111.05311/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 50 references that are in the map.
- First posted on arXiv 9 Nov 2021.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Deep Learning without Poor Local Minima](https://mlsanity.com/paper/1605.07110/) (2016)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Qualitatively characterizing neural network optimization problems](https://mlsanity.com/paper/1412.6544/) (2014)
- [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)
- [Spurious Local Minima are Common in Two-Layer ReLU Neural Networks](https://mlsanity.com/paper/1712.08968/) (2017)
- [Topology and Geometry of Half-Rectified Network Optimization](https://mlsanity.com/paper/1611.01540/) (2016)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Explaining Landscape Connectivity of Low-cost Solutions for Multilayer Nets](https://mlsanity.com/paper/1906.06247/) (2019)
- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)
- [Shaping the learning landscape in neural networks around wide flat minima](https://mlsanity.com/paper/1905.07833/) (2019)
- [Comparing Dynamics: Deep Neural Networks versus Glassy Systems](https://mlsanity.com/paper/1803.06969/) (2018)
- [Gradient Descent Learns One-hidden-layer CNN: Don't be Afraid of Spurious Local Minima](https://mlsanity.com/paper/1712.00779/) (2017)
- [Landscape Connectivity and Dropout Stability of SGD Solutions for Over-parameterized Neural Networks](https://mlsanity.com/paper/1912.10095/) (2019)
- [Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms](https://mlsanity.com/paper/1901.05374/) (2019)
- [Glassy nature of the hard phase in inference problems](https://mlsanity.com/paper/1805.05857/) (2018)
- [Quantum Control Landscapes Are Almost Always Trap Free](https://mlsanity.com/paper/1608.06198/) (2016)

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

- [Ravines in quantum cost landscapes: opportunities for improved VQA predictions](https://mlsanity.com/paper/2607.01329/) (2026)

## Abstract (arXiv)

Variational training of parameterized quantum circuits (PQCs) underpins many workflows employed on near-term noisy intermediate scale quantum (NISQ) devices. It is a hybrid quantum-classical approach that minimizes an associated cost function in order to train a parameterized ansatz. In this paper we adapt the qualitative loss landscape characterization for neural networks introduced in citegoodfellow2014qualitatively,li2017visualizing and tests for connectivity used in citedraxler2018essentially to study the loss landscape features in PQC training. We present results for PQCs trained on a simple regression task, using the bilayer circuit ansatz, which consists of alternating layers of parameterized rotation gates and entangling gates. Multiple circuits are trained with 3 different batch gradient optimizers: stochastic gradient descent, the quantum natural gradient, and Adam. We identify large features in the landscape that can lead to faster convergence in training workflows.