Mode connectivity in the loss landscape of parameterized quantum circuits
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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.
Key facts. Cited by 1 paper 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
28 of 50 references.
References · 28
- 2014Adam: A Method for Stochastic Optimizationcited by 37,240
- 2017Visualizing the Loss Landscape of Neural Netscited by 1,130
- 2018Supervised learning with quantum enhanced feature spacescited by 665
- 2018Barren plateaus in quantum neural network training landscapescited by 630
- 2018Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNscited by 588
- 2018Gradient Descent Finds Global Minima of Deep Neural Networkscited by 574
- 2020The power of quantum neural networkscited by 379
- 2020The effect of data encoding on the expressive power of variational quantum machine learning modelscited by 333
- 2019Parameterized quantum circuits as machine learning modelscited by 332
- 2018Essentially No Barriers in Neural Network Energy Landscapecited by 330
- 2014The Loss Surfaces of Multilayer Networkscited by 280
- 2016Deep Learning without Poor Local Minimacited by 234
16 more
- 2020Noise-Induced Barren Plateaus in Variational Quantum Algorithmscited by 193
- 2014Qualitatively characterizing neural network optimization problemscited by 188
- 2021Connecting ansatz expressibility to gradient magnitudes and barren plateauscited by 180
- 2019Quantum Natural Gradientcited by 106
- 2017Spurious Local Minima are Common in Two-Layer ReLU Neural Networkscited by 104
- 2016Topology and Geometry of Half-Rectified Network Optimizationcited by 102
- 2020Entanglement Induced Barren Plateauscited by 101
- 2019Explaining Landscape Connectivity of Low-cost Solutions for Multilayer Netscited by 63
- 2021Equivalence of quantum barren plateaus to cost concentration and narrow gorgescited by 53
- 2019Shaping the learning landscape in neural networks around wide flat minimacited by 47
- 2018Comparing Dynamics: Deep Neural Networks versus Glassy Systemscited by 42
- 2017Gradient Descent Learns One-hidden-layer CNN: Don't be Afraid of Spurious Local Minimacited by 40
- 2019Landscape Connectivity and Dropout Stability of SGD Solutions for Over-parameterized Neural Networkscited by 35
- 2019Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithmscited by 31
- 2018Glassy nature of the hard phase in inference problemscited by 9
- 2016Quantum Control Landscapes Are Almost Always Trap Freecited by 4
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Citing papers per year: 2026: 1.
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