Layerwise learning for quantum neural networks
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Abstract With the increased focus on quantum circuit learning for near-term applications on quantum devices, in conjunction with unique challenges presented by cost function landscapes of parametrized quantum circuits, strategies for effective training are becoming increasingly important. In order to ameliorate some of these challenges, we investigate a layerwise learning strategy for parametrized quantum circuits. The circuit depth is incrementally grown during optimization, and only subsets of parameters are updated in each training step. We show that when considering sampling noise, this strategy can help avoid the problem of barren plateaus of the error surface due to the low depth of circuits, low number of parameters trained in one step, and larger magnitude of gradients compared to training the full circuit. These properties make our algorithm preferable for execution on noisy intermediate-scale quantum devices. We demonstrate our approach on an image-classification task on handwritten digits, and show that layerwise learning attains an 8% lower generalization error on average in comparison to standard learning schemes for training quantum circuits of the same size. Additionally, the percentage of runs that reach lower test errors is up to 40% larger compared to training the full circuit, which is susceptible to creeping onto a plateau during training.
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An initialization strategy was developed specifically to address BPs in deep circuits by selecting at random a subset of parameters and choosing the remaining ones so that the circuit is a sequence of shallow unitaries that evaluates to the identity.
“Additionally, in Refs. [29, 205] an initialization strategy was developed specifically to address BPs in deep circuits. Here, one selects at random a subset of parameters in θ , and chooses the value of the remaining ones so that the circuit is a sequence of shallow unitaries that evaluates to the identity.”
From Variational quantum algorithms (2021) · cites this paper as [205]
Split into 2 atoms — 0 confirmed, 1 partially supported, 0 disputed, 1 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredThese quantum machine learning approaches need careful consideration of subtle issues that do not appear in classical algorithms and are strongly intertwined with the underlying hardware.
“Regardless of the conditions of their advantages, these approaches need careful consideration of subtle issues (see, e.g., Refs.[112-115]) that do not appear in classical algorithms and are, in particular, strongly intertwined with the underlying hardware.”
From Neutral atom quantum computing hardware: performance and end-user perspective (2023) · cites this paper as [113]
The entries of the Hessian vanish exponentially with the size of the system in models that are in a barren plateau.
“It was found that the entries of the Hessian vanish exponentially with the size of the system in models that are in a barren plateau.”
From The power of quantum neural networks (2021) · cites this paper as [32]
In the quantum realm, the negative effect of barren plateaus on training quantum neural networks has been linked to the Hessian matrix.
“In the quantum realm, the negative effect of barren plateaus on training quantum neural networks has been linked to the Hessian matrix [32].”
From The power of quantum neural networks (2021) · cites this paper as [32]
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Noisy intermediate-scale quantum (NISQ) algorithms
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Large gradients via correlation in random parameterized quantum circuits
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Equivalence of quantum barren plateaus to cost concentration and narrow gorges
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Learnability of Quantum Neural Networks
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Biology and medicine in the landscape of quantum advantages
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Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers
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A hybrid quantum–classical neural network with deep residual learning
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Anomaly detection with variational quantum generative adversarial networks
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Matrix product state pre-training for quantum machine learning
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Quantum computing of the Li6 nucleus via ordered unitary coupled clusters
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Barren plateaus in quantum tensor network optimization
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Adaptive pruning-based optimization of parameterized quantum circuits
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Decomposition of matrix product states into shallow quantum circuits
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Learning quantum data with the quantum earth mover’s distance
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Reformulation of the No-Free-Lunch Theorem for Entangled Datasets
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Variational quantum algorithms for trace distance and fidelity estimation
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A semi-agnostic ansatz with variable structure for variational quantum algorithms
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Generative Quantum Machine Learning via Denoising Diffusion Probabilistic Models
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Classification of Remote Sensing Images With Parameterized Quantum Gates
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Quantum generative adversarial networks with multiple superconducting qubits
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Development of variational quantum deep neural networks for image recognition
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Advances in Quantum Machine Learning and Deep Learning for Image Classification: A Survey
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Variational Learning for Quantum Artificial Neural Networks
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Quantum Machine Learning for Next-G Wireless Communications: Fundamentals and the Path Ahead
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Hybrid classical-quantum autoencoder for anomaly detection
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Abrupt transitions in variational quantum circuit training
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Reflection equivariant quantum neural networks for enhanced image classification
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Detecting and quantifying entanglement on near-term quantum devices
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Universal effectiveness of high-depth circuits in variational eigenproblems
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Training saturation in layerwise quantum approximate optimization
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Applying QNLP to Sentiment Analysis in Finance
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Hybrid quantum ResNet for car classification and its hyperparameter optimization
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ResQNets: a residual approach for mitigating barren plateaus in quantum neural networks
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Natural evolutionary strategies for variational quantum computation
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Quantum self-supervised learning
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Toward Trainability of Quantum Neural Networks
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Hamiltonian operator approximation for energy measurement and ground state preparation
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Mitigating Barren Plateaus of Variational Quantum Eigensolvers
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Climate Change Through Quantum Lens: Computing and Machine Learning
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A Quantum-Classical Hybrid Solution for Deep Anomaly Detection
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An invitation to distributed quantum neural networks
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Long-time simulations with high fidelity on quantum hardware
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Engineered dissipation to mitigate barren plateaus
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Hamiltonian Operator Approximation for Energy Measurement and Ground-State Preparation
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Variational quantum linear solver with a dynamic ansatz
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Entanglement entropy production in Quantum Neural Networks
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Learning Shallow Quantum Circuits
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The impact of cost function globality and locality in hybrid quantum neural networks on NISQ devices
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Bibliometric Analysis and Visualization of Quantum Engineering Technology
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- Authors
- Skolik, A., McClean, J. R., Mohseni, M., van der Smagt, P., & Leib, M.
- Affiliations
- Leiden University (NL)
- Google (United States) (US)
- Corresponding author
- Skolik, Andrea
- Venue
- Quantum Machine Intelligence
- Published
- 2021-01-25
- Volume
- 3
- Issue
- 1
- ISSN
- 2524-4906 (ISSN-L)
- 2524-4914
- OpenAlex
- W3004252283
- Cited by
- 324
- References
- 63
- Citations by year
- 2026: 43 · 2025: 58 · 2024: 65 · 2023: 59 · 2022: 46 · 2021: 48 · 2020: 5
- FWCI
- 19.09
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Locations
- Quantum Machine Intelligence (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- Funders
- Horizon 2020 (828826)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- quantum neural networks, variational quantum circuits, barren plateaus, NISQ devices, circuit depth, sampling noise, image classification, handwritten digits, generalization error
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