Absence of Barren Plateaus in Quantum Convolutional Neural Networks

Pesah, Arthur; Cerezo, M.; Wang, Samson; Volkoff, Tyler; Sornborger, Andrew; Coles, Patrick J.

doi:10.1103/physrevx.11.041011

Cited by 183 publications

(121 citation statements)

References 43 publications

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“…In this work we study the trainability and the existence of barren plateaus in QML models. Our work represents a general treatment that goes beyond previous analysis of gradient scaling and trainability in specific QML models [49][50][51][52][53][54][55][56]. Our main results are two-fold.…”

Section: Introductionmentioning

confidence: 85%

Subtleties in the trainability of quantum machine learning models

Thanasilp¹,

Wang²,

Nghiem³

et al. 2021

Preprint

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A new paradigm for data science has emerged, with quantum data, quantum models, and quantum computational devices. This field, called Quantum Machine Learning (QML), aims to achieve a speedup over traditional machine learning for data analysis. However, its success usually hinges on efficiently training the parameters in quantum neural networks, and the field of QML is still lacking theoretical scaling results for their trainability. Some trainability results have been proven for a closely related field called Variational Quantum Algorithms (VQAs). While both fields involve training a parametrized quantum circuit, there are crucial differences that make the results for one setting not readily applicable to the other. In this work we bridge the two frameworks and show that gradient scaling results for VQAs can also be applied to study the gradient scaling of QML models. Our results indicate that features deemed detrimental for VQA trainability can also lead to issues such as barren plateaus in QML. Consequently, our work has implications for several QML proposals in the literature. In addition, we provide theoretical and numerical evidence that QML models exhibit further trainability issues not present in VQAs, arising from the use of a training dataset. We refer to these as dataset-induced barren plateaus. These results are most relevant when dealing with classical data, as here the choice of embedding scheme (i.e., the map between classical data and quantum states) can greatly affect the gradient scaling.

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Section: Introductionmentioning

confidence: 85%

Subtleties in the trainability of quantum machine learning models

Thanasilp¹,

Wang²,

Nghiem³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…As shown in Fig. 5, high trainability can be achieved in QNNs with at most a polynomially decaying gradient [66,67], such as the convolutional QNN and QNN with a tree tensor structure or with a step controlled structure. Other structures that are mild or entirely absent from BPs include the Hamiltonian variational ansatz (HVA) [68], and system-agnostic ansatzs based on trainable Fourier coefficients of Hamiltonian system parameters [69].…”

Section: Algorithm Design For Mitigating Barren-plateau Effectsmentioning

confidence: 99%

The Optimization Landscape of Hybrid Quantum-Classical Algorithms: from Quantum Control to NISQ Applications

Ge¹,

Wu²,

Rabitz³

2022

Preprint

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“…This limitation of QNNs makes it unclear whether or not the QNNs can provide any advantage over their classical counterparts. However, recently there have been some efforts to understand and overcome the issue of barren plateaus in QNNs [50,51], opening the doors for real world applications of QNNs.…”

Section: Generalizationerror(%) =mentioning

confidence: 99%

Design Space Exploration of Hybrid Quantum–Classical Neural Networks

Kashif

Al-Kuwari

2021

Electronics

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The unprecedented success of classical neural networks and the recent advances in quantum computing have motivated the research community to explore the interplay between these two technologies, leading to the so-called quantum neural networks. In fact, universal quantum computers are anticipated to both speed up and improve the accuracy of neural networks. However, whether such quantum neural networks will result in a clear advantage on noisy intermediate-scale quantum (NISQ) devices is still not clear. In this paper, we propose a systematic methodology for designing quantum layer(s) in hybrid quantum–classical neural network (HQCNN) architectures. Following our proposed methodology, we develop different variants of hybrid neural networks and compare them with pure classical architectures of equivalent size. Finally, we empirically evaluate our proposed hybrid variants and show that the addition of quantum layers does provide a noticeable computational advantage.

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Absence of Barren Plateaus in Quantum Convolutional Neural Networks

Cited by 183 publications

References 43 publications

Subtleties in the trainability of quantum machine learning models

Subtleties in the trainability of quantum machine learning models

The Optimization Landscape of Hybrid Quantum-Classical Algorithms: from Quantum Control to NISQ Applications

Design Space Exploration of Hybrid Quantum–Classical Neural Networks

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