Quantum-enhanced neural networks in the neural tangent kernel framework

Nakaji, Kouhei; Tezuka, Hiroyuki; Yamamoto, Naoki

doi:10.48550/arxiv.2109.03786

Cited by 8 publications

(8 citation statements)

References 27 publications

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“…Besides, it is noted that quantum neural tangent kernel (QNTK) theory [51][52][53] is developed recently, which can be applied to QNNs.…”

Section: Discussionmentioning

confidence: 99%

Efficient Quantum Feature Extraction for CNN-based Learning

Dou¹,

Cui²

2022

Preprint

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Recent work has begun to explore the potential of parametrized quantum circuits (PQCs) as general function approximators. In this work, we propose a quantum-classical deep network structure to enhance classical CNN model discriminability. The convolutional layer uses linear filters to scan the input data. Moreover, we build PQC, which is a more potent function approximator, with more complex structures to capture the features within the receptive field. The feature maps are obtained by sliding the PQCs over the input in a similar way as CNN. We also give a training algorithm for the proposed model. The hybrid models used in our design are validated by numerical simulation. We demonstrate the reasonable classification performances on MNIST and we compare the performances with models in different settings. The results disclose that the model with ansatz in high expressibility achieves lower cost and higher accuracy.

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“…Besides, it is noted that quantum neural tangent kernel (QNTK) theory [51][52][53] is developed recently, which can be applied to QNNs.…”

Section: Discussionmentioning

confidence: 99%

Efficient Quantum Feature Extraction for CNN-based Learning

Dou¹,

Cui²

2022

Preprint

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“…Interestingly, the circuit-based QNN can be viewed as a kernel method with a quantum-enhanced feature map [161,176,296]. Furthermore, analysis has been performed in the neural tangent kernel framework [179] to show the benefits of using a quantum-enhanced feature map [161] in conjunction with a classical NN [250].…”

Section: Quantum Feedforward Neural Networkmentioning

confidence: 99%

A Survey of Quantum Computing for Finance

Herman¹,

Googin²,

Liu³

et al. 2022

Preprint

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Quantum computers are expected to surpass the computational capabilities of classical computers during this decade and have transformative impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from quantum computing, not only in the medium and long terms, but even in the short term. This survey paper presents a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on Monte Carlo integration, optimization, and machine learning, showing how these solutions, adapted to work on a quantum computer, can help solve more efficiently and accurately problems such as derivative pricing, risk analysis, portfolio optimization, natural language processing, and fraud detection. We also discuss the feasibility of these algorithms on near-term quantum computers with various hardware implementations and demonstrate how they relate to a wide range of use cases in finance. We hope this article will not only serve as a reference for academic researchers and industry practitioners but also inspire new ideas for future research.

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“…Tremendous classical kernel methods [45,46] have been proposed to learn the non-linear functions or decision boundaries. With the rapid development of quantum computers, there is a growing interest in exploring whether the quantum kernel method can surpass the classical kernel [35,36,39,[47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. Here we leverage the quantum kernel as our kernel function, which is defined as…”

Section: Preliminariesmentioning

confidence: 99%

Provable Advantage in Quantum Phase Learning via Quantum Kernel Alphatron

Wu¹,

Wu²,

Wang³

et al. 2021

Preprint

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Can we use a quantum computer to speed up classical machine learning in solving problems of practical significance? Here, we study this open question focusing on the quantum phase learning problem, an important task in many-body quantum physics. We prove that, under widely believed complexity theory assumptions, quantum phase learning problem cannot be efficiently solved by machine learning algorithms using classical resources and classical data. Whereas using quantum data, we theoretically prove the universality of quantum kernel Alphatron in efficiently predicting quantum phases, indicating quantum advantages in this learning problem. We numerically benchmark the algorithm for a variety of problems, including recognizing symmetry-protected topological phases and symmetry-broken phases. Our results highlight the capability of quantum machine learning in efficient prediction of quantum phases.

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Quantum-enhanced neural networks in the neural tangent kernel framework

Cited by 8 publications

References 27 publications

Efficient Quantum Feature Extraction for CNN-based Learning

Efficient Quantum Feature Extraction for CNN-based Learning

A Survey of Quantum Computing for Finance

Provable Advantage in Quantum Phase Learning via Quantum Kernel Alphatron

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