Quantum Kernel Methods for Solving Differential Equations

Paine, Annie E.; Elfving, Vincent E.; Kyriienko, Oleksandr

doi:10.48550/arxiv.2203.08884

Cited by 4 publications

(2 citation statements)

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“…Encoding layers are critical for developing QNN as the data-encoding strategy largely defines the QNN expressivity, e.g., the features QNN can represent [ 59 , 61 ]. Feature maps are critical building blocks for developing scientific quantum machine learning and Differentiable Quantum Circuit (DQC) [ 62 , 63 , 64 ]. Variational Layers.…”

Section: Quantum Neural Network Technologies and Methodologiesmentioning

confidence: 99%

Programming Quantum Neural Networks on NISQ Systems: An Overview of Technologies and Methodologies

Markidis

2023

Entropy

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Noisy Intermediate-Scale Quantum (NISQ) systems and associated programming interfaces make it possible to explore and investigate the design and development of quantum computing techniques for Machine Learning (ML) applications. Among the most recent quantum ML approaches, Quantum Neural Networks (QNN) emerged as an important tool for data analysis. With the QNN advent, higher-level programming interfaces for QNN have been developed. In this paper, we survey the current state-of-the-art high-level programming approaches for QNN development. We discuss target architectures, critical QNN algorithmic components, such as the hybrid workflow of Quantum Annealers and Parametrized Quantum Circuits, QNN architectures, optimizers, gradient calculations, and applications. Finally, we overview the existing programming QNN frameworks, their software architecture, and associated quantum simulators.

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Section: Quantum Neural Network Technologies and Methodologiesmentioning

confidence: 99%

Programming Quantum Neural Networks on NISQ Systems: An Overview of Technologies and Methodologies

Markidis

2023

Entropy

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“…There has also been some progress made on realizing quantum convolutional neural networks [30,31], and quantum graph neural networks [32]. The work on other supervised QML tasks are on regression [21,33], solving linear [34,35] and differential equations [36,37,33]. Even more generally, quantum computing has shown promises of speedups in financial applications [38] including portfolio optimization [39,40], risk prediction [41,42] and pricing of financial contracts [43,44].…”

Section: Related Workmentioning

confidence: 99%

Classical ensemble of Quantum-classical ML algorithms for Phishing detection in Ethereum transaction networks

Ray¹,

Guddanti²,

Ajith³

et al. 2022

Preprint

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Ethereum is one of the most valuable blockchain networks in terms of the total monetary value locked in it, and arguably been the most active network where new blockchain innovations in research and applications are demonstrated. But, this also leads to Ethereum network being susceptible to a wide variety of threats and attacks in an attempt to gain unreasonable advantage or to undermine the value of the users. Even with the state-of-art classical ML algorithms, detecting such attacks is still hard. This motivated us to build a hybrid system of quantum-classical algorithms that improves phishing detection in financial transaction networks. This paper presents a classical ensemble pipeline of classical and quantum algorithms and a detailed study benchmarking existing Quantum Machine Learning (QML) algorithms such as Quantum Support Vector Machine (QSVM) and Variational Quantum Classifier (VQC). With the current generation of quantum hardware available, smaller datasets are more suited to the QML models and most research restricts to hundreds of samples. However, we experimented on different data sizes and report results with a test data of 12K transaction nodes, which is to the best of the authors knowledge the largest QML experiment run so far on any real quantum hardware. The classical ensembles of quantum-classical models improved the macro F-score as well as phishing F-score. One key observation is QSVM constantly gives lower false positives, thereby higher precision compared with any other classical or quantum network, which is always preferred for any anomaly detection problem. This is true for QSVMs when used individually or via bagging of same models or in combination with other classical/quantum models making it the most advantageous quantum algorithm so far. The proposed ensemble framework is generic and can be applied for any classification task. All codes are available as tutorial notebooks: https://github.com/anupamaray/EnsembleQML_application along with the data required to reproduce the results reported.

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Extracting a function encoded in amplitudes of a quantum state by tensor network and orthogonal function expansion

Miyamoto

Ueda

2023

Quantum Inf Process

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There are quantum algorithms for finding a function f satisfying a set of conditions, such as solving partial differential equations, and these achieve exponential quantum speedup compared to existing classical methods, especially when the number d of the variables of f is large. In general, however, these algorithms output the quantum state which encodes f in the amplitudes, and reading out the values of f as classical data from such a state can be so time-consuming that the quantum speedup is ruined. In this study, we propose a general method for this function readout task. Based on the function approximation by a combination of tensor network and orthogonal function expansion, we present a quantum circuit and its optimization procedure to obtain an approximating function of f that has a polynomial number of degrees of freedom with respect to d and is efficiently evaluable on a classical computer. We also conducted a numerical experiment to approximate a finance-motivated function to demonstrate that our method works.

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Quantum Kernel Methods for Solving Differential Equations

Cited by 4 publications

References 50 publications

Programming Quantum Neural Networks on NISQ Systems: An Overview of Technologies and Methodologies

Programming Quantum Neural Networks on NISQ Systems: An Overview of Technologies and Methodologies

Classical ensemble of Quantum-classical ML algorithms for Phishing detection in Ethereum transaction networks

Extracting a function encoded in amplitudes of a quantum state by tensor network and orthogonal function expansion

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