A Shifted Power Method for Homogenous Polynomial Optimization over Unit Spheres

Wang, Shuquan

doi:10.5539/jmr.v7n2p175

Cited by 3 publications

(2 citation statements)

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“…Basis encoding. Many quantum machine learning algorithms assume that the inputs x to the computation are encoded as binary strings represented by a computational basis state of the qubits [12,21]. For example, x = 01001 is represented by the 5-qubit basis state |01001 .…”

Section: A Feature-encoding Circuitsmentioning

confidence: 99%

Quantum Machine Learning in Feature Hilbert Spaces

2019

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The basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely to efficiently perform computations in an intractably large Hilbert space. In this paper we explore some theoretical foundations of this link and show how it opens up a new avenue for the design of quantum machine learning algorithms. We interpret the process of encoding inputs in a quantum state as a nonlinear feature map that maps data to quantum Hilbert space. A quantum computer can now analyse the input data in this feature space. Based on this link, we discuss two approaches for building a quantum model for classification. In the first approach, the quantum device estimates inner products of quantum states to compute a classically intractable kernel. This kernel can be fed into any classical kernel method such as a support vector machine. In the second approach, we can use a variational quantum circuit as a linear model that classifies data explicitly in Hilbert space. We illustrate these ideas with a feature map based on squeezing in a continuous-variable system, and visualise the working principle with 2-dimensional mini-benchmark datasets.arXiv:1803.07128v1 [quant-ph]

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Section: A Feature-encoding Circuitsmentioning

confidence: 99%

Quantum Machine Learning in Feature Hilbert Spaces

2019

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“…Based on quantum parallel processing, the related quantum algorithm is expected to exponentially speed up [3][4][5]. There currently exist several kinds of quantum classifiers, one are inspired by their corresponding classical classifiers with their kernel parts replaced by quantum circuits [6][7][8][9][10], some are inspired by neural networks [11][12][13][14][15], in which a plenty of qubits and quantum gates are commonly supplied to achieve the data storage [11,13,14] and parameter optimization [15], and others [16][17][18][19][20][21][22][23][24][25][26] are proposed with a hybrid quantum-classical (HQC) structure where the evaluations are performed by quantum hardware while the parameters are optimized with classical methods in classical computer.…”

Section: Introductionmentioning

confidence: 99%

Quantum algorithm for neural network enhanced multi-class parallel classification

Zhang¹,

He²,

Zhao³

2022

Preprint

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Using the properties of quantum superposition, we propose a quantum classification algorithm to efficiently perform multi-class classification tasks, where the training data are loaded into parameterized operators which are applied to the basis of the quantum state in quantum circuit composed by sample register and label register, and the parameters of quantum gates are optimized by a hybrid quantum-classical method, which is composed of a trainable quantum circuit and a gradientbased classical optimizer. After several quantum-to-class repetitions, the quantum state is optimal that the state in sample register is the same as that in label register. For a classification task of Lclass, the analysis shows that the space and time complexity of the quantum circuit are O(L * logL) and O(logL), respectively. The numerical simulation results of 2-class task and 5-class task show that the proposed algorithm has a higher classification accuracy, faster convergence and higher expression ability. The classification accuracy and the speed of converging can also be improved by increasing the number times of applying multi-qubit controlled operators on the quantum circuit, especially for multiple classes classification.

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