Quantum kernel principal component analysis method

Abstract

The invention discloses a quantum kernel principal component analysis method. The method comprises the steps: combining the truncation Taylor expansion and the Hamiltonian quantity simulation technology, and achieving the effective Hamiltonian quantity simulation of a general nonlinear kernel matrix; preparing a kernel matrix quantum state by adopting quantum arithmetic to serve as input of a quantum phase estimation algorithm, realizing the quantum characteristic value solution of the kernel matrix, and finally outputting a target quantum state subjected to quantum kernel principal componentanalysis by combining controlled rotation, solution operation and quantum sampling operation. The method solves the problem that an existing quantum principal component analysis algorithm cannot be matched with a nonlinear dimension reduction task, and exponentially accelerates an existing classical kernel principal component analysis algorithm by means of the unique parallel advantage of quantumcomputation.

Description

technical field [0001] The invention relates to a quantum kernel principal component analysis method, in particular to a quantum kernel principal component analysis method based on Taylor approximation and Hamiltonian simulation. Background technique [0002] The existing quantum principal component analysis algorithm shows that it can obtain significant acceleration compared to the classical principal component analysis algorithm: Lloyd proposed a quantum state tomography algorithm based on principal component analysis (Principle Component Analysis) in 2013, which can be in polynomial time The principal components are generated in the form of quantum states, which has an exponential acceleration compared to classical principal component analysis. In 2016, Cong and Duan et al. proposed a quantum linear discriminant analysis algorithm, which replaced the covariance matrix of the data set with the scatter matrix, and finally generated the principal components that constitute a...

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Problems solved by technology

[0003] The purpose of the present invention is to provide a quantum kernel principal component analysis method based on Taylor approximation and Hamiltonian simulation, which solves the problem that the existing quantum principal component analysis algorithm cannot match the nonlinear dimensionality reduction task. Advantages, exponentially speed up the existing classical kernel principal component analysis algorithm

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