Selectable accurate quantum principal component analysis method and application

Abstract

The invention belongs to the technical field of quantum machine learning, and discloses a selectable accurate quantum principal component analysis method and application, wherein based on a quantum singular value threshold decomposition algorithm, compared with traditional quantum principal component analysis, the flexibility is high, main components, namely main characteristic value characteristic vectors, are output by controlling thresholds, and all components, namely all eigenvalue eigenvectors, can be output, and compared with the previous improved algorithm, the algorithm reduces the number of quantum gates in the parallel direction, and the result is more accurate. According to the invention, the accurate quantum principal component analysis algorithm selected by the invention mainly comprises seven steps of inputting a covariance matrix quantum state, extracting a characteristic value through phase estimation, converting the characteristic value, performing controlled overturning, performing inverse transformation, measuring, extracting and screening the characteristic value through phase estimation, and finally outputting the characteristic value greater than a given threshold value and a corresponding characteristic vector; and the method can be used as a subroutine of other algorithms in the field of quantum machine learning, and the execution efficiency of the wholealgorithm is improved.

Description

technical field [0001] The invention belongs to the technical field of quantum machine learning, and in particular relates to an optional accurate quantum principal component analysis method and its application. Background technique [0002] At present: data from all walks of life is growing explosively, and the data volume, data structure, and data types are becoming more and more complex. These massive data bring technical challenges to traditional machine learning algorithms. The machine learning algorithm combined with the characteristics of quantum computing can accelerate the traditional algorithm. The N-dimensional data set only needs logN bits. The exponential acceleration makes the applicability of quantum algorithms in various industries of great significance. As an exponentially accelerated dimensionality reduction algorithm, quantum principal component analysis provides an effective tool for processing explosive data. [0003] At present, the commonly used exist...

AI Technical Summary

Problems solved by technology

[0010] (1) The traditional quantum principal component analysis algorithm can only output all components

[0011] (2) Although the improved principal component analysis algorithm based on two-step quantum singular value threshold decomposition can selectively output principal components, the inaccurate results affect the success rate of the algorithm

[0012] (2) At present, the number of quantum gates required by the technology is large, and it is easy to be affected by more noise on the existing quantum analog computer

[0013] The difficulty in solving the above problems and defects is: if the selected output quantum principal component analysis algorithm completely depends on the quantum singular value threshold decomposition algorithm, it is not easy to obtain an accurate value, because the quantum singular value threshold decomposition algorithm needs to adjust parameters to improve the success probability of the algorithm to obtain an approximate value , so it is difficult to find an accurate and simple alternative to the circuit design of quantum principal component analysis

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