# Classical and Quantum Algorithms for Tensor Principal Component Analysis

@article{Hastings2019ClassicalAQ, title={Classical and Quantum Algorithms for Tensor Principal Component Analysis}, author={Matthew B. Hastings}, journal={ArXiv}, year={2019}, volume={abs/1907.12724} }

We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical spectral algorithm, and a super-polynomial speedup over classical algorithms that use only polynomial space. The classical algorithms that we present are related to, but slightly different from those presented recently in Ref. 1. In particular, we have an… CONTINUE READING

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## The Kikuchi Hierarchy and Tensor PCA

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