Classical and Quantum Algorithms for Tensor Principal Component Analysis
This work addresses large-scale inference problems, suggesting potential applications for quantum computers, though it appears incremental as it builds on existing spectral methods with specific improvements.
The authors tackled the problem of tensor principal component analysis by developing classical and quantum spectral algorithms, achieving a quartic speedup and exponentially smaller space usage with the quantum version compared to classical methods, and improved recovery thresholds for both even and odd order tensors.
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 improved threshold for recovery and the algorithms we present work for both even and odd order tensors. These results suggest that large-scale inference problems are a promising future application for quantum computers.