Classical and Quantum Algorithms for Tensor Principal Component Analysis

Matthew B. Hastings
2020 Quantum  
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. \cite{wein2019kikuchi}. In
more » ... 9kikuchi}. 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.
doi:10.22331/q-2020-02-27-237 fatcat:j6w5svsujbhhdf3kygb6mqmuvy