Nonnegative/Binary matrix factorization with a D-Wave quantum annealer

PLoS One. 2018 Dec 10;13(12):e0206653. doi: 10.1371/journal.pone.0206653. eCollection 2018.

Abstract

D-Wave quantum annealers represent a novel computational architecture and have attracted significant interest. Much of this interest has focused on the quantum behavior of D-Wave machines, and there have been few practical algorithms that use the D-Wave. Machine learning has been identified as an area where quantum annealing may be useful. Here, we show that the D-Wave 2X can be effectively used as part of an unsupervised machine learning method. This method takes a matrix as input and produces two low-rank matrices as output-one containing latent features in the data and another matrix describing how the features can be combined to approximately reproduce the input matrix. Despite the limited number of bits in the D-Wave hardware, this method is capable of handling a large input matrix. The D-Wave only limits the rank of the two output matrices. We apply this method to learn the features from a set of facial images and compare the performance of the D-Wave to two classical tools. This method is able to learn facial features and accurately reproduce the set of facial images. The performance of the D-Wave shows some promise, but has some limitations. It outperforms the two classical codes in a benchmark when only a short amount of computational time is allowed (200-20,000 microseconds), but these results suggest heuristics that would likely outperform the D-Wave in this benchmark.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Machine Learning*
  • Models, Theoretical*
  • Quantum Theory*

Grants and funding

The authors acknowledge the support from a Los Alamos National Laboratory (LANL) Laboratory Directed Research and Development project 20180481ER and a LANL Information Science & Technology Rapid Response project. DO was partially supported by the National Nuclear Security Administration’s Advanced Simulation and Computing program. VVV was partially supported by the DiaMonD project (An Integrated Multifaceted Approach to Mathematics at the Interfaces of Data, Models, and Decisions, U.S. Department of Energy Office of Science, Grant #11145687). LBA was supported by a LANL J. Robert Oppenheimer Fellowship. The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.