Tomography and generative training with quantum Boltzmann machines

Mária Kieferová and Nathan Wiebe
Phys. Rev. A 96, 062327 – Published 22 December 2017

Abstract

The promise of quantum neural nets, which utilize quantum effects to model complex data sets, has made their development an aspirational goal for quantum machine learning and quantum computing in general. Here we provide methods of training quantum Boltzmann machines. Our work generalizes existing methods and provides additional approaches for training quantum neural networks that compare favorably to existing methods. We further demonstrate that quantum Boltzmann machines enable a form of partial quantum state tomography that further provides a generative model for the input quantum state. Classical Boltzmann machines are incapable of this. This verifies the long-conjectured connection between tomography and quantum machine learning. Finally, we prove that classical computers cannot simulate our training process in general unless BQP=BPP, provide lower bounds on the complexity of the training procedures and numerically investigate training for small nonstoquastic Hamiltonians.

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  • Received 14 January 2017
  • Revised 1 August 2017

DOI:https://doi.org/10.1103/PhysRevA.96.062327

©2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Mária Kieferová

  • Institute for Quantum Computing, University of Waterloo, Ontario, Canada and Macquarie University, NSW, 2109, Australia

Nathan Wiebe

  • Microsoft Research, Washington, USA

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Issue

Vol. 96, Iss. 6 — December 2017

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