Decision and function problems based on boson sampling

Georgios M. Nikolopoulos and Thomas Brougham
Phys. Rev. A 94, 012315 – Published 11 July 2016

Abstract

Boson sampling is a mathematical problem that is strongly believed to be intractable for classical computers, whereas passive linear interferometers can produce samples efficiently. So far, the problem remains a computational curiosity, and the possible usefulness of boson-sampling devices is mainly limited to the proof of quantum supremacy. The purpose of this work is to investigate whether boson sampling can be used as a resource of decision and function problems that are computationally hard, and may thus have cryptographic applications. After the definition of a rather general theoretical framework for the design of such problems, we discuss their solution by means of a brute-force numerical approach, as well as by means of nonboson samplers. Moreover, we estimate the sample sizes required for their solution by passive linear interferometers, and it is shown that they are independent of the size of the Hilbert space.

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  • Received 2 March 2016

DOI:https://doi.org/10.1103/PhysRevA.94.012315

©2016 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Georgios M. Nikolopoulos1,* and Thomas Brougham2

  • 1Institute of Electronic Structure & Laser, FORTH, P.O. Box 1385, GR-70013 Heraklion, Greece
  • 2School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom

  • *nikolg@iesl.forth.gr

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Vol. 94, Iss. 1 — July 2016

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