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Verification of Quantum Computation: An Overview of Existing Approaches

Authors
  • Gheorghiu, Alexandru1
  • Kapourniotis, Theodoros2
  • Kashefi, Elham1, 3
  • 1 University of Edinburgh, School of Informatics, Edinburgh, UK , Edinburgh (United Kingdom)
  • 2 University of Warwick, Department of Physics, Coventry, UK , Coventry (United Kingdom)
  • 3 Université Pierre et Marie Curie, CNRS LIP6, Paris, France , Paris (France)
Type
Published Article
Journal
Theory of Computing Systems
Publisher
Springer US
Publication Date
Jul 06, 2018
Volume
63
Issue
4
Pages
715–808
Identifiers
DOI: 10.1007/s00224-018-9872-3
Source
Springer Nature
Keywords
License
Green

Abstract

Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can check whether quantum computers are indeed producing correct results. This task, known as quantum verification, has been highlighted as a significant challenge on the road to scalable quantum computing technology. We review the most significant approaches to quantum verification and compare them in terms of structure, complexity and required resources. We also comment on the use of cryptographic techniques which, for many of the presented protocols, has proven extremely useful in performing verification. Finally, we discuss issues related to fault tolerance, experimental implementations and the outlook for future protocols.

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