Application of a Resource Theory for Magic States to Fault-Tolerant Quantum Computing

Mark Howard and Earl Campbell
Phys. Rev. Lett. 118, 090501 – Published 3 March 2017
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Abstract

Motivated by their necessity for most fault-tolerant quantum computation schemes, we formulate a resource theory for magic states. First, we show that robustness of magic is a well-behaved magic monotone that operationally quantifies the classical simulation overhead for a Gottesman-Knill-type scheme using ancillary magic states. Our framework subsequently finds immediate application in the task of synthesizing non-Clifford gates using magic states. When magic states are interspersed with Clifford gates, Pauli measurements, and stabilizer ancillas—the most general synthesis scenario—then the class of synthesizable unitaries is hard to characterize. Our techniques can place nontrivial lower bounds on the number of magic states required for implementing a given target unitary. Guided by these results, we have found new and optimal examples of such synthesis.

  • Figure
  • Received 11 October 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.090501

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Mark Howard* and Earl Campbell

  • Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom

  • *m.howard@sheffield.ac.uk
  • earltcampbell@gmail.com

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Issue

Vol. 118, Iss. 9 — 3 March 2017

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