Contextuality as a Resource for Models of Quantum Computation with Qubits

Juan Bermejo-Vega, Nicolas Delfosse, Dan E. Browne, Cihan Okay, and Robert Raussendorf

Phys. Rev. Lett. 119, 120505 – Published 21 September 2017

Abstract

A central question in quantum computation is to identify the resources that are responsible for quantum speed-up. Quantum contextuality has been recently shown to be a resource for quantum computation with magic states for odd-prime dimensional qudits and two-dimensional systems with real wave functions. The phenomenon of state-independent contextuality poses a priori an obstruction to characterizing the case of regular qubits, the fundamental building block of quantum computation. Here, we establish contextuality of magic states as a necessary resource for a large class of quantum computation schemes on qubits. We illustrate our result with a concrete scheme related to measurement-based quantum computation.

Received 16 November 2016

DOI:https://doi.org/10.1103/PhysRevLett.119.120505

Physics Subject Headings (PhySH)

Computational complexity Quantum computation Quantum foundations

General PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Juan Bermejo-Vega^1,2, Nicolas Delfosse^3,4, Dan E. Browne⁵, Cihan Okay⁶, and Robert Raussendorf⁷

¹Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
²Max-Planck Institut für Quantum Optics, Theory Division, 85748 Garching, Germany
³Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
⁴Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
⁵Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
⁶Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada
⁷Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada