Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator

Keren Li, Yidun Wan, Ling-Yan Hung, Tian Lan, Guilu Long, Dawei Lu, Bei Zeng, and Raymond Laflamme
Phys. Rev. Lett. 118, 080502 – Published 23 February 2017
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Abstract

Topological orders can be used as media for topological quantum computing—a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular S and T matrices. In particular, we employ a nuclear magnetic resonance quantum simulator to study the properties of three topologically ordered matter phases described by the string-net model with two string types, including the Z2 toric code, doubled semion, and doubled Fibonacci. The third one, non-Abelian Fibonacci order is notably expected to be the simplest candidate for universal topological quantum computing. Our experiment serves as the basic module, built on which one can simulate braiding of non-Abelian anyons and ultimately, topological quantum computation via the braiding, and thus provides a new approach of investigating topological orders using quantum computers.

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  • Received 27 August 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.080502

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Keren Li1,2, Yidun Wan3,4,5, Ling-Yan Hung6,3,4, Tian Lan5, Guilu Long1, Dawei Lu2,*, Bei Zeng2,7,8, and Raymond Laflamme2,5,8

  • 1State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
  • 2Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, N2L 3G1 Ontario, Canada
  • 3Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China
  • 4Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
  • 5Perimeter Institute for Theoretical Physics, Waterloo, N2L 2Y5 Ontario, Canada
  • 6State Key Laboratory of Surface Physics and Department of Physics, Fudan University, 220 Handan Road, Shanghai 200433, China
  • 7Department of Mathematics & Statistics, University of Guelph, Guelph, Nag 2W1 Ontario, Canada
  • 8Canadian Institute for Advanced Research, Toronto, M5G 1Z8 Ontario, Canada

  • *d29lu@uwaterloo.ca

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Issue

Vol. 118, Iss. 8 — 24 February 2017

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