title: Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator.
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 Z_{2} 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.
authors.affiliation: State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China.|Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, N2L 3G1 Ontario, Canada.
authors.forename: Keren
authors.initials: K
authors.lastname: Li
authors.affiliation: Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China.|Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.|Perimeter Institute for Theoretical Physics, Waterloo, N2L 2Y5 Ontario, Canada.
authors.forename: Yidun
authors.initials: Y
authors.lastname: Wan
authors.affiliation: Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China.|Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.|State Key Laboratory of Surface Physics and Department of Physics, Fudan University, 220 Handan Road, Shanghai 200433, China.
authors.forename: Ling-Yan
authors.initials: LY
authors.lastname: Hung
authors.affiliation: Perimeter Institute for Theoretical Physics, Waterloo, N2L 2Y5 Ontario, Canada.
authors.forename: Tian
authors.initials: T
authors.lastname: Lan
authors.affiliation: State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China.
authors.forename: Guilu
authors.initials: G
authors.lastname: Long
authors.affiliation: Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, N2L 3G1 Ontario, Canada.
authors.forename: Dawei
authors.initials: D
authors.lastname: Lu
authors.affiliation: Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, N2L 3G1 Ontario, Canada.|Department of Mathematics & Statistics, University of Guelph, Guelph, Nag 2W1 Ontario, Canada.|Canadian Institute for Advanced Research, Toronto, M5G 1Z8 Ontario, Canada.
authors.forename: Bei
authors.initials: B
authors.lastname: Zeng
authors.affiliation: Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, N2L 3G1 Ontario, Canada.|Perimeter Institute for Theoretical Physics, Waterloo, N2L 2Y5 Ontario, Canada.|Canadian Institute for Advanced Research, Toronto, M5G 1Z8 Ontario, Canada.
authors.forename: Raymond
authors.initials: R
authors.lastname: Laflamme