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Chin. Phys. B, 2020, Vol. 29(7): 070501    DOI: 10.1088/1674-1056/ab8893
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Probe of topological invariants using quantum walks of a trapped ion in coherent state space

Ya Meng(蒙雅)1,2, Feng Mei(梅锋)1,2, Gang Chen(陈刚)1,2,3, Suo-Tang Jia(贾锁堂)1,2
1 State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China;
2 Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China;
3 Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan 250358, China
Abstract  We present a protocol to realize topological discrete-time quantum walks, which comprise a sequence of spin-dependent flipping displacement operations and quantum coin tossing operations, with a single trapped ion. It is demonstrated that the information of bulk topological invariants can be extracted by measuring the average projective phonon number when the walk takes place in coherent state space. Interestingly, the specific chiral symmetry owned by our discrete-time quantum walks simplifies the measuring process. Furthermore, we prove the robustness of such bulk topological invariants by introducing dynamical disorder and decoherence. Our work provides a simple method to measure bulk topological features in discrete-time quantum walks, which can be experimentally realized in the system of single trapped ions.
Keywords:  topological quantum walk      topological invariant      trapped ion      coherent state space  
Received:  25 February 2020      Revised:  06 April 2020      Accepted manuscript online: 
PACS:  05.40.Fb (Random walks and Levy flights)  
  03.67.Ac (Quantum algorithms, protocols, and simulations)  
  03.65.Vf (Phases: geometric; dynamic or topological)  
  37.10.Vz (Mechanical effects of light on atoms, molecules, and ions)  
Fund: Project supported by the National Key R&D Program of China (Grant No. 2017YFA0304203), the National Natural National Science Foundation of China (Grant Nos. 11604392 and 11674200), the Changjiang Scholars and Innovative Research Team in Universities of Ministry of Education of China (Grant No. IRT_17R70), the Fund for Shanxi “1331 Project” Key Subjects Construction, and the 111 Project, China (Grant No. D18001).
Corresponding Authors:  Feng Mei, Gang Chen     E-mail:;

Cite this article: 

Ya Meng(蒙雅), Feng Mei(梅锋), Gang Chen(陈刚), Suo-Tang Jia(贾锁堂) Probe of topological invariants using quantum walks of a trapped ion in coherent state space 2020 Chin. Phys. B 29 070501

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