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The Topological Basis Realization for Six Qubits and the Corresponding Heisenberg Spin\(-\frac {1}{2}\) Chain Model

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Abstract

In this paper, we construct a new set of orthonormal topological basis states for six qubits with the topological single loop d = 2. By acting on the subspace, we get a new five-dimensional (5D) reduced matrix. In addition, it is shown that the Heisenberg XXX spin-\(\frac {1}{2}\) chain of six qubits can be constructed from the Temperley-Lieb algebra (TLA) generator, both the energy ground state and the spin singlet states of the system can be described by the set of topological basis states.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11575042, 11405026 and 11205028), Government of China through CSC (Grant No. 201506625070), and the Plan for Scientific and Technological Development of Jilin Province (No. 20150520083JH and 20130522145JH), and Faculty Development Foundation Program of Northeast Normal University (15B2XZJ008).

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    Authors and Affiliations

    1. Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun, 130024, China

      Qi Yang, Yue Cao, Shiyin Chen, Yue Teng, Yanli Meng, Gangcheng Wang, Chunfang Sun & Kang Xue

    2. Center for Advanced Optoelectronic Functional Materials Research, and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun, 130024, China

      Qi Yang, Yue Cao, Shiyin Chen, Yue Teng, Yanli Meng, Gangcheng Wang, Chunfang Sun & Kang Xue

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    1. Qi Yang
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    2. Yue Cao
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    3. Shiyin Chen
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    4. Yue Teng
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    5. Yanli Meng
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    6. Gangcheng Wang
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    7. Chunfang Sun
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    8. Kang Xue
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    Correspondence to Chunfang Sun.

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    Qi Yang and Yue Cao contributed equally to the work.

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    Yang, Q., Cao, Y., Chen, S. et al. The Topological Basis Realization for Six Qubits and the Corresponding Heisenberg Spin\(-\frac {1}{2}\) Chain Model. Int J Theor Phys 57, 1839–1847 (2018). https://doi.org/10.1007/s10773-018-3709-3

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    • DOI: https://doi.org/10.1007/s10773-018-3709-3

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