Implementation of ternary Shor's algorithm based on vibrational states of an ion in anharmonic potential

doi:10.1088/1674-1056/24/3/033701

›› 2015, Vol. 24 ›› Issue (3): 33701-033701.doi: 10.1088/1674-1056/24/3/033701

• ATOMIC AND MOLECULAR PHYSICS • 上一篇下一篇

Implementation of ternary Shor's algorithm based on vibrational states of an ion in anharmonic potential

刘威^{a b}, 陈书明^{a b}, 张见^{a b}, 吴春旺^c, 吴伟^c, 陈平形^c

a College of Computer, National University of Defense Technology, Changsha 410073, China;
b Science and Technology on Parallel and Distributed Processing Laboratory (PDL), National University of Defense Technology, Changsha 410073, China;
c College of Science, National University of Defense Technology, Changsha 410073, China

收稿日期:2014-06-03 修回日期:2014-10-28 出版日期:2015-03-05 发布日期:2015-03-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 61205108) and the High Performance Computing (HPC) Foundation of National University of Defense Technology, China.

Implementation of ternary Shor's algorithm based on vibrational states of an ion in anharmonic potential

Liu Wei (刘威)^{a b}, Chen Shu-Ming (陈书明)^{a b}, Zhang Jian (张见)^{a b}, Wu Chun-Wang (吴春旺)^c, Wu Wei (吴伟)^c, Chen Ping-Xing (陈平形)^c

a College of Computer, National University of Defense Technology, Changsha 410073, China;
b Science and Technology on Parallel and Distributed Processing Laboratory (PDL), National University of Defense Technology, Changsha 410073, China;
c College of Science, National University of Defense Technology, Changsha 410073, China

Received:2014-06-03 Revised:2014-10-28 Online:2015-03-05 Published:2015-03-05
Contact: Liu Wei E-mail:wliu@nudt.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 61205108) and the High Performance Computing (HPC) Foundation of National University of Defense Technology, China.

摘要/Abstract

摘要： It is widely believed that Shor's factoring algorithm provides a driving force to boost the quantum computing research. However, a serious obstacle to its binary implementation is the large number of quantum gates. Non-binary quantum computing is an efficient way to reduce the required number of elemental gates. Here, we propose optimization schemes for Shor's algorithm implementation and take a ternary version for factorizing 21 as an example. The optimized factorization is achieved by a two-qutrit quantum circuit, which consists of only two single qutrit gates and one ternary controlled-NOT gate. This two-qutrit quantum circuit is then encoded into the nine lower vibrational states of an ion trapped in a weakly anharmonic potential. Optimal control theory (OCT) is employed to derive the manipulation electric field for transferring the encoded states. The ternary Shor's algorithm can be implemented in one single step. Numerical simulation results show that the accuracy of the state transformations is about 0.9919.

关键词: ternary Shor', s algorithm, anharmonic ion trapping, optimal control theory, vibrational state

Abstract: It is widely believed that Shor's factoring algorithm provides a driving force to boost the quantum computing research. However, a serious obstacle to its binary implementation is the large number of quantum gates. Non-binary quantum computing is an efficient way to reduce the required number of elemental gates. Here, we propose optimization schemes for Shor's algorithm implementation and take a ternary version for factorizing 21 as an example. The optimized factorization is achieved by a two-qutrit quantum circuit, which consists of only two single qutrit gates and one ternary controlled-NOT gate. This two-qutrit quantum circuit is then encoded into the nine lower vibrational states of an ion trapped in a weakly anharmonic potential. Optimal control theory (OCT) is employed to derive the manipulation electric field for transferring the encoded states. The ternary Shor's algorithm can be implemented in one single step. Numerical simulation results show that the accuracy of the state transformations is about 0.9919.

Key words: ternary Shor's algorithm, anharmonic ion trapping, optimal control theory, vibrational state

中图分类号: (Ion trapping)

37.10.Ty

03.67.Ac (Quantum algorithms, protocols, and simulations) 03.67.Lx (Quantum computation architectures and implementations)

刘威, 陈书明, 张见, 吴春旺, 吴伟, 陈平形. Implementation of ternary Shor's algorithm based on vibrational states of an ion in anharmonic potential[J]. , 2015, 24(3): 33701-033701.

Liu Wei (刘威), Chen Shu-Ming (陈书明), Zhang Jian (张见), Wu Chun-Wang (吴春旺), Wu Wei (吴伟), Chen Ping-Xing (陈平形). Implementation of ternary Shor's algorithm based on vibrational states of an ion in anharmonic potential[J]. Chin. Phys. B, 2015, 24(3): 33701-033701.

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Implementation of ternary Shor's algorithm based on vibrational states of an ion in anharmonic potential

Implementation of ternary Shor's algorithm based on vibrational states of an ion in anharmonic potential

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