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

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

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.

Keywords: ternary Shor's algorithm anharmonic ion trapping optimal control theory vibrational state

Received: 03 June 2014
Revised: 28 October 2014
Accepted manuscript online:

PACS:	37.10.Ty	(Ion trapping)
	03.67.Ac	(Quantum algorithms, protocols, and simulations)
	03.67.Lx	(Quantum computation architectures and implementations)

Fund: 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.

Corresponding Authors: Liu Wei
E-mail: wliu@nudt.edu.cn

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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 2015 Chin. Phys. B 24 033701

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

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