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. No...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.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.61205108)the High Performance Computing(HPC)Foundation of National University of Defense Technology,China
文摘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.
