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2020•Unpublished venueOpen access

Entanglement in Shor's Factoring Algorithm

Jianing Tan, Zhihao Liu, Hanwu Chen

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Abstract

Quantum algorithms are well known for their higher efficiency compared to their classical counterparts.However, the origin of the speed-up offered by quantum algorithms is a debatable question.Using entanglement measure based on coefficient matrix, we investigate the entanglement features of the quantum states used in Shor's factoring algorithm.The results show that if and only if the order r is 1, the algorithm generates no entanglement.Finally, compare with published studies results (Proceedings: Mathematical, Physical and Engineering Sciences, 459(2036): 2011-2032, 2003, Physical Review A, 72(6): 062308, 2005), we give counter examples to show that previous researches neglect partially entanglement.

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Quantum algorithms are well known for their higher efficiency compared to their classical counterparts.However, the origin of the speed-up offered by quantum algorithms is a debatable question.Using entanglement measure based on coefficient matrix, we investigate the entanglement features of the quantum states used in Shor's factoring algorithm.The results show that if and only if the order r is 1, the algorithm generates no entanglement.Finally, compare with published studies results (Proceedings: Mathematical, Physical and Engineering Sciences, 459(2036): 2011-2032, 2003, Physical Review A, 72(6): 062308, 2005), we give counter examples to show that previous researches neglect partially entanglement.

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Available abstract

Quantum algorithms are well known for their higher efficiency compared to their classical counterparts.However, the origin of the speed-up offered by quantum algorithms is a debatable question.Using entanglement measure based on coefficient matrix, we investigate the entanglement features of the quantum states used in Shor's factoring algorithm.The results show that if and only if the order r is 1, the algorithm generates no entanglement.Finally, compare with published studies results (Proceedings: Mathematical, Physical and Engineering Sciences, 459(2036): 2011-2032, 2003, Physical Review A, 72(6): 062308, 2005), we give counter examples to show that previous researches neglect partially entanglement.

Key concepts: Quantum entanglement, Factoring, Quantum computer, Algorithm, Quantum algorithm, Computer science, Quantum, Measure (data warehouse)

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