Shor's algorithm outperforms its classical counterpart in efficient prime factorization.We explore the coherence and entanglement dynamics of the evolved states within Shor's algorithm,showing that the coheren...Shor's algorithm outperforms its classical counterpart in efficient prime factorization.We explore the coherence and entanglement dynamics of the evolved states within Shor's algorithm,showing that the coherence in each step relies on the dimension of register or the order,and discuss the relations between geometric coherence and geometric entanglement.We investigate how unitary operators induce variations in coherence and entanglement,and analyze the variations of coherence and entanglement within the entire algorithm,demonstrating that the overall effect of Shor's algorithm tends to deplete coherence and produce entanglement.Our research not only deepens the understanding of this algorithm but also provides methodological references for studying resource dynamics in other quantum algorithms.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.12161056,12075159,12171044)Natural Science Foundation of Jiangxi Province(Grant No.20232ACB211003)+1 种基金Beijing Natural Science Foundation(Grant No.Z190005)the specific research fund of the Innovation Platform for Academicians of Hainan Province。
文摘Shor's algorithm outperforms its classical counterpart in efficient prime factorization.We explore the coherence and entanglement dynamics of the evolved states within Shor's algorithm,showing that the coherence in each step relies on the dimension of register or the order,and discuss the relations between geometric coherence and geometric entanglement.We investigate how unitary operators induce variations in coherence and entanglement,and analyze the variations of coherence and entanglement within the entire algorithm,demonstrating that the overall effect of Shor's algorithm tends to deplete coherence and produce entanglement.Our research not only deepens the understanding of this algorithm but also provides methodological references for studying resource dynamics in other quantum algorithms.
