We propose a new two-fold integration transformation in p-q phase space∫∫^∞-∞dpdq/π e^2i（p-x）（q-y）f（p,q）≡G（x,y）,which possesses some well-behaved transformation properties. We apply this transformation t...We propose a new two-fold integration transformation in p-q phase space∫∫^∞-∞dpdq/π e^2i（p-x）（q-y）f（p,q）≡G（x,y）,which possesses some well-behaved transformation properties. We apply this transformation to the Weyl ordering of operators, especially those Q-P ordered and P-Q ordered operators.展开更多
Using the Weyl ordering of operators expansion formula （Hong-Yi Fan, J. Phys.A 25 （1992） 3443） this paper finds a kind of two-fold integration transformation about the Wigner operator △（ q＇,p） q-number transf...Using the Weyl ordering of operators expansion formula （Hong-Yi Fan, J. Phys.A 25 （1992） 3443） this paper finds a kind of two-fold integration transformation about the Wigner operator △（ q＇,p） q-number transform） in phase space quantum mechanics,∫∫∞-∞dp＇dq＇/π △（q＇,p＇）e-2i（ p-p＇）（ q-q＇）=δ（ p-P）δ（ q-Q）,∫∫∞-∞dqdpδ（p-P）δ（q-Q）e2i（p-p＇）（q-q＇）=△（q＇,p＇）,whereQ,P are the coordinate and momentum operators, respectively. We apply it to study mutual converting formulae among Q-P ordering, P-Q ordering and Weyl ordering of operators. In this way, the contents of phase space quantum mechanics can be enriched. The formula of the Weyl ordering of operators expansion and the technique of integration within the Weyl ordered product of operators are used in this discussion.展开更多
Perfect state transfer(PST)has great significance due to its applications in quantum information processing and quantum computation.The main problem we study in this paper is to determine whether the two-fold Cayley t...Perfect state transfer(PST)has great significance due to its applications in quantum information processing and quantum computation.The main problem we study in this paper is to determine whether the two-fold Cayley tree,an extension of the Cayley tree,admits perfect state transfer between two roots using quantum walks.We show that PST can be achieved by means of the so-called nonrepeating quantum walk[Phys.Rev.A 89042332(2014)]within time steps that are the distance between the two roots;while both the continuous-time quantum walk and the typical discrete-time quantum walk with Grover coin approaches fail.Our results suggest that in some cases the dynamics of a discrete-time quantum walk may be much richer than that of the continuous-time quantum walk.展开更多
Traditional route planners commonly focus on finding the shortest path between two points in terms of travel distance or time over road networks.However,in real cases,especially in the era of smart cities where many k...Traditional route planners commonly focus on finding the shortest path between two points in terms of travel distance or time over road networks.However,in real cases,especially in the era of smart cities where many kinds of transportation-related data become easily available,recent years have witnessed an increasing demand of route planners that need to optimize for multiple criteria,e.g.,finding the route with the highest accumulated scenic score along(utility)while not exceeding the given travel time budget(cost).Such problem can be viewed as a variant of arc orienteering problem(AOP),which is well-known as an NP-hard problem.In this paper,targeting a more realistic AOP,we allow both scenic score(utility)and travel time(cost)values on each arc of the road network are time-dependent(2TD-AOP),and propose a memetic algorithm to solve it.To be more specific,within the given travel time budget,in the phase of initiation,for each population,we iteratively add suitable arcs with high scenic score and build a path from the origin to the destination via a complicate procedure consisting of search region narrowing,chromosome encoding and decoding.In the phase of the local search,each path is improved via chromosome selection,local-improvement-based mutation and crossover operations.Finally,we evaluate the proposed memetic algorithm in both synthetic and real-life datasets extensively,and the experimental results demonstrate that it outperforms the baselines.展开更多
基金National Natural Science Foundation of China under Grant Nos.10775097 and 10874174
文摘We propose a new two-fold integration transformation in p-q phase space∫∫^∞-∞dpdq/π e^2i（p-x）（q-y）f（p,q）≡G（x,y）,which possesses some well-behaved transformation properties. We apply this transformation to the Weyl ordering of operators, especially those Q-P ordered and P-Q ordered operators.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174)Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘Using the Weyl ordering of operators expansion formula （Hong-Yi Fan, J. Phys.A 25 （1992） 3443） this paper finds a kind of two-fold integration transformation about the Wigner operator △（ q＇,p） q-number transform） in phase space quantum mechanics,∫∫∞-∞dp＇dq＇/π △（q＇,p＇）e-2i（ p-p＇）（ q-q＇）=δ（ p-P）δ（ q-Q）,∫∫∞-∞dqdpδ（p-P）δ（q-Q）e2i（p-p＇）（q-q＇）=△（q＇,p＇）,whereQ,P are the coordinate and momentum operators, respectively. We apply it to study mutual converting formulae among Q-P ordering, P-Q ordering and Weyl ordering of operators. In this way, the contents of phase space quantum mechanics can be enriched. The formula of the Weyl ordering of operators expansion and the technique of integration within the Weyl ordered product of operators are used in this discussion.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61802002 and 61701004)the Natural Science Foundation of Anhui Province,China(Grant No.1708085MF162)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20171458)。
文摘Perfect state transfer(PST)has great significance due to its applications in quantum information processing and quantum computation.The main problem we study in this paper is to determine whether the two-fold Cayley tree,an extension of the Cayley tree,admits perfect state transfer between two roots using quantum walks.We show that PST can be achieved by means of the so-called nonrepeating quantum walk[Phys.Rev.A 89042332(2014)]within time steps that are the distance between the two roots;while both the continuous-time quantum walk and the typical discrete-time quantum walk with Grover coin approaches fail.Our results suggest that in some cases the dynamics of a discrete-time quantum walk may be much richer than that of the continuous-time quantum walk.
基金the National Key Research and Development Project of China(2017YFB1002000)the National Natural Science Foundation of China(Grant Nos.61602067 and 61872050)+2 种基金the Fundamental Research Funds for the Central Universities(2018cdqyjsj0024)the Chongqing Basic and Frontier Research Program(cstc2018jcyj AX0551)the Frontier Interdisciplinary Research Funds for the Central Universities(106112017cdjqj188828)。
文摘Traditional route planners commonly focus on finding the shortest path between two points in terms of travel distance or time over road networks.However,in real cases,especially in the era of smart cities where many kinds of transportation-related data become easily available,recent years have witnessed an increasing demand of route planners that need to optimize for multiple criteria,e.g.,finding the route with the highest accumulated scenic score along(utility)while not exceeding the given travel time budget(cost).Such problem can be viewed as a variant of arc orienteering problem(AOP),which is well-known as an NP-hard problem.In this paper,targeting a more realistic AOP,we allow both scenic score(utility)and travel time(cost)values on each arc of the road network are time-dependent(2TD-AOP),and propose a memetic algorithm to solve it.To be more specific,within the given travel time budget,in the phase of initiation,for each population,we iteratively add suitable arcs with high scenic score and build a path from the origin to the destination via a complicate procedure consisting of search region narrowing,chromosome encoding and decoding.In the phase of the local search,each path is improved via chromosome selection,local-improvement-based mutation and crossover operations.Finally,we evaluate the proposed memetic algorithm in both synthetic and real-life datasets extensively,and the experimental results demonstrate that it outperforms the baselines.
