In this context,we study three different strategies to improve the time complexity of the widely used adiabatic evolution algorithms when solving a particular class of quantum search problems where both the initial an...In this context,we study three different strategies to improve the time complexity of the widely used adiabatic evolution algorithms when solving a particular class of quantum search problems where both the initial and final Hamiltonians are one-dimensional projector Hamiltonians on the corresponding ground state.After some simple analysis,we find the time complexity improvement is always accompanied by the increase of some other "complexities" that should be considered.But this just gives the implication that more feasibilities can be achieved in adiabatic evolution based quantum algorithms over the circuit model,even though the equivalence between the two has been shown.In addition,we also give a rough comparison between these different models for the speedup of the problem.展开更多
Software systems are a typical kind of man-made complex systems. Understanding their evolutions can lead to better software engineering practices. In this paper, the authors use complex network theory as a tool to ana...Software systems are a typical kind of man-made complex systems. Understanding their evolutions can lead to better software engineering practices. In this paper, the authors use complex network theory as a tool to analyze the evolution of object-oriented （OO） software from a multi-granularity perspective. First, a multi-granularity software networks model is proposed to represent the topological structures of a multi-version software system from three levels of granularity. Then, some parameters widely used in complex network theory are applied to characterize the software networks. By tracing the parameters＇ values in consecutive software systems, we have a better understanding about software evolution. A case study is conducted on an open source OO project, Azureus, as an example to illustrate our approach, and some underlying evolution characteristics are uncovered. These results provide a different dimension to our understanding of software evolutions and also are very useful for the design and development of OO software systems.展开更多
In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully ...In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using.展开更多
In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimen...In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model - an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 61173050)
文摘In this context,we study three different strategies to improve the time complexity of the widely used adiabatic evolution algorithms when solving a particular class of quantum search problems where both the initial and final Hamiltonians are one-dimensional projector Hamiltonians on the corresponding ground state.After some simple analysis,we find the time complexity improvement is always accompanied by the increase of some other "complexities" that should be considered.But this just gives the implication that more feasibilities can be achieved in adiabatic evolution based quantum algorithms over the circuit model,even though the equivalence between the two has been shown.In addition,we also give a rough comparison between these different models for the speedup of the problem.
基金This research is supported by the National Basic Research 973 Program of China under Grant No 2007CB310801, the National Natural Science Foundation of China under Grant Nos. 60873083 and 61003073 the Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20090141120022 the Fundamental Research Funds for the Central Universities of China under Grant Nos. 114013 and 6082005 and the Scientific Research Fund of Zhejiang Provincial Education Department under Grant No. Y201018008.
文摘Software systems are a typical kind of man-made complex systems. Understanding their evolutions can lead to better software engineering practices. In this paper, the authors use complex network theory as a tool to analyze the evolution of object-oriented （OO） software from a multi-granularity perspective. First, a multi-granularity software networks model is proposed to represent the topological structures of a multi-version software system from three levels of granularity. Then, some parameters widely used in complex network theory are applied to characterize the software networks. By tracing the parameters＇ values in consecutive software systems, we have a better understanding about software evolution. A case study is conducted on an open source OO project, Azureus, as an example to illustrate our approach, and some underlying evolution characteristics are uncovered. These results provide a different dimension to our understanding of software evolutions and also are very useful for the design and development of OO software systems.
基金Supported by the National Natural Science Foundation of China under Grant Nos.61402188 and 61173050the support from the China Postdoctoral Science Foundation under Grant No.2014M552041
文摘In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using.
基金Supported by the National Natural Science Foundation of China under Grant No. 61173050
文摘In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model - an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.
