After half a century research, the mechanical theorem proving in geometries has become an active research topic in the automated reasoning field. This review involves three approaches on automated generating readable ...After half a century research, the mechanical theorem proving in geometries has become an active research topic in the automated reasoning field. This review involves three approaches on automated generating readable machine proofs for geometry theorems which include search methods, coordinate-free methods, and formal logic methods. Some critical issues about these approaches are also discussed. Furthermore, the authors propose three further research directions for the readable machine proofs for geometry theorems, including geometry inequalities, intelligent geometry softwares and machine learning.展开更多
Quantum circuit model has been widely explored for various quantum applications such as Shors algorithm and Grovers searching algorithm.Most of previous algorithms are based on the qubit systems.Herein a proposal for ...Quantum circuit model has been widely explored for various quantum applications such as Shors algorithm and Grovers searching algorithm.Most of previous algorithms are based on the qubit systems.Herein a proposal for a universal circuit is given based on the qudit system,which is larger and can store more information.In order to prove its universality for quantum applications,an explicit set of one-qudit and two-qudit gates is provided for the universal qudit computation.The one-qudit gates are general rotation for each two-dimensional subspace while the two-qudit gates are their controlled extensions.In comparison to previous quantum qudit logical gates,each primitive qudit gate is only dependent on two free parameters and may be easily implemented.In experimental implementation,multilevel ions with the linear ion trap model are used to build the qudit systems and use the coupling of neighbored levels for qudit gates.The controlled qudit gates may be realized with the interactions of internal and external coordinates of the ion.展开更多
基金supported by the Funds of the Chinese Academy of Sciences for Key Topics in Innovation Engineering under Grant No.KJCX2-YW-S02
文摘After half a century research, the mechanical theorem proving in geometries has become an active research topic in the automated reasoning field. This review involves three approaches on automated generating readable machine proofs for geometry theorems which include search methods, coordinate-free methods, and formal logic methods. Some critical issues about these approaches are also discussed. Furthermore, the authors propose three further research directions for the readable machine proofs for geometry theorems, including geometry inequalities, intelligent geometry softwares and machine learning.
基金supported by the National Natural Science Foundation of China(Grant Nos.61303039 and 11226336)the Fundamental Research Funds for the Central Universities(Grant No.2682014CX095)the Science Foundation Ireland(SFI)under the International Strategic CooperationAward Grant Number SFI/13/ISCA/2845
文摘Quantum circuit model has been widely explored for various quantum applications such as Shors algorithm and Grovers searching algorithm.Most of previous algorithms are based on the qubit systems.Herein a proposal for a universal circuit is given based on the qudit system,which is larger and can store more information.In order to prove its universality for quantum applications,an explicit set of one-qudit and two-qudit gates is provided for the universal qudit computation.The one-qudit gates are general rotation for each two-dimensional subspace while the two-qudit gates are their controlled extensions.In comparison to previous quantum qudit logical gates,each primitive qudit gate is only dependent on two free parameters and may be easily implemented.In experimental implementation,multilevel ions with the linear ion trap model are used to build the qudit systems and use the coupling of neighbored levels for qudit gates.The controlled qudit gates may be realized with the interactions of internal and external coordinates of the ion.
