Quantum computing offers unprecedented computational power, enabling simultaneous computations beyond traditional computers. Quantum computers differ significantly from classical computers, necessitating a distinct ap...Quantum computing offers unprecedented computational power, enabling simultaneous computations beyond traditional computers. Quantum computers differ significantly from classical computers, necessitating a distinct approach to algorithm design, which involves taming quantum mechanical phenomena. This paper extends the numbering of computable programs to be applied in the quantum computing context. Numbering computable programs is a theoretical computer science concept that assigns unique numbers to individual programs or algorithms. Common methods include Gödel numbering which encodes programs as strings of symbols or characters, often used in formal systems and mathematical logic. Based on the proposed numbering approach, this paper presents a mechanism to explore the set of possible quantum algorithms. The proposed approach is able to construct useful circuits such as Quantum Key Distribution BB84 protocol, which enables sender and receiver to establish a secure cryptographic key via a quantum channel. The proposed approach facilitates the process of exploring and constructing quantum algorithms.展开更多
Aworld-renowned expert on non-conforming finite elementmethods,Prof.Zhong-Ci Shi,had left a lasting impact on the overarching development of Chinese computational mathematics and scientific computing as well as comput...Aworld-renowned expert on non-conforming finite elementmethods,Prof.Zhong-Ci Shi,had left a lasting impact on the overarching development of Chinese computational mathematics and scientific computing as well as computational mathematics worldwide through his tireless and visionary leadership.His dedication to developing academic programs in many leading Chinese universities and institutions,along with his stewardship in establishing national computational research programs,played a fundamental role in elevating Chinese computational research status to a global recognition.Several generations of Chinese scholars benefited from his guidance and teaching,and this focused issue of original research contributions from 33 Chinese and international scientist teams bears witness to the profound influence of Prof.Shi on their research careers by his lifetime of work spanning over six decades.Beyond being an accomplished mathematician,Prof.Shi had lived a life of a cultured man who radiated vigor and warmth,imbuing his life with heartiness,openness,and honesty.展开更多
Paired-permanent approach for VB theory is extensively developed. Canonical expansion of a paired-permanent is deduced. Furthermore, it is shown that a paired-permanent may be expressed in terms of the products of sub...Paired-permanent approach for VB theory is extensively developed. Canonical expansion of a paired-permanent is deduced. Furthermore, it is shown that a paired-permanent may be expressed in terms of the products of sub-paired-permanents of any given order and their corresponding minors. An ab initio spin-free valence bond program, called Xiamen, is implemented by using paired-permanent approach. Test calculation shows that Xiamen package is more efficient than some other programs based on the traditional VB algorithm, and it provides a new practical tool for quantum chemistry.展开更多
文摘Quantum computing offers unprecedented computational power, enabling simultaneous computations beyond traditional computers. Quantum computers differ significantly from classical computers, necessitating a distinct approach to algorithm design, which involves taming quantum mechanical phenomena. This paper extends the numbering of computable programs to be applied in the quantum computing context. Numbering computable programs is a theoretical computer science concept that assigns unique numbers to individual programs or algorithms. Common methods include Gödel numbering which encodes programs as strings of symbols or characters, often used in formal systems and mathematical logic. Based on the proposed numbering approach, this paper presents a mechanism to explore the set of possible quantum algorithms. The proposed approach is able to construct useful circuits such as Quantum Key Distribution BB84 protocol, which enables sender and receiver to establish a secure cryptographic key via a quantum channel. The proposed approach facilitates the process of exploring and constructing quantum algorithms.
文摘Aworld-renowned expert on non-conforming finite elementmethods,Prof.Zhong-Ci Shi,had left a lasting impact on the overarching development of Chinese computational mathematics and scientific computing as well as computational mathematics worldwide through his tireless and visionary leadership.His dedication to developing academic programs in many leading Chinese universities and institutions,along with his stewardship in establishing national computational research programs,played a fundamental role in elevating Chinese computational research status to a global recognition.Several generations of Chinese scholars benefited from his guidance and teaching,and this focused issue of original research contributions from 33 Chinese and international scientist teams bears witness to the profound influence of Prof.Shi on their research careers by his lifetime of work spanning over six decades.Beyond being an accomplished mathematician,Prof.Shi had lived a life of a cultured man who radiated vigor and warmth,imbuing his life with heartiness,openness,and honesty.
基金the National Natural Science Foundation of China (Grant Nos. 20073033, 20023001 and 29892166).
文摘Paired-permanent approach for VB theory is extensively developed. Canonical expansion of a paired-permanent is deduced. Furthermore, it is shown that a paired-permanent may be expressed in terms of the products of sub-paired-permanents of any given order and their corresponding minors. An ab initio spin-free valence bond program, called Xiamen, is implemented by using paired-permanent approach. Test calculation shows that Xiamen package is more efficient than some other programs based on the traditional VB algorithm, and it provides a new practical tool for quantum chemistry.
