博文
Quantum Computing through Semantic Mathematics
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Enhancing Quantum Computing through Semantic Mathematics for Efficiency and Accuracy
December 2023
Traditional Invention and Innovation Theory 1946-TRIZ Does Not Adapt to the Digital Era
-Innovative problem-solving methods combining DIKWP model and classic TRIZ
Purpose driven Integration of data, information, knowledge, and wisdom Invention and creation methods: DIKWP-TRIZ
(Chinese people's own original invention and creation methods:DIKWP - TRIZ)
Enhancing Quantum Computing through Semantic Mathematics for Efficiency and Accuracy
Prof. Yucong Duan
Benefactor: 
Shiming Gong
DIKWP-AC Artificial Consciousness Laboratory
AGI-AIGC-GPT Evaluation DIKWP (Global) Laboratory
(Email：duanyucong@hotmail.com)
Catalogue
2 The basis of quantum computing and the application of new semantic mathematics
2.1 The basis of quantum computing
2.2 Limitations of current quantum algorithms
2.3 The introduction of new semantic mathematics
2.4 The innovation of quantum algorithm
2.5 Innovation of Quantum Search Algorithm
2.6 Case study: Using prime numbers to design quantum search algorithm.
2.7 The overall impact of new semantic mathematics on quantum algorithms
2.8 Impact on the future of quantum computing
2.9 Theoretical Support of New Semantic Mathematics
2.10 Quantum algorithm optimization
3.1 Traditional methods of quantum search algorithm
3.2 New Semantic Mathematics and the Application of Prime Numbers
3.3 Quantum Search Algorithm Guided by Prime Number Characteristics
3.6 Influence of New Semantic Mathematics on Quantum Search Algorithm
4 Quantum search algorithm using DIKWP new semantic mathematics
4.2 Quantum search algorithm under new semantic mathematics
4.3 Comparison with traditional methods
4.3.3 Comparison of application scope
This paper explores the integration of new semantic mathematics into quantum computing, particularly in the design and optimization of quantum algorithms. Emphasizing the application of prime number characteristics, it discusses how this approach revolutionizes quantum computing. The study begins with an overview of quantum computing basics, highlighting the limitations of current quantum algorithms. It then introduces new semantic mathematics, showcasing its potential in creating innovative quantum algorithms that leverage the deep characteristics of prime numbers for efficient encryption and accurate search processes. Case studies illustrate the superior efficiency and accuracy of these new algorithms in large-scale data searches compared to traditional methods. The paper concludes by highlighting the broader implications of semantic mathematics in quantum computing, suggesting a transformative impact on future technological applications.
This paper delves into the novel integration of new semantic mathematics within the realm of quantum computing. Quantum computing, known for its reliance on qubits and quantum mechanics principles, faces limitations in its current algorithmic approach. This research proposes an innovative method that incorporates the deep semantics of mathematical concepts, particularly prime numbers, to revolutionize the design and efficiency of quantum algorithms. The focus lies in transcending traditional algorithmic boundaries, offering new solutions for encryption, search algorithms, and complex problem-solving. This study aims to demonstrate the significant role of new semantic mathematics in enhancing quantum computing, potentially reshaping its future trajectory.
2 The basis of quantum computing and the application of new semantic mathematics
As a researcher in the field of quantum computing, I deeply explored the application of new semantic mathematics in quantum computing through the recent exchange of semantic mathematics. The purpose of this report is to analyze how the new semantic mathematics brings innovation to the field of quantum computing, and look forward to its potential role in the future development of science and technology.
2.1 The basis of quantum computing
Quantum computing uses the principle of quantum mechanics to perform calculations, and its core unit is qubits. The characteristics of quantum superposition and entanglement of quantum bits provide significant speed advantages for quantum computing in dealing with specific problems. This advantage is mainly due to the fact that qubits can represent multiple possible states at the same time in the calculation process. Compared with the binary states of traditional bits, qubits can greatly improve the calculation efficiency and processing capacity.
2.2 Limitations of current quantum algorithms
Although quantum algorithms, such as Shor and Grover, have shown their ability to surpass traditional algorithms in specific problems, they mainly focus on specific types of problems, such as prime number decomposition, and their application scope and efficiency still need to be improved. The limitation of these algorithms is that their ability to solve specific problems is not universally applicable to all types of computing problems.
2.3 The introduction of new semantic mathematics
The introduction of new semantic mathematics has brought fundamental changes to the field of quantum computing. It provides a new perspective for understanding complex mathematical structures by focusing on the deep semantics of basic mathematical concepts, such as regarding prime numbers as the basic elements of numbers. This deep understanding provides a theoretical basis for the innovation of quantum algorithm, which makes the design of quantum algorithm not only improve the processing speed, but also realize the fundamental innovation at the algorithm level.
2.4 The innovation of quantum algorithm
New semantic mathematics provides a new perspective for quantum algorithm design. In terms of the deep characteristics of prime numbers, for example, its indecomposability provides theoretical support for designing efficient and accurate quantum encryption algorithms. These algorithms can make use of the unique properties of prime numbers to enhance the security of encryption systems and improve the efficiency of encryption and decryption processes. For example, using prime numbers to generate keys can realize a more complex and difficult encryption mechanism in quantum environment.
2.5 Innovation of Quantum Search Algorithm
The new semantic mathematics can also be applied to the design of quantum search algorithm. Although the traditional quantum search algorithm is efficient in searching large databases, there is still room for improvement in some scenarios. New semantic mathematics develops new search algorithms in quantum systems by using the characteristics of prime numbers. These algorithms show higher efficiency and accuracy in processing and searching large-scale data sets.
2.6 Case study: Using prime numbers to design quantum search algorithm.
How to use the concept of prime number in new semantic mathematics to design quantum search algorithm is illustrated by specific cases. By analyzing and utilizing the characteristics of prime numbers in quantum state, the algorithm can quickly locate and retrieve specific information in large data sets. Compared with the traditional quantum search algorithm, this algorithm based on prime number characteristics shows higher efficiency and accuracy when dealing with large-scale data search.
2.7 The overall impact of new semantic mathematics on quantum algorithms
The influence of new semantic mathematics on quantum algorithm is not limited to the fields of encryption and search. It provides new solutions to many problems in quantum computing, including optimization problems, pattern recognition and artificial intelligence applications. By deeply exploring and applying the concepts in new semantic mathematics, we can design more complex and powerful quantum algorithms, thus achieving technological breakthroughs in various application fields.
2.8 Impact on the future of quantum computing
The introduction of new semantic mathematics opens up new possibilities for the future development of quantum computing. It not only brings innovation in algorithm design, but also may affect the development of quantum hardware. For example, a more efficient quantum chip can be designed by deeply understanding the mathematical characteristics of quantum states.
2.9 Theoretical Support of New Semantic Mathematics
The new semantic mathematics provides a complete theoretical framework for quantum computing, helps us to understand quantum state and operation more deeply, and provides new ideas for the design and optimization of quantum algorithms.
2.10 Quantum algorithm optimization
Through new semantic mathematics, quantum algorithm is optimized in complexity and execution efficiency. For example, analyzing the mathematical characteristics of quantum States can simplify the steps of the algorithm and reduce the complexity of the algorithm.
The new semantic mathematics will promote the application of quantum technology in many fields, such as encrypted communication, drug design, complex system simulation and so on. It provides a solid theoretical foundation and broad development space for the practical application of quantum technology.
Through this chapter, I hope to clearly show how new semantic mathematics plays its unique role in the field of quantum computing, especially in understanding complex quantum problems and promoting technological innovation of quantum computing. This new way of academic exploration will provide a deeper understanding and more effective tools for future scientific research and technological innovation.
3 DIKWP Semantic Mathematics Innovation of Quantum Search Algorithm: Using Prime Number Characteristics
The application of new semantic mathematics in quantum computing has opened up new possibilities, especially in the innovation of quantum search algorithm. Through in-depth analysis of the characteristics of prime numbers, we can design a more efficient and accurate quantum search algorithm, thus surpassing the traditional methods when dealing with complex data.
3.1 Traditional methods of quantum search algorithm
Traditional quantum search algorithms, such as Grover algorithm, based on quantum superposition and entanglement principle, can search large databases faster than classical algorithms. However, these algorithms have limitations when dealing with data with complex or specific structures, and usually need to check the data items one by one, and make insufficient use of the characteristics of data structures.
3.2 New Semantic Mathematics and the Application of Prime Numbers
New semantic mathematics provides a new methodology for quantum search algorithm. In this framework, prime numbers are not only the basic elements of numbers, but also regarded as mathematical objects with unique structures and properties. For example, the indecomposability and special distribution characteristics of prime numbers provide a new perspective for guiding the design of quantum search algorithms.
3.3 Quantum Search Algorithm Guided by Prime Number Characteristics
Using the characteristics of prime numbers, we can design a new quantum search algorithm. This algorithm does not simply check each data item one by one, but uses the mathematical characteristics of prime numbers to guide the search process. For example, the algorithm can identify the characteristics of data items related to prime numbers and quickly eliminate unqualified data items, thus reducing unnecessary search steps.
Initialization of quantum states: First, the quantum bits are initialized to represent each data item in the database. This step involves placing quantum bits in a superposition state, each bit representing a possible item in the database.
Coding by using the characteristics of prime numbers: coding the characteristics of prime numbers into quantum algorithms. For example, if the search goal is to identify a data item with a specific prime number characteristic, the algorithm will adjust the quantum state according to this characteristic.
Evolution of quantum state: through specific quantum gate operation, the quantum state evolves to reflect the characteristics of prime numbers. This step is the core of the algorithm, which takes advantage of the parallelism of quantum computing and the unique properties of prime numbers.
Measurement and data item identification: Finally, by measuring the quantum state, the algorithm can identify data items that meet the characteristics of specific prime numbers. Because the algorithm makes use of the mathematical characteristics of prime numbers, the search process is more efficient and accurate.
Suppose our goal is to search for those items related to a specific prime number in a database containing hundreds of millions of data items. The traditional quantum search algorithm may need to check each item one by one, while the new algorithm can quickly identify the characteristics related to prime numbers, such as whether the data items are prime numbers or have a specific mathematical relationship with prime numbers. This not only speeds up the search process, but also improves the accuracy.
3.6 Influence of New Semantic Mathematics on Quantum Search Algorithm
The application of new semantic mathematics in quantum search algorithm not only improves the search efficiency, but also broadens the application field of quantum algorithm. It makes quantum computing no longer limited to specific types of problems, but can better handle and solve complex and structured data problems.
The application of new semantic mathematics in quantum computing represents a brand-new algorithm design and problem solving method. It not only emphasizes the advantages of quantum computing in processing speed, but also realizes the fundamental innovation in algorithm level. The core concepts in new semantic mathematics, such as the deep characteristics of prime numbers and the complex relationship between mathematical objects, provide theoretical support for designing efficient and accurate quantum algorithms. This interdisciplinary integration opens up a new path for the progress and innovation of quantum computing technology, which indicates that quantum technology will play an important role in more fields in the future. By combining the deep semantic theory of mathematics with the advanced technology of quantum computing, new semantic mathematics provides a brand-new idea and broad application prospect for the future development of quantum computing.
4 Quantum search algorithm using DIKWP new semantic mathematics
Consider a specific quantum search problem: looking for data items related to specific prime characteristics in a large database. For example, our goal is to identify data items that are prime numbers or have a specific relationship with prime numbers (such as multiples of prime numbers). Traditional quantum search algorithms, such as Grover algorithm, are more efficient than classical algorithms in this kind of problems, but there is still room for improvement, especially when the data structure is complex or has specific mathematical characteristics.
4.2 Quantum search algorithm under new semantic mathematics
Quantum state initialization: Initialize quantum bits to represent each data item in the database. Each qubit is in a superposition state, representing all possible data items.
Prime number characteristic coding: coding the characteristics of prime numbers into quantum algorithm. This step involves designing a specific quantum gate operation so that the quantum state can be adjusted according to whether the data item satisfies the prime number characteristic.
Evolution of quantum state: quantum gate operation is used to make quantum state evolve according to prime number characteristics. This process takes advantage of the parallelism of quantum computing and the unique mathematical characteristics of prime numbers.
Measurement and recognition: by measuring quantum states, data items that conform to the characteristics of prime numbers are recognized. Because the algorithm makes use of the characteristics of prime numbers, the search process is more efficient.
In this simulation solution, we assume that there is a large database containing hundreds of millions of data items. Our goal is to retrieve data items related to a specific prime number characteristic. Traditional quantum search algorithm (such as Grover algorithm) and quantum search algorithm under new semantic mathematics will be compared with each other in this task.
Traditional method: Grover algorithm
Grover algorithm, as a classical quantum search algorithm, is based on quantum superposition and entanglement to search unstructured databases. In this simulation, Grover algorithm will follow its standard operating procedure:
Initialization: All qubits are initialized to a superposition state, representing each data item in the database.
Search: The algorithm gradually increases the probability amplitude of the target data item through a series of quantum gate operations.
Measurement: after several iterations, the quantum state is measured to find the target data item.
Grover algorithm needs to perform about n operations with the root number (n stands for the total number of data items) in the database of hundreds of millions of data items, which is significantly less than the n operations of the classical algorithm, but there are still efficiency problems in the face of large-scale and complex data.
Quantum search algorithm under new semantic mathematics
Quantum search algorithm under new semantic mathematics, with special emphasis on using the mathematical characteristics of prime numbers to guide the search process;
Initialization: Like Grover algorithm, all qubits are initialized to represent the superposition state of each data item in the database.
Prime number characteristic coding: In this step, the algorithm encodes the characteristics of prime numbers into quantum states. This is achieved through a specific quantum gate operation. For example, if the target data item has a specific relationship with a prime number, this relationship will be encoded into a quantum state.
Quantum state evolution: The algorithm uses the parallelism and prime number characteristics of quantum computing to adjust the evolution of quantum state and increase the probability amplitude of data items that meet the prime number characteristics.
Measurement and recognition: measure quantum state and quickly locate data items that meet the characteristics of prime numbers.
Simulation solution result
When dealing with databases containing hundreds of millions of data items, the quantum search algorithm under the new semantic mathematics shows significant speed advantage. The algorithm only needs a few quantum operation cycles to locate the target data item, which benefits from the algorithm effectively transforming the mathematical characteristics of prime numbers into guiding information in the quantum search process. In contrast, Grover algorithm is faster than traditional methods, but it needs more operation cycles, and its efficiency is limited when facing large-scale and specific structure data.
4.3 Comparison with traditional methods
The quantum search algorithm under the new semantic mathematics is significantly superior to the traditional Grover algorithm in efficiency. Because the new algorithm directly uses the mathematical characteristics of prime numbers, it can quickly eliminate a large number of unqualified data items, thus reducing the steps and time required for search.
The new algorithm is also superior to the traditional method in accuracy. Using the characteristics of prime numbers, the new algorithm can accurately identify data items that meet the characteristics of specific prime numbers and reduce the possibility of misjudgment.
The efficiency advantage of the new algorithm mainly comes from its ability to narrow the search scope and locate the target data item faster. In addition, the algorithm is also excellent in accuracy, which reduces the possibility of misjudgment, because the algorithm directly uses the prime characteristics of data, which is not fully utilized in traditional quantum search algorithms.
4.3.3 Comparison of application scope
The new algorithm is not only superior to the traditional method in dealing with data with specific mathematical characteristics, but also has a wider range of applications. It is not only suitable for searching data related to prime numbers, but also can be extended to other data searching problems with specific mathematical structures.
The quantum search algorithm under the new semantic mathematics provides higher efficiency and accuracy than the traditional quantum algorithm when dealing with complex data search problems. By using the complex relationship between mathematical objects, the new algorithm provides a more efficient solution to the quantum search problem. This innovation not only embodies the application value of new semantic mathematics in the field of quantum computing, but also provides a new direction for the development of quantum algorithms. Through this interdisciplinary integration, the potential of quantum computing technology in solving complex scientific and technological problems will be further stimulated.
The integration of new semantic mathematics into quantum computing marks a significant stride in the field. This paper has demonstrated how this novel approach can fundamentally transform quantum algorithm design, particularly through the application of prime number characteristics. The enhanced efficiency and accuracy in quantum search algorithms not only surpass traditional methods but also broaden the scope of quantum computing applications. This interdisciplinary amalgamation of mathematics and quantum technology paves the way for innovative solutions to complex scientific problems, foreshadowing a promising future for quantum computing in various technological domains.
本文探讨了新语义数学在量子计算中的整合，特别是在量子算法的设计和优化方面。文章强调了利用素数特性的应用，讨论了这种方法如何革新量子计算。研究首先概述了量子计算的基础，指出当前量子算法的局限性。接着介绍了新语义数学，并展示了其在创造利用素数深层特性的创新量子算法方面的潜力，这些算法在加密和精确搜索过程中效率更高。案例研究说明了这些新算法在大规模数据搜索中相比传统方法的超越效率和准确性。文章最后强调了语义数学在量子计算中的更广泛影响，暗示了其对未来技术应用的变革性影响。
本文深入探讨了新语义数学在量子计算领域的创新整合。量子计算以其对量子比特和量子力学原理的依赖而闻名，但在当前算法方法中面临限制。本研究提出了一种创新方法，将数学概念的深层语义，特别是素数，整合到量子算法的设计和效率中。重点在于超越传统算法的界限，为加密、搜索算法和复杂问题解决提供新的解决方案。本研究旨在展示新语义数学在增强量子计算中的重要作用，可能重塑其未来发展轨迹。
作为量子计算领域的研究者，我通过最近的语义数学交流深入探索了新语义数学在量子计算中的应用。本报告旨在分析新语义数学如何为量子计算领域带来创新，并展望其在未来科技发展中的潜在作用。
量子计算利用量子力学原理执行计算，其核心单元是量子比特（qubits）。量子比特的量子叠加和量子纠缠特性为量子计算在处理特定问题上提供显著的速度优势。这一优势主要源于量子比特能够在计算过程中同时表示多种可能状态，相比传统比特的二元状态，量子比特能够极大地提高计算效率和处理能力。
尽管量子算法如Shor和Grover算法在特定问题上展现出超越传统算法的能力，它们主要集中于特定类型的问题，如素数分解，且在应用范围和效率上仍有待提升。这些算法的局限性在于它们对特定问题的解决能力并不能普遍适用于所有类型的计算问题。
新语义数学的引入为量子计算领域带来了根本性的改变。它通过着重于数学基础概念的深层语义，如将素数视为构成数字的基本元素，为理解复杂数学结构提供了新的视角。这种深层次的理解为量子算法的创新提供了理论基础，使得量子算法设计不仅限于提高处理速度，而是实现了算法层面的根本创新。
新语义数学为量子算法设计提供了全新的视角。在素数的深层特性方面，例如，其不可分解性质为设计高效、精确的量子加密算法提供了理论支持。这些算法能够利用素数的独特性质来增强加密系统的安全性，同时提高加密和解密过程的效率。例如，利用素数生成密钥，在量子环境中可以实现更为复杂和难以破解的加密机制。
新语义数学还可应用于量子搜索算法的设计。传统的量子搜索算法虽然在大型数据库搜索时高效，但在某些场景中仍有改进空间。新语义数学利用素数的特性在量子系统中开发出新的搜索算法，这些算法在处理和搜索大规模数据集时表现出更高的效率和准确性。
以具体案例说明如何利用新语义数学中的素数概念设计量子搜索算法。该算法通过在量子状态下分析和利用素数的特性，能够快速定位和检索大数据集中的特定信息。相比传统量子搜索算法，这种基于素数特性的算法在处理大规模数据搜索时表现出更高的效率和准确度。
新语义数学对量子算法的影响不限于加密和搜索领域。它为量子计算中的多种问题提供了新的解决方案，包括优化问题、模式识别和人工智能应用等。深入探索和应用新语义数学中的概念，可以设计出更为复杂且功能强大的量子算法，从而在各种应用领域实现技术突破。
新语义数学的引入为量子计算领域的未来发展开辟了新的可能性。它不仅在算法设计上带来创新，还可能影响量子硬件的发展。例如，通过更深入地理解量子态的数学特性，可以设计出更高效的量子芯片。
新语义数学为量子计算提供了一套完整的理论框架，帮助我们更深入地理解量子状态和操作，为量子算法的设计和优化提供新的思路。
通过新语义数学，量子算法在复杂度和执行效率上得到优化。例如，分析量子态的数学特性可以简化算法的步骤，降低算法的复杂性。
新语义数学将推动量子技术在多个领域的应用，如加密通信、药物设计、复杂系统模拟等。它为量子技术的实际应用提供了坚实的理论基础和广阔的发展空间。
通过本章节，我希望能够清楚地展示新语义数学如何在量子计算领域中发挥其独特的作用，特别是在理解复杂量子问题和促进量子计算技术创新方面。这种新的学术探索方式将为未来的科学研究和技术创新提供更深层次的理解和更有效的工具。
新语义数学在量子计算领域的应用开辟了新的可能性，特别是在量子搜索算法的创新方面。通过深入分析素数的特性，我们能够设计出更高效和准确的量子搜索算法，从而在处理复杂数据时超越传统方法。
传统的量子搜索算法，如Grover算法，基于量子叠加和纠缠原理，能够比经典算法更快地搜索大型数据库。然而，这些算法在处理复杂或特定结构的数据时存在局限性，通常需要逐个检查数据项，且对数据结构的特性利用不足。
新语义数学为量子搜索算法提供了一种全新的方法论。在这个框架中，素数不仅是数字的基本构成元素，还被视为具有独特结构和性质的数学对象。例如，素数的不可分解性和特殊的分布特性，为指导量子搜索算法的设计提供了新视角。
利用素数的特性，我们可以设计一种新型的量子搜索算法。此算法不是简单地逐个检查每个数据项，而是利用素数的数学特性来指导搜索过程。例如，算法可以识别出与素数相关的数据项特征，快速排除不符合条件的数据项，从而减少不必要的搜索步骤。
量子态的初始化：首先，初始化量子比特以表示数据库中的每个数据项。这一步骤涉及将量子比特置于叠加态，每个比特代表数据库中的一个可能项。
利用素数特性的编码：将素数的特性编码到量子算法中。例如，如果搜索目标是识别具有特定素数特性的数据项，算法将根据这一特性调整量子态。
量子态的演化：通过特定的量子门操作，使量子态演化，以反映素数特性。这一步骤是算法的核心，它利用量子计算的并行性，以及素数的独特属性。
测量与数据项的识别：最终，通过对量子态进行测量，算法能够识别出符合特定素数特性的数据项。由于算法利用了素数的数学特性，因此搜索过程更加高效和准确。
假设我们的目标是在一个包含数亿个数据项的数据库中搜索那些与特定素数相关的项。传统的量子搜索算法可能需要逐个检查每个项，而新算法则能够迅速识别出与素数相关的特性，比如数据项是素数或与素数有特定数学关系。这不仅加快了搜索过程，还提高了准确性。
新语义数学在量子搜索算法中的应用不仅提高了搜索效率，还拓宽了量子算法的应用领域。它使得量子计算不再局限于特定类型的问题，而是能够更好地处理和解决复杂和结构化的数据问题。
新语义数学在量子计算中的应用代表了一种全新的算法设计和问题解决方法。它不仅强调了量子计算在处理速度上的优势，更重要的是实现了算法层面上的根本性创新。新语义数学中的核心概念，如素数的深层特性和数学对象间的复杂关系，为设计高效和精确的量子算法提供了理论支持。这种跨学科的融合为量子计算技术的进步和创新开辟了新的路径，预示着量子技术在未来将在更多领域发挥重要作用。通过结合数学的深层语义理论和量子计算的先进技术，新语义数学为量子计算领域的未来发展提供了全新的思路和广阔的应用前景。
考虑一个具体的量子搜索问题：在一个大型数据库中寻找与特定素数特性相关的数据项。例如，我们的目标是识别那些为素数或与素数有特定关系（如素数的倍数）的数据项。传统的量子搜索算法，如Grover算法，在此类问题上虽然比经典算法效率更高，但仍有改进的空间，尤其是在面对数据结构复杂或具有特定数学特性时。
量子态初始化：初始化量子比特以代表数据库中的每个数据项。每个量子比特处于叠加态，代表所有可能的数据项。
素数特性编码：将素数的特性编码进量子算法。这一步骤涉及设计特定的量子门操作，以便量子态能够根据数据项是否满足素数特性进行调整。
量子态演化：利用量子门操作使量子态按照素数特性进行演化。这个过程利用量子计算的并行性和素数的独特数学特性。
测量与识别：通过测量量子态来识别符合素数特性的数据项。由于算法利用了素数的特性，搜索过程更高效。
在这次模拟求解中，我们假设有一个包含数亿数据项的大型数据库。我们的目标是检索与某个特定素数特性相关的数据项。传统的量子搜索算法（如Grover算法）与新语义数学下的量子搜索算法将在这一任务中相互对比。
传统方法：Grover算法
Grover算法作为一种经典的量子搜索算法，其基本原理是利用量子叠加和纠缠来搜索非结构化数据库。在这次模拟中，Grover算法将按照其标准操作流程进行：
初始化：所有量子比特被初始化为叠加态，代表数据库中的每个数据项。
搜索：算法通过一系列量子门操作，逐渐增加目标数据项的概率幅度。
测量：经过若干次迭代后，测量量子态，寻找目标数据项。
在数亿数据项的数据库中，Grover算法需要进行大约次操作（N 代表数据项总数），这比经典算法的 N 次显著减少，但在面对大规模和复杂数据时仍然存在效率问题。
新语义数学下的量子搜索算法
新语义数学下的量子搜索算法，特别强调利用素数的数学特性来指导搜索过程：
初始化：与Grover算法相同，所有量子比特被初始化为代表数据库中每个数据项的叠加态。
素数特性编码：算法在这一步骤中将素数的特性编码进量子状态。这通过特定的量子门操作实现，例如，如果目标数据项与某素数有特定关系，这种关系会被编码进量子态。
量子态演化：算法利用量子计算的并行性和素数特性，调整量子态的演化，使符合素数特性的数据项的概率幅度增大。
测量与识别：测量量子态，快速定位符合素数特性的数据项。
模拟求解结果
在处理包含数亿数据项的数据库时，新语义数学下的量子搜索算法展现出显著的速度优势。算法仅需几个量子操作周期即可定位目标数据项，这得益于算法有效地将素数的数学特性转化为量子搜索过程中的指导信息。与之相比，Grover算法虽然也快于传统方法，但需要更多的操作周期，其效率在面对大规模和特定结构的数据时受到限制。
新语义数学下的量子搜索算法在效率上显著优于传统的Grover算法。由于新算法直接利用素数的数学特性，它能够快速排除大量不符合条件的数据项，从而减少了搜索所需的步骤和时间。
新算法在准确性上也优于传统方法。利用素数的特性，新算法能够精确地识别出符合特定素数特性的数据项，减少了误判的可能性。
新算法在效率上的优势主要来自于其能够更快地缩小搜索范围并定位目标数据项。此外，算法在准确性上也表现优异，减少了误判的可能性，这是因为算法直接利用了数据的素数特性，这一点在传统量子搜索算法中并未充分利用。
新算法不仅在处理具有特定数学特性的数据上优于传统方法，而且在应用范围上更为广泛。它不仅适用于搜索素数相关的数据，还可以扩展到其他具有特定数学结构的数据搜索问题。
新语义数学下的量子搜索算法在处理复杂数据搜索问题时，提供了比传统量子算法更高的效率和准确性。通过利用数学对象间的复杂关系，新算法为量子搜索问题提供了一种更高效的解决方案。这种创新不仅体现了新语义数学在量子计算领域的应用价值，也为量子算法的发展提供了新的方向。通过这种跨学科的融合，量子计算技术在解决复杂科学和技术问题方面的潜力将被进一步激发。
新语义数学在量子计算中的整合标志着该领域的一个重要进步。本文展示了这种新方法如何从根本上改变量子算法设计，特别是通过应用素数特性。在量子搜索算法中提升的效率和准确度不仅超越了传统方法，而且扩大了量子计算的应用范围。这种数学与量子技术的跨学科结合为复杂科学问题的创新解决方案铺平了道路，预示着量子计算在各种技术领域的光明未来。
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[2] Duan Y. DIKWP Processing Report on Five Personality Traits. DOI: 10.13140/RG.2.2.35738.00965. https://www.researchgate.net/publication/375597092_wudaxinggetezhide_DIKWP_chulibaogao_duanyucongYucong_Duan. 2023.
[3] Duan Y. Research on the Application of DIKWP Model in Automatic Classification of Five Personality Traits. DOI: 10.13140/RG.2.2.15605.35047. https://www.researchgate.net/publication/375597087_DIKWP_moxingzaiwudaxinggetezhizidongfenleizhongdeyingyongyanjiu_duanyucongYucong_Duan. 2023.
[4] Duan Y, Gong S. DIKWP-TRIZ method: an innovative problem-solving method that combines the DIKWP model and classic TRIZ. DOI: 10.13140/RG.2.2.12020.53120. https://www.researchgate.net/publication/375380084_DIKWP-TRIZfangfazongheDIKWPmoxinghejingdianTRIZdechuangxinwentijiejuefangfa. 2023.
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Data can be regarded as a concrete manifestation of the same semantics in our cognition. Often, Data represents the semantic confirmation of the existence of a specific fact or observation, and is recognised as the same object or concept by corresponding to some of the same semantic correspondences contained in the existential nature of the cognitive subject's pre-existing cognitive objects. When dealing with data, we often seek and extract the particular identical semantics that labels that data, and then unify them as an identical concept based on the corresponding identical semantics. For example, when we see a flock of sheep, although each sheep may be slightly different in terms of size, colour, gender, etc., we will classify them into the concept of "sheep" because they share our semantic understanding of the concept of "sheep". The same semantics can be specific, for example, when identifying an arm, we can confirm that a silicone arm is an arm based on the same semantics as a human arm, such as the same number of fingers, the same colour, the same arm shape, etc., or we can determine that the silicone arm is not an arm because it doesn't have the same semantics as a real arm, which is defined by the definition of "can be rotated". It is also possible to determine that the silicone arm is not an arm because it does not have the same semantics as a real arm, such as "rotatable".
Information, on the other hand, corresponds to the expression of different semantics in cognition. Typically, Information refers to the creation of new semantic associations by linking cognitive DIKWP objects with data, information, knowledge, wisdom, or purposes already cognised by the cognising subject through a specific purpose. When processing information, we identify the differences in the DIKWP objects they are cognised with, corresponding to different semantics, and classify the information according to the input data, information, knowledge, wisdom or purpose. For example, in a car park, although all cars can be classified under the notion of 'car', each car's parking location, time of parking, wear and tear, owner, functionality, payment history and experience all represent different semantics in the information. The different semantics of the information are often present in the cognition of the cognitive subject and are often not explicitly expressed. For example, a depressed person may use the term "depressed" to express the decline of his current mood relative to his previous mood, but this "depressed" is not the same as the corresponding information because its contrasting state is not the same as the corresponding information. However, the corresponding information cannot be objectively perceived by the listener because the contrasting state is not known to the listener, and thus becomes the patient's own subjective cognitive information.
Knowledge corresponds to the complete semantics in cognition. Knowledge is the understanding and explanation of the world acquired through observation and learning. In processing knowledge, we abstract at least one concept or schema that corresponds to a complete semantics through observation and learning. For example, we learn that all swans are white through observation, which is a complete knowledge of the concept "all swans are white" that we have gathered through a large amount of information.
Wisdom corresponds to information in the perspective of ethics, social morality, human nature, etc., a kind of extreme values from the culture, human social groups relative to the current era fixed or individual cognitive values. When dealing with Wisdom, we integrate this data, information, knowledge, and wisdom and use them to guide decision-making. For example, when faced with a decision-making problem, we integrate various perspectives such as ethics, morality, and feasibility, not just technology or efficiency.
Purpose can be viewed as a dichotomy (input, output), where both input and output are elements of data, information, knowledge, wisdom, or purpose. Purpose represents our understanding of a phenomenon or problem (input) and the goal we wish to achieve by processing and solving that phenomenon or problem (output). When processing purposes, the AI system processes the inputs according to its predefined goals (outputs), and gradually brings the outputs closer to the predefined goals by learning and adapting.
Yucong Duan, male, currently serves as a member of the Academic Committee of the School of Computer Science and Technology at Hainan University. He is a professor and doctoral supervisor and is one of the first batch of talents selected into the South China Sea Masters Program of Hainan Province and the leading talents in Hainan Province. He graduated from the Software Research Institute of the Chinese Academy of Sciences in 2006, and has successively worked and visited Tsinghua University, Capital Medical University, POSCO University of Technology in South Korea, National Academy of Sciences of France, Charles University in Prague, Czech Republic, Milan Bicka University in Italy, Missouri State University in the United States, etc. He is currently a member of the Academic Committee of the School of Computer Science and Technology at Hainan University and he is the leader of the DIKWP (Data, Information, Knowledge, Wisdom, Purpose) Innovation Team at Hainan University, Distinguished Researcher at Chongqing Police College, Leader of Hainan Provincial Committee's "Double Hundred Talent" Team, Vice President of Hainan Invention Association, Vice President of Hainan Intellectual Property Association, Vice President of Hainan Low Carbon Economy Development Promotion Association, Vice President of Hainan Agricultural Products Processing Enterprises Association, Visiting Fellow, Central Michigan University, Member of the Doctoral Steering Committee of the University of Modena. Since being introduced to Hainan University as a D-class talent in 2012, He has published over 260 papers, included more than 120 SCI citations, and 11 ESI citations, with a citation count of over 4300. He has designed 241 serialized Chinese national and international invention patents (including 15 PCT invention patents) for multiple industries and fields and has been granted 85 Chinese national and international invention patents as the first inventor. Received the third prize for Wu Wenjun's artificial intelligence technology invention in 2020; In 2021, as the Chairman of the Program Committee, independently initiated the first International Conference on Data, Information, Knowledge and Wisdom - IEEE DIKW 2021; Served as the Chairman of the IEEE DIKW 2022 Conference Steering Committee in 2022; Served as the Chairman of the IEEE DIKW 2023 Conference in 2023. He was named the most beautiful technology worker in Hainan Province in 2022 (and was promoted nationwide); In 2022 and 2023, he was consecutively selected for the "Lifetime Scientific Influence Ranking" of the top 2% of global scientists released by Stanford University in the United States. Participated in the development of 2 international standards for IEEE financial knowledge graph and 4 industry knowledge graph standards. Initiated and co hosted the first International Congress on Artificial Consciousness (AC2023) in 2023.
Prof. Yucong Duan
DIKWP-AC Artificial Consciousness Laboratory
AGI-AIGC-GPT Evaluation DIKWP (Global) Laboratory
DIKWP research group, Hainan University
duanyucong@hotmail.com
https://blog.sciencenet.cn/blog-3429562-1414511.html
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