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Translation of Quantum Circuits into Quantum Turing Machines for Deutsch and Deutsch-Jozsa Problems
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作者 Giuseppe Corrente 《Journal of Quantum Computing》 2020年第3期137-145,共9页
We want in this article to show the usefulness of Quantum Turing Machine(QTM)in a high-level didactic context as well as in theoretical studies.We use QTM to show its equivalence with quantum circuit model for Deutsch... We want in this article to show the usefulness of Quantum Turing Machine(QTM)in a high-level didactic context as well as in theoretical studies.We use QTM to show its equivalence with quantum circuit model for Deutsch and Deutsch-Jozsa algorithms.Further we introduce a strategy of translation from Quantum Circuit to Quantum Turing models by these examples.Moreover we illustrate some features of Quantum Computing such as superposition from a QTM point of view and starting with few simple examples very known in Quantum Circuit form. 展开更多
关键词 Deutsch-Jozsa algorithm Quantum Computing quantum turing machine
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Approximation and universality of fuzzy Turing machines 被引量:1
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作者 LI YongMing 《Science in China(Series F)》 2008年第10期1445-1465,共21页
Fuzzy Turing machines are the formal models of fuzzy algorithms or fuzzy computations. In this paper we give several different formulations of fuzzy Turing machine, which correspond to nondeterministic fuzzy Turing ma... Fuzzy Turing machines are the formal models of fuzzy algorithms or fuzzy computations. In this paper we give several different formulations of fuzzy Turing machine, which correspond to nondeterministic fuzzy Turing machine using max-* composition for some t-norm* (or NFTM*, for short), nondeterministic fuzzy Turing machine (or NFTM), deterministic fuzzy Turing machine (or DFTM), and multi-tape versions of fuzzy Turing machines. Some distinct results compared to those of ordinary Turing machines are obtained. First, it is shown that NFTM*, NFTM, and DFTM are not necessarily equivalent in the power of recognizing fuzzy languages if the t-norm* does not satisfy finite generated condition, but are equivalent in the approximation sense. That is to say, we can approximate an NFTM* by some NFTM with any given accuracy; the related constructions are also presented. The level characterization of fuzzy recursively enumerable languages and fuzzy recursive languages are exploited by ordinary r.e. languages and recursive languages. Second, we show that universal fuzzy Turing machine exists in the approximated sense. There is a universal fuzzy Turing machine that can simulate any NFTM* on it with a given accuracy. 展开更多
关键词 fuzzy turing machine fuzzy recursively enumerable language fuzzy recursive language universal fuzzy turing machine fuzzy algorithm
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A secure outsourced Turing- equivalent computation scheme against semi-honest workers using fully homomorphic encryption
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作者 方昊 胡爱群 《Journal of Southeast University(English Edition)》 EI CAS 2016年第3期267-271,共5页
A scheme that can realize homomorphic Turing- equivalent privacy-preserving computations is proposed, where the encoding of the Turing machine is independent of its inputs and running time. Several extended private in... A scheme that can realize homomorphic Turing- equivalent privacy-preserving computations is proposed, where the encoding of the Turing machine is independent of its inputs and running time. Several extended private information retrieval protocols based on fully homomorphic encryption are designed, so that the reading and writing of the tape of the Turing machine, as well as the evaluation of the transition function of the Turing machine, can be performed by the permitted Boolean circuits of fully homomorphic encryption schemes. This scheme overwhelms the Turing-machine-to- circuit conversion approach, which also implements the Turing-equivalent computation. The encoding of a Turing- machine-to-circuit conversion approach is dependent on both the input data and the worst-case runtime. The proposed scheme efficiently provides the confidentiality of both program and data of the delegator in the delegator-worker model of outsourced computation against semi-honest workers. 展开更多
关键词 turing machine fully homomorphic encryption outsourced computation
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Comparison among Classical,Probabilistic and Quantum Algorithms for Hamiltonian Cycle Problem
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作者 Giuseppe Corrente Carlo Vincenzo Stanzione Vittoria Stanzione 《Journal of Quantum Computing》 2023年第1期55-70,共16页
The Hamiltonian cycle problem(HCP),which is an NP-complete problem,consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once.In this paper we compare some algorith... The Hamiltonian cycle problem(HCP),which is an NP-complete problem,consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once.In this paper we compare some algorithms to solve a Hamiltonian cycle problem,using different models of computations and especially the probabilistic and quantum ones.Starting from the classical probabilistic approach of random walks,we take a step to the quantum direction by involving an ad hoc designed Quantum Turing Machine(QTM),which can be a useful conceptual project tool for quantum algorithms.Introducing several constraints to the graphs,our analysis leads to not-exponential speedup improvements to the best-known algorithms.In particular,the results are based on bounded degree graphs(graphs with nodes having a maximum number of edges)and graphs with the right limited number of nodes and edges to allow them to outperform the other algorithms. 展开更多
关键词 Quantum computing probabilistic computing hamiltonian cycle problem random walk quantum turing machine
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High Energy Physics and Cosmology as Computation 被引量:3
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作者 Mohamed S. El Naschie 《American Journal of Computational Mathematics》 2016年第3期185-199,共16页
The present paper is basically written as a non-apologetic strong defence of the thesis that computation is part and parcel of a physical theory and by no means a mere numerical evaluation of the prediction of a theor... The present paper is basically written as a non-apologetic strong defence of the thesis that computation is part and parcel of a physical theory and by no means a mere numerical evaluation of the prediction of a theory which comes towards the end. Various general considerations as well as specific examples are given to illustrate and support our arguments. These examples range from the practical aspect to almost esoteric considerations but at the end, everything converges towards a unity of theory and computation presented in the form of modern fractal logic and transfinite quantum field theory in a Cantorian spacetime. It is true that all our examples are taken from physics but our discussion is applicable in equal measure to a much wider aspect of life. 展开更多
关键词 Fractal Logic E-Infinity Theory Cantorian-Fractal Spacetime P. Erdos A. turing Computer Transfinite turing Machine A. Connes Noncommutative Geometry von Neumann Continuous Geometry Golden Mean Computer Pointless Geometry Fuzzy Sets Fuzzy Logic
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Enumeration Order Equivalence in Rational Numbers
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作者 Saeed Asaeedi Farzad Didehvar Aliakbar Safilian 《Computer Technology and Application》 2013年第11期615-619,共5页
The enumeration of elements of c.e. sets in the theory of computability and computational complexity has already been investigated. However, the order of this enumeration has received less attention. The enumeration o... The enumeration of elements of c.e. sets in the theory of computability and computational complexity has already been investigated. However, the order of this enumeration has received less attention. The enumeration orders of elements of c.e. sets by means of Turing machines on natural numbers are investigated. In this paper, we consider the enumeration orders of elements of c.e. sets on rational numbers. We present enumeration order reducibility and enumeration order equivalence on rational numbers and propose some lemmas and theorems on these concepts. Also, we show that the theories here hold for Rc and we could repeat the same theories in this domain, in a same way. 展开更多
关键词 turing machine LISTINGS enumeration order reducibility enumeration order equivalence
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Dimensional Complexity and Algorithmic Efficiency
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作者 Alexander Odilon Ngu 《International Journal of Modern Nonlinear Theory and Application》 2022年第1期1-10,共10页
This paper uses the concept of algorithmic efficiency to present a unified theory of intelligence. Intelligence is defined informally, formally, and computationally. We introduce the concept of dimensional complexity ... This paper uses the concept of algorithmic efficiency to present a unified theory of intelligence. Intelligence is defined informally, formally, and computationally. We introduce the concept of dimensional complexity in algorithmic efficiency and deduce that an optimally efficient algorithm has zero time complexity, zero space complexity, and an infinite dimensional complexity. This algorithm is used to generate the number line. 展开更多
关键词 Symbolic Intelligence Dimensional Complexity Algorithmic Efficiency Notational Unification turing Complete Machine Unified Theory
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Parallel Turing Machine, a Proposal 被引量:1
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作者 Peng Qu Jin Yah +1 位作者 You-Hui Zhang Guang R. Gao 《Journal of Computer Science & Technology》 SCIE EI CSCD 2017年第2期269-285,共17页
We have witnessed the tremendous momentum of the second spring of parallel computing in recent years. But, we should remember the low points of the field more than 20 years ago and review the lesson that has led to th... We have witnessed the tremendous momentum of the second spring of parallel computing in recent years. But, we should remember the low points of the field more than 20 years ago and review the lesson that has led to the question at that point whether "parallel computing will soon be relegated to the trash heap reserved for promising technologies that never quite make it" in an article entitled "the death of parallel computing" written by the late Ken Kennedy -- a prominent leader of parallel computing in the world. Facing the new era of parallel computing, we should learn from the robust history of sequential computation in the past 60 years. We should study the foundation established by the model of Tuhring machine (1936) and its profound impact in this history. To this end, this paper examines the disappointing state of the work in parallel Turing machine models in the past 50 years of parallel computing research. Lacking a solid yet intuitive parallel Turing machine model will continue to be a serious challenge in the future parallel computing. Our paper presents an attempt to address this challenge by presenting a proposal of a parallel Turing machine model. We also discuss why we start our work in this paper from a parallel Turing machine model instead of other choices. 展开更多
关键词 parallel turing machine codelet abstract architecture parallel computing
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On a class of quantum Turing machine halting deterministically
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作者 LIANG Min YANG Li 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2013年第5期941-946,共6页
We consider a subclass of quantum Turing machines (QTM), named stationary rotational quantum Turing machine (SR-QTM), which halts deterministically and has deterministic tape head position. A quantum state transition ... We consider a subclass of quantum Turing machines (QTM), named stationary rotational quantum Turing machine (SR-QTM), which halts deterministically and has deterministic tape head position. A quantum state transition diagram (QSTD) is proposed to describe SR-QTM. With QSTD, we construct a SR-QTM which is universal for all near-trivial transformations. This indicates there exists a QTM which is universal for the above subclass. Finally we show that SR-QTM is computational equivalent with ordinary QTM in the bounded error setting. It can be seen that SR-QTMs have deterministic tape head position and halt deterministically, and thus the halting scheme problem will not exist for this class of QTMs. 展开更多
关键词 quantum turing machine quantum circuit halting scheme quantum computational complexity
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A Set-Theoretical Lemma That Implies an Abstract Form of Gdel's Theorem
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作者 爱德华.阿罗约 徐利治 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2005年第4期647-650,共4页
We propose a simple set-theoretical lemma that implies Godel's Incompleteness Theorem. Also mentioned are some related consequences.
关键词 Enumerably infinite set Godel's Incompleteness Theorem turing machines.
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