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A quantum algorithm based on entanglement measure for classifying Boolean multivariate function into novel hidden classes

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RESULTS IN PHYSICS 2019年 15卷 102549-000页

作者： Zidan, Mohammed Abdel-Aty, Abdel-Haleem Duc Manh Nguyen Mohamed, Ahmed S. A. Al-Sbou, Yazeed Eleuch, Hichem Abdel-Aty, Mahmoud Univ Sci & Technol Zewail City Sci & Technol Giza 12578 Egypt CPSM Zewail City Sci & Technol Giza 12578 Egypt Univ Bisha Coll Sci Dept Phys POB 344 Bisha 61922 Saudi Arabia Al Azhar Univ Fac Sci Phys Dept Assiut 71524 Egypt Univ Ulsan Coding & Informat Theory Lab Ulsan 44610 South Korea Cairo Univ Fac Engn Dept Engn Math & Phys Giza 12613 Egypt Appl Sci Univ Res & Grad Studies POB 5055 Manama 55222 Bahrain Abu Dhabi Univ Coll Arts & Sci Dept Appl Sci & Math Abu Dhabi U Arab Emirates Texas A&M Univ Inst Quantum Sci & Engn College Stn TX 77843 USA Sohag Univ Fac Sci Dept Math Sohag Egypt

In this paper, we propose a novel algorithm that solves a generalized version of the Deutsch-Jozsa problem. The proposed algorithm has the potential to classify an oracle U-F, that represents an unknown Boolean function on n Boolean variables, to one of 2(n) different classes instead of only two classes which are constant and balanced classes in the case of Deutsch-Jozsa algorithm. The proposed algorithm is based on the use of entanglement measure to explore 2(n) - 2 additional classes compared to the standard Deutsch-Jozsa algorithm. In addition, the comparison between the proposed quantum algorithm and the classical one is investigated in details. The comparison shows that the proposed algorithm is faster when the number of Boolean variables exceed 14 variables.

关键词： quantum information quantum algorithm Deutsch-Jozsa algorithm quantum entanglement measure

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Comparing Grover’s quantum Search algorithm with Classical algorithm on Solving Satisfiability Problem

Comparing Grover’s Quantum Search Algorithm with Classical ...

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IEEE Integrated STEM Education Conference (ISEC)

作者： Runqian Wang Princeton International School of Math and Science USA

ISBN: (纸本)9781665413848

The emergence of quantum computing provides us the possibility of solving tasks that might take years classically in just a few minutes. For certain problems, quantum computing exhibits quantum supremacy, meaning that the quantum solution runs exponentially faster than classical algorithms and is able to completely take over classical computers. This high efficiency of quantum computing comes not only from the hardware but also the software, quantum algorithms. The algorithms utilize the qubits to make calculations in order to fulfill specific tasks with the lowest time complexity possible. One such algorithm is named the Grover’s algorithm, which is able to perform database search in $\mathcal{O}(\sqrt{N})$, and it runs much faster than the traditional algorithm that takes $\mathcal{O}(N)$ time to solve the same task. For example, when the task is to find the even integers from N integers, traditional computation will need to run through all of the N integers one by one, making at least N steps of calculation, while by using Grover’s algorithm only around $\sqrt{N}$ calculations are needed. This exponential speed-up makes Grover’s algorithm one of the most important quantum algorithms. Grover’s algorithm has a wide application in many fields and is able to improve the time complexity exponentially. One task that can be solved using Grover’s algorithm is the satisfiability problem. This type of problem asks the computer to find a set of values (commonly true or false) for several variables such that they satisfy certain constraints. We use k-SAT problems to refer to satisfiability problems with k boolean variables to be determined. Grover’s algorithm can effectively solve the k-SAT problem by performing the database search on $2 ^{N}$ possible states of the variables. The algorithm’s square root optimization on searching helps to improve the efficiency of this solution significantly. Furthermore, this optimization of Grover’s algorithm may play a more important role

关键词： Computers quantum algorithm Databases Software algorithms Qubit Search problems Software

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quantum algorithm for Triangle Finding in Sparse Graphs

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algorithmICA 2017年第3期79卷 941-959页

作者： Le Gall, Francois Nakajima, Shogo Univ Tokyo Dept Comp Sci Grad Sch Informat Sci & Technol Tokyo Japan

This paper presents a quantum algorithm for triangle finding over sparse graphs that improves over the previous best quantum algorithm for this task by Buhrman et al. (SIAM J Comput 34(6):1324-1330, 2005). Our algorithm is based on the recent (O) over tilde (n(5/4))-query algorithm given by Le Gall (Proceedings of the 55th IEEE annual symposium on foundations of computer science, pp 216-225, 2014) for triangle finding over dense graphs (here n denotes the number of vertices in the graph). We show in particular that triangle finding can be solved with O(n(5/4-epsilon)) queries for some constant epsilon > 0 whenever the graph has at most O(n(2-c))edges for some constant c > 0.

关键词： quantum algorithm quantum walk Triangle finding

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quantum algorithm for K-Nearest Neighbors Classification Based on the Metric of Hamming Distance

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INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2017年第11期56卷 3496-3507页

作者： Ruan, Yue Xue, Xiling Liu, Heng Tan, Jianing Li, Xi Anhui Univ Technol Sch Comp Sci & Technol Maanshan 243005 Peoples R China Southeast Univ Minist Educ Key Lab Comp Network & Informat Integrat Nanjing 210096 Jiangsu Peoples R China Southeast Univ Sch Comp Sci & Engn Nanjing 210096 Jiangsu Peoples R China

K-nearest neighbors (KNN) algorithm is a common algorithm used for classification, and also a sub-routine in various complicated machine learning tasks. In this paper, we presented a quantum algorithm (QKNN) for implementing this algorithm based on the metric of Hamming distance. We put forward a quantum circuit for computing Hamming distance between testing sample and each feature vector in the training set. Taking advantage of this method, we realized a good analog for classical KNN algorithm by setting a distance threshold value t to select k - n e a r e s t neighbors. As a result, QKNN achieves O(n (3)) performance which is only relevant to the dimension of feature vectors and high classification accuracy, outperforms Llyod's algorithm (Lloyd et al. 2013) and Wiebe's algorithm (Wiebe et al. 2014).

关键词： quantum algorithm K-nearest neighbors algorithm Hamming distance Classification Machine learning

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quantum algorithm for Triangle Finding in Sparse Graphs 26th

Quantum Algorithm for Triangle Finding in Sparse Graphs

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26th International Symposium on algorithms and Computation (ISAAC)

作者： Le Gall, Francois Nakajima, Shogo Univ Tokyo Dept Comp Sci Grad Sch Informat Sci & Technol Tokyo Japan

ISBN: (纸本)9783662489710;9783662489703

关键词： quantum algorithm quantum walk Triangle finding

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A quantum query algorithm for computing the degree of a perfect nonlinear Boolean function

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quantum INFORMATION PROCESSING 2019年第3期18卷 62-62页

作者： Wu, WanQing Zhang, HuanGuo Hebei Univ Sch Cyber Secur & Comp Baoding 071002 Peoples R China Wuhan Univ Comp Sch Wuhan 430072 Hubei Peoples R China

The degree of a Boolean function is a basic primitive that has applications in coding theory and cryptography. This paper considers a problem of computing the degree of a perfect nonlinear Boolean function in a quantum system. The details are as follows: Given a promise that the function f is either linear or perfect nonlinear in Fdn, we propose a quantum algorithm 1 to distinguish which case it is with a high probability, where d is an even number. Furtherly, for computing the degree of a perfect nonlinear Boolean function f, we present a quantum algorithm 2 to solve it by calling quantum algorithm 1 when d=2. The quantum query complexity of the proposed quantum algorithm 2 is O(s), and the space complexity (the number of quantum logic gate) is O(2s), where s+1=deg(f). The analysis shows that the quantum algorithm 2 proposed in this paper is more efficient than any classical algorithm for solving this problem.

关键词： quantum algorithm Perfect nonlinear Boolean function Degree

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Dynamic Contraction of Tensor with quantum algorithm 13

Dynamic Contraction of Tensor with Quantum Algorithm

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13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD)

作者： Zhang, Yinsheng Zhao, Hongjian Minakov, Fyodor O. Capital Normal Univ Beijing Peoples R China Inst Sci & Tech Informat China Beijing Peoples R China Huawei Technol Co Ltd Shenzhen Peoples R China

ISBN: (纸本)9781538621653

In the paper, contraction of a dynamic vector (i.e., both the number and the individuals of elements in the vector are non-deterministic) in a tensor is programmed. It accumulates complete N-combinations of one element of every M-set by recursion algorithm for object-oriented programming. Here, N is dynamic, i.e., uncertain before user's programming. This algorithm has overcome the difficulty of writing loop sentences in uncertain arity, yet the complexity of computation is exponential. So a quantum algorithm is proposed for realizing the computation in an acceptable time.

关键词： contraction accumulation vector tensor quantum algorithm recursion loop

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A Modified quantum Search algorithm

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INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2018年第12期57卷 3668-3681页

作者： Mehri-Dehnavi, Hossein Dashtianeh, Hasan Kuchaksaraei, Hossein Yahyavi Khoshdareh, Masumeh Mahmoodi Movahhedian, Hossein Rahimi, Robabeh Babol Noshirvani Univ Technol Dept Phys Shariati Ave Babol Sar *** Iran Shahrood Univ Technol Dept Phys Seventh Tir Sq Shahrood Iran Univ Chicago Dept Radiat & Cellular Oncol Chicago IL 60637 USA Univ Miami Sch Med Miami FL USA

We show that by adding a workspace qubit to Ahmed Younes, et al. algorithm (Younes et al. AIP Conf. Proc. 734:171, 2004, 2008), and applying newly defined partial diffusion operators on subsystems, the algorithm's... 详细信息

关键词： Search algorithm quantum algorithm Grover search algorithm

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An efficient quantum algorithm for spectral estimation

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NEW JOURNAL OF PHYSICS 2017年第3期19卷 033005-033005页

作者： Steffens, Adrian Rebentrost, Patrick Marvian, Iman Eisert, Jens Lloyd, Seth Free Univ Berlin Dahlem Ctr Complex Quantum Syst D-14195 Berlin Germany MIT Elect Res Lab Cambridge MA 02139 USA MIT Dept Mech Engn Cambridge MA 02139 USA

We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of exponentially damped sinusoids. Our algorithm provides a quantum speedup in a natural regime where the sampling rate is much higher than the number of sinusoid components. Along the way, we develop techniques that are expected to be useful for other quantum algorithms as well-consecutive phase estimations to efficiently make products of asymmetric low rank matrices classically accessible and an alternative method to efficiently exponentiate non-Hermitian matrices. Our algorithm features an efficient quantum-classical division of labor: the time-critical steps are implemented in quantum superposition, while an interjacent step, requiring much fewer parameters, can operate classically. We show that frequencies and damping factors can be obtained in time logarithmic in the number of sampling points, exponentially faster than known classical algorithms.

关键词： quantum algorithm spectral estimation quantum phase estimation matrix exponentiation quantum signal processing

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quantum algorithms for the Physical Layer: Potential Applications to Physical Layer Security

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IEEE ACCESS 2025年 13卷 13988-14009页

作者： Matsumine, Toshiki Ochiai, Hideki Shikata, Junji Yokohama Natl Univ Inst Adv Sci Yokohama 2408501 Japan Osaka Univ Grad Sch Engn Osaka 5650871 Japan Yokohama Natl Univ Grad Sch Environm & Informat Sci Yokohama 2408501 Japan

The field of quantum technologies has garnered considerable interest and witnessed noteworthy progress in recent years. It is also anticipated that these technologies will continue to flourish and exert a considerable influence on society, i.e., a plethora of real-world problems that cannot be solved by classical algorithms are believed to benefit from the implementation of quantum algorithms. Meanwhile, as an alternative to cryptographic methods, physical layer security (PLS) has been extensively studied as a means to realize secure wireless communication that is resistant to attacks by both classical and quantum computers, i.e., quantum-safe. While the prevailing approach to PLS has been based on classical algorithms, this could potentially be accelerated by the application of quantum algorithms. This paper examines the potential applications of various quantum algorithms, including quantum annealing, hybrid quantum-classical algorithms, and Grover-based algorithms, to the the PLS problems. In particular, we begin with a concise overview of their applications to physical layer techniques and then proceed to discuss their use in addressing the challenges of secret message transmission and secret key generation from wireless channels.

关键词： Logic gates quantum computing quantum algorithm Optimization Annealing Qubit quantum annealing Cryptography Computers Approximation algorithms Hybrid quantum-classical algorithms multi-input multi-output (MIMO) physical layer security (PLS) quantum algorithms quantum annealing (QA) quantum approximate optimization algorithm (QAOA) reconfigurable intelligent surface (RIS) secret key generation (SKG)

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