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A Exact quantum learning algorithm for the 2-Junta Problem in Constant Time

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2022年第8期61卷 1-9页

作者： Chen, Chien-Yuan Natl Univ Kaohsiung Dept Comp Sci & Informat Engn 700Kaohsiung Univ Rd Kaohsiung Taiwan

This study proposes an exact quantum learning algorithm for finding two dependent variables to solve the 2-junta problem. A 2-junta is a Boolean function f : {0,1}(n) -> {0,1} that depends on only 2 out of n variables. In 2021, Chen proposed an exact quantum learning algorithm for solving the 2-junta problem by performing the function operation O(log(2)n) times in the worst case. However, our proposed quantum algorithm only requires three function operations in the worst case using the modified black-box function of El-Wazan et al.

关键词： quantum algorithm quantum learning algorithm The 2-junta problem

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quantum algorithms for learning Walsh spectra of multi-output Boolean functions

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quantum INFORMATION PROCESSING 2019年第6期18卷 1-31页

作者： Cui, Jingyi Guo, Jiansheng Xu, Linhong Li, Mingming Informat Sci & Technol Inst Zhengzhou Henan Peoples R China

In classical cryptography, many cryptographic primitives could be treated as multi-output Boolean functions. The analysis of such functions is of great interest for cryptologists owing to their wide ranges of applications. Since each multi-output Boolean function can be uniquely determined by its Walsh transform, the Walsh spectra could reveal the properties of multi-output Boolean functions. In this paper, several quantum algorithms for learning Walsh spectra of multi-output Boolean functions are proposed. Firstly, with the usage of the amplitude estimation algorithm based on the Monte Carlo method, we present a quantum algorithm that allows one to estimate the Walsh coefficient of a multi-output Boolean function at a specified point with an additive error E and probability at least 1-. The corresponding query complexity is O(E-1log-1). There is an almost quadratic speedup over the classical algorithm. Secondly, we propose a generalized phase kick-back technique for multi-output Boolean functions to encode multiple Walsh coefficients on the amplitudes of states. Based on this generalized technique, a quantum Goldreich-Levin algorithm for arbitrary multi-output Boolean function F:{0,1}n{0,1}m where m,nZ is proposed to find those Walsh coefficients satisfying the threshold boundary condition with probability at least 1-. The whole query complexity is O2m+5+n/23 log2m+5n2. Finally, by using the same idea of the swap-test circuit, the query complexity of the modified quantum Goldreich-Levin algorithm could be lowered to O achieving a further speedup when is no less than O(2-n/2+6n). Those two quantum Goldreich-Levin algorithms have their own advantages in implementation and query complexity.

关键词： quantum computation quantum learning algorithm Multi-output Boolean function Walsh spectrum Goldreich-Levin theorem

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Conglomeration of deep neural network and quantum learning for object detection: Status quo review

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KNOWLEDGE-BASED SYSTEMS 2024年 288卷

作者： Sinha, Piyush Kumar Marimuthu, R. Vellore Inst Technol Sch Elect Engn Vellore 632014 Tamil Nadu India

The practice of deep neural framework specific to convolutional neural networks (ConNeuNets) in domain of object detection is substantial. The existing deep ConNeuNets give higher accuracy provided higher value of training time on a high -end graphical processing unit (GPU). On the other hand, in classification domain of object detection, quantum learning algorithms have shown temporal exponential reduction. However, this has happened in regard to relatively smaller sized dataset when compared to usual data-set-size employment on state -of -the -art deep ConNeuNets. Considering the training -time for conventional deep network-model, power consumption while training the deep model on a dedicated hardware and present state of quantum computing hardware it is reliable to examine the prospect of interaction between quantum algorithms and deep model paradigms. Approximately 69 % of output index in case of quantum -gates -based fabricated system of quantum volume (4096) and rise of explainable domain of study in deep learning due to its non-exact comprehension invoke to probe into the same prospect of interaction. So, this paper tries to review the existing methods and prospect of object detection using quantum learning concepts on existing deep neural framework.

关键词： Anchor box ConNeuNets Elliptical contour Object detection quantum computer hardware quantum learning algorithm

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An exact quantum logarithmic time algorithm for the 3-junta problem

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quantum INFORMATION PROCESSING 2024年第6期23卷 232-232页

作者： Chen, Chien-Yuan Natl Univ Kaohsiung Dept Comp Sci & Informat Engn 700 Kaohsiung Univ Rd Kaohsiung Taiwan

To tackle the 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3$$\end{document}-junta problem, this work provides an exact quantum learning algorithm for discovering three dependent variables. A 3-junta is a Boolean function f:0,1n -> 0,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f:{\left\{\text{0,1}\right\}}<^>{n}\to \left\{0, 1\right\}$$\end{document} that is dependent on just three of the n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} variables. Chen suggested an exact quantum learning method in 2021 for solving the 3-junta problem with one uncomplemented product by executing the function operation Olog2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O\left(\text{log}_algorithmn\right)$$\end{document} times in the worst-case. In this work, the modified black-box function is used to solve the 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3$$\end{document}-junta problem. In the worst-case, our proposed quantum algorithm takes Olog2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \use

关键词： quantum algorithm quantum learning algorithm The 3-junta problem The junta problem

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An exact quantum algorithm for testing Boolean functions with one uncomplemented product of two variables

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quantum INFORMATION PROCESSING 2020年第7期19卷 213-213页

作者： Chen, Chien-Yuan Natl Univ Kaohsiung Dept Comp Sci & Informat Engn 700 Kaohsiung Univ Rd Kaohsiung Taiwan

In this paper, we propose a novel quantum learning algorithm, based on Younes' quantum circuit, to find dependent variables of the Boolean function f: {0,1}(n)->{0,1} with one uncomplemented product of two variables. Typically, in the worst-case scenario, two dependent variables are found by evaluating the function O (n) times. However, our proposed quantum algorithm only requires O (log(2)n) function operations in the worst-case. Additionally, we evaluate the average number to perform the function. In the average case, our algorithm requires O (1) function operations.

关键词： quantum algorithm quantum learning algorithm The Bernstein-Vazirani algorithm

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An Exact quantum Polynomial-Time algorithm for Solving k-Junta Problem with One Uncomplemented Product

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INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2022年第3期61卷 1-19页

作者： Chen, Chien-Yuan Natl Univ Kaohsiung Dept Comp Sci & Informat Engn 700Kaohsiung Univ Rd Kaohsiung Taiwan

This study modifies Chen's algorithm, the first exact quantum algorithm for testing 2-junta, and proposes an exact quantum learning algorithm for finding four dependent variables of the Boolean function f : {0, 1}(n) -> {0, 1} with one uncomplemented product of four variables. Typically, the dependent variables are obtained by evaluating the function 2n times in the worst-case. However, our proposed quantum algorithm only requires 8log(2)n function operations in the worst-case. Additionally, we analyze the average-case of our algorithms. Our algorithm requires on the average 10.16 function operations at the most. Furthermore, we propose an exact quantum learning algorithm for finding k dependent variables of the Boolean function with one uncomplemented product of k variables, where k > 4. Based on our analysis, the proposed quantum algorithm only requires 4klog(2)n function operations in the worst-case, provided that k is given. Additionally, in the average-case, the proposed algorithm requires 16/5k function operations at the most to find k dependent variables.

关键词： quantum algorithm quantum learning algorithm The Bernstein-Vazirani algorithm

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An Exact quantum algorithm for the 2-Junta Problem

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INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2021年第1期60卷 80-91页

作者： Chen, Chien-Yuan Natl Univ Kaohsiung Dept Comp Sci & Informat Engn 700 Kaohsiung Univ Rd Kaohsiung Taiwan

This paper proposes a novel quantum learning algorithm based on Bernstein and Vazirani's quantum circuit to find the dependent variables of the 2-junta problem. Typically, for a given Boolean function f : {0, 1}(n) -> {0, 1} that depends on only 2 out of n variables, the dependent variables are obtained by evaluating the function 4n times in the worst-case. However, the proposed quantum algorithm only requires O(log(2)n) function operations in the worst-case. Moreover, the algorithm requires an average of 5.3 function operations at the most when n >= 8.

关键词： quantum algorithm quantum learning algorithm The Bernstein-Vazirani algorithm

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An exact quantum algorithm for testing 3-junta in Boolean functions with one uncomplemented product

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quantum INFORMATION PROCESSING 2021年第1期20卷 36-36页

作者： Chen, Chien-Yuan Natl Univ Kaohsiung Dept Comp Sci & Informat Engn 700 Kaohsiung Univ Rd Kaohsiung Taiwan

This paper modifies Chen's algorithm, which is the first exact quantum algorithm for testing 2-junta, and proposes an exact quantum learning algorithm for finding dependent variables of the Boolean function f: with one uncomplemented product of three variables. Typically, the dependent variables are obtained by evaluating the function 2n times in the worst case. However, our proposed quantum algorithm only requires O function operations in the worst case. In addition, the average number to perform the function is evaluated. Our algorithm requires an average of 7.23 function operations at the most when n >= 16. We also show that our algorithm cannot solve k-junta problem with one uncomplemented product if 4 <= k

关键词： quantum algorithm quantum learning algorithm The Bernstein-Vazirani algorithm

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