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 variab...
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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 quantumalgorithm only requires three function operations in the worst case using the modified black-box function of El-Wazan et al.
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 tra...
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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 quantumalgorithms 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 quantumlearning concepts on existing deep neural framework.
To tackle the 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargi...
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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 quantumlearning 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 quantumalgorithm takes Olog2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \use
This study modifies Chen's algorithm, the first exact quantumalgorithm for testing 2-junta, and proposes an exact quantum learning algorithm for finding four dependent variables of the Boolean function f : {0, 1}...
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This study modifies Chen's algorithm, the first exact quantumalgorithm 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 quantumalgorithm 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 quantumalgorithm 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.
This paper modifies Chen's algorithm, which is the first exact quantumalgorithm for testing 2-junta, and proposes an exact quantum learning algorithm for finding dependent variables of the Boolean function f: wit...
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This paper modifies Chen's algorithm, which is the first exact quantumalgorithm 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 quantumalgorithm 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
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...
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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 quantumalgorithm 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.
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 applicat...
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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 quantumalgorithms 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 quantumalgorithm 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.
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 vari...
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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 quantumalgorithm 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.
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