We give generalized quantum counting algorithm to increase universality of quantum counting algorithm. Non-uniform initial amplitude distribution is possible due to the diversity of situations on counting problems or ...
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We give generalized quantum counting algorithm to increase universality of quantum counting algorithm. Non-uniform initial amplitude distribution is possible due to the diversity of situations on counting problems or external noise in the amplitude initialization procedure. We give the reason why quantum counting algorithm is invalid on this situation. By modeling in three-dimensional space spanned by unmarked state, marked state and free state to the entire Hilbert space of n qubits, we find Grover iteration can be regarded as improper rotation in the space. This allows us to give formula to solve counting problem. Furthermore, we express initial amplitude distribution in the eigenvector basis of improper rotation matrix. This is necessary to obtain mathematical analysis of counting problem on various situations. Finally, we design four simulation experiments, the results of which show that compared with original quantum counting algorithm, generalized quantum counting algorithm wins great satisfaction from three aspects: (1) Whether initial amplitude distribution is uniform;(2) the diversity of situations on counting problems;and (3) whether phase estimation technique can get phase exactly.
For some certain problems, quantumalgorithms are theoretically able to solve them quickly than classical algorithms. But the role of entanglement in achieving the quantum computational speedup is not fully understood...
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For some certain problems, quantumalgorithms are theoretically able to solve them quickly than classical algorithms. But the role of entanglement in achieving the quantum computational speedup is not fully understood. By theoretical analysis and numerical calculation of four practical use cases, we investigate the entanglement features of the quantum states employed in quantum phase estimation algorithm and quantum counting algorithm. The results show that whether these two algorithms generate entanglement depend on whether the input quantum state of the second register is a superposition state of the eigenstates.
We study entanglement in the steps before quantum Fourier Transform (pre-QFT) part of the quantum Phase Estimation and the quantum counting algorithms (QPEA-QCA) with the use of three entanglement detection tools. In ...
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We study entanglement in the steps before quantum Fourier Transform (pre-QFT) part of the quantum Phase Estimation and the quantum counting algorithms (QPEA-QCA) with the use of three entanglement detection tools. In particular we focus on the sensitivity of entanglement to the input value (the phase phi and the ratio of marked elements MN ) in some basic cases. One starts from numerical observations and deduce some general results in particular regarding the classes of entanglement. More precisely, when the second register of both algorithms (i.e. the register on which a specific unitary operator act, see section 2) is initialized in the non-entangled superposition of two (separable) eigenvectors, one proves that the QPEA and QCA curves of entanglement evolution are the same up to a scalar multiplication of the parameter phi. One demonstrates that a local minimum is obtained and corresponds to an EPR (Einstein-Podolsky-Rosen) state and finally one proves that, up to Stochastic Local Operation and Classical Communication (SLOCC), all states, except for a few values of phi, are equivalent to the product of a separable state and a generalized GHZ (Greenberger-Horen-Zeilinger) state , i.e. GHZn+1=12(00...0+11...1) .
quantum computation models have profoundly impacted cryptanalysis. Differential cryptanalysis is one of the most fundamental methods in cryptanalysis of block ciphers, and one of the variations of this attack is relat...
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quantum computation models have profoundly impacted cryptanalysis. Differential cryptanalysis is one of the most fundamental methods in cryptanalysis of block ciphers, and one of the variations of this attack is related-key differential cryptanalysis. In this paper, quantum related-key differential cryptanalysis is implemented in two main stages of classical version. We employ Bernstein-Vazirani algorithm to find related-key differential characteristics in the first stage. Building on this basis, the second stage combines quantum maximum algorithm and quantum counting algorithm to recover correct key pair by quantum random access memory model. Compared to classical related-key differential cryptanalysis, the first stage achieves exponential acceleration, while the second stage accelerates at O(K), where K2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K<^>2$$\end{document} represents the number of candidate key pairs.
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