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Optimized quantum circuit implementation of sATURNIN for grover’s algorithm

International Journal of Information Technology (singapore) 2024年第5期16卷 2955-2964页

作者： Allu, swamy Naidu Naidu, T. Appala Rao, K. Gangadhara Department of Computer Science and Engineering Acharya Nagarjuna University Andhra Pradesh Guntur 522510 India CR Rao Advanced Institute of Mathematics Statistics and Computer Science UoH Campus Telangana Hyderabad 500046 India

In 2019, sATURNIN a light-weighted block cipher was proposed for post-quantum security. In this research, we try to examine the security strength of sATURNIN by implementing its quantum circuit to apply grover’s algorithm for brute-force key search from classical complexity O(N) to quantum complexity O(N/2). We present sATURNIN’s novel quantum structure resource calculation, implementation, and security hardness evaluation based on the NIsT proposal for post-quantum security strength. Our proposed quantum circuit implementation requires 872 qubits. As per our evaluation, increasing the number of iterations in this algorithm doesn’t adequately increase its security hardiness against quantum assaults on the IBM QIsKIT quantum computer simulator. © The Author(s), under exclusive licence to Bharati Vidyapeeth's Institute of Computer Applications and Management 2024.

关键词： grover’s algorithm Post-quantum Quantum computing sATURNIN block cipher

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O(logN) algorithm for Amplitude Amplification and O(logN) algorithms for Amplitude Transfer in grover’s algorithm

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American Journal of Computational Mathematics 2024年第2期14卷 169-188页

作者： Ying Liu Department of Engineering Technology Savannah State University Savannah Georgia USA

grovers algorithm is a category of quantum algorithms that can be applied to many problems through the exploitation of quantum parallelism. The Amplitude Amplification in grovers algorithm is T = O(N). This paper introduces two new algorithms for Amplitude Amplification in grovers algorithm with a time complexity of T = O(logN), aiming to improve efficiency in quantum computing. The difference between grovers algorithm and our first algorithm is that the Amplitude Amplification ratio in grovers algorithm is an arithmetic series and ours, a geometric one. Because our Amplitude Amplification ratios converge much faster, the time complexity is improved significantly. In our second algorithm, we introduced a new concept, Amplitude Transfer where the marked state is transferred to a new set of qubits such that the new qubit state is an eigenstate of measurable variables. When the new qubit quantum state is measured, with high probability, the correct solution will be obtained.

关键词： Quantum Computing Oracle Amplitude Amplification grover’s algorithm

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Time Complexity of the Oracle Phase in grover’s algorithm

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American Journal of Computational Mathematics 2024年第1期14卷 1-10页

作者： Ying Liu Department of Engineering Technology Savannah State University Savannah Georgia

since grover’s algorithm was first introduced, it has become a category of quantum algorithms that can be applied to many problems through the exploitation of quantum parallelism. The original application was the unstructured search problems with the time complexity of O(). In grover’s algorithm, the key is Oracle and Amplitude Amplification. In this paper, our purpose is to show through examples that, in general, the time complexity of the Oracle Phase is O(N), not O(1). As a result, the time complexity of grover’s algorithm is O(N), not O(). As a secondary purpose, we also attempt to restore the time complexity of grover’s algorithm to its original form, O(), by introducing an O(1) parallel algorithm for unstructured search without repeated items, which will work for most cases. In the worst-case scenarios where the number of repeated items is O(N), the time complexity of the Oracle Phase is still O(N) even after additional preprocessing.

关键词： Quantum Computing Oracle Amplitude Amplification grover’s algorithm

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Explaining grover’s algorithm with a colony of ants: a pedagogical model for making quantum technology comprehensible

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Physics Education 2024年第3期59卷 035003-035003页

作者： schalkers, Merel A Dankers, Kamiel Wimmer, Michael Vermaas, Pieter Department of Applied Mathematics Delft University of Technology Delft Netherlands Qutech and Kavli Institute of Nanoscience Delft University of Technology Delft Netherlands Department of Philosophy Delft University of Technology Delft Netherlands

The rapid growth of quantum technologies requires an increasing number of physicists, computer scientists, and engineers who can work on these technologies. For educating these professionals, quantum mechanics should stop being perceived as incomprehensible. In this paper we contribute to this change by presenting a pedagogical model for explaining grover’s search algorithm, a prominent quantum algorithm. This model visualizes the three main steps of grover’s algorithm and, in addition to explaining the algorithm itself, introduces three key principles of quantum mechanics: superposition, interference, and state collapse at measurement. The pedagogical model, visualized by a video, is called the ant colony maze model. It represents the search problems as finding the exit of a maze, and visualizes grover’s search algorithm as a strategy by which a colony of ants finds that exit. © 2024 The Author(s). Published by IOP Publishing Ltd.

关键词： grover’s algorithm quantum computing quantum search algorithm

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grover’s algorithm in a 4-Qubit search space

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Journal of Quantum Computing 2021年第4期3卷 137-150页

作者： saasha Joshi Deepti Gupta Department of Computer Science and Engineering University Institute of Engineering and TechnologyPanjab UniversityChandigarh160014India

This paper provides an introduction to a quantum search algorithm,known as grover’s algorithm,for unsorted search *** algorithm is implemented in a search space of 4 qubits using the Python-based Qiskit sDK by *** providing detailed proof,the computational complexity of the algorithm is generalized to n *** implementation results obtained from the IBM QAsM simulator and IBMQ santiago quantum backend are analyzed and ***,the paper discusses the challenges faced in implementation and real-life applications of the algorithm ***,the implementation and analysis depict the advantages of this quantum search algorithm over its classical counterparts.

关键词： grover’s algorithm unsorted search Oracle amplitude amplification quantum computing

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Optimized General Uniform Quantum state Preparation

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Journal of Quantum Computing 2024年第1期6卷 15-24页

作者： Mark Ariel Levin University of Maryland College ParkMaryland20742USA

Quantum algorithms for unstructured search problems rely on the preparation of a uniform superposition,traditionally achieved through Hadamard ***,this incidentally creates an auxiliary search space consisting of nonsensical answers that do not belong in the search space and reduce the efficiency of the algorithm due to the need to neglect,un-compute,or destructively interfere with *** approaches to removing this auxiliary search space yielded large circuit depth and required the use of ancillary *** have developed an optimized general solver for a circuit that prepares a uniformsuperposition of any N states whileminimizing depth andwithout the use of ancillary *** showthat this algorithmis efficient,especially in its use of two wire gates,and that it has been verified on an IonQ quantum computer and through application to a quantum unstructured search algorithm.

关键词： state preparation unstructured search grover’s algorithm

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Circuit Design for k-Coloring Problem and Its Implementation in Any Dimensional Quantum system

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sN Computer science 2021年第6期2卷 1-17页

作者： saha, Amit saha, Debasri Chakrabarti, Amlan A. K. Choudhury School of Information Technology University of Calcutta Calcutta 700 106 India

With the evolution of quantum computing, researchers nowadays tend to incline to find solutions to NP-complete problems using quantum algorithms to gain asymptotic advantage. In this paper, we solve k-coloring problem (NP-complete problem) using grover’s algorithm in any dimensional quantum system or any d-ary quantum system for the first time to the best of our knowledge, where d≥ 2. Till date, k-coloring problem has been implemented only in binary and ternary quantum systems, hence, we abide to d= 2 or d= 3 , that is for binary and ternary quantum systems for comparing our proposed work with the state-of-the-art techniques. Our comparator-based approach has reduced the qubit cost, compared to the state-of-the-art binary quantum systems (saha et al. in IEEE Int symp smart Electron syst 1:17–22, 2020). Further in this paper, with the help of newly proposed ternary comparator, a substantial reduction in quantum gate count for the ternary oracle circuit of the k-coloring problem than the previous approaches has been obtained. Later, this proposed comparator-based approach helps to generalize the implementation of the k-coloring problem in any dimensional quantum system. An end-to-end automated framework has been put forward for implementing the k-coloring problem for any undirected and unweighted graph on any available near-term quantum devices or Noisy Intermediate-scale Quantum (NIsQ) devices or multi-valued quantum simulator, which helps in generalizing our approach. © 2021, The Author(s), under exclusive licence to springer Nature singapore Pte Ltd.

关键词： grover’s algorithm k-Coloring problem Multi-valued quantum circuit synthesis NIsQ

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Quantum Branch-and-Bound algorithm and its Application to the Travelling salesman Problem

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Journal of Mathematical sciences (United states) 2019年第2期241卷 168-184页

作者： Markevich, E.A. Trushechkin, A.s. National Research Nuclear University MEPhI Moscow Russian Federation Steklov Mathematical Insitute of the Russian Academy of Sciences Moscow Russian Federation National University of Science and Technology MISiS Moscow Russian Federation

We propose a quantum branch-and-bound algorithm based on the general scheme of the branch-and-bound method and the quantum nested searching algorithm and examine its computational efficiency. We also compare this algorithm with a similar classical algorithm on the example of the travelling salesman problem. We show that in the vast majority of problems, the classical algorithm is quicker than the quantum algorithm due to greater adaptability. However, the operation time of the quantum algorithm is constant for all problem, whereas the classical algorithm runs very slowly for certain problems. In the worst case, the quantum branch-and-bound algorithm is proved to be several times more efficient than the classical algorithm. © 2019, springer science+Business Media, LLC, part of springer Nature.

关键词： 68Q12 81P68 branch-and-bound method grover’s algorithm quantum computer quantum computing quantum search travelling salesman problem

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secure Big Data using QKD protocols

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Procedia Computer science 2019年 148卷 21-29页

作者： H. Amellal A. Meslouhi A.El Allati University Mohammed V Faculty of Sciences Av. Ibn Battouta Rabat B.P 1014 Morocco Laboratory RD Engineering Sciences Faculty of Sciences and Techniques Ajdir Al-Hoceima B.P. 3 C.P. 32003 Morocco

In this paper, we study the Big Data security based on quantum information theory. In fact, we discuss the opportunities offered by quantum Key distribution (QKD) protocols and quantum algorithms to increase the security level of Big data. In this respect, we used the BB84 protocol to transfer the sent qubits via a quantum channel and grover’s algorithm to search in Nosql databases in quantum environment. In order to analyze the effectiveness of quantum information theory on big data, we compare the obtained results with those of classical approaches

关键词： Big Data security Nosql data bases quantum Key distribution grover’s algorithm

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groverův algoritmus v kvantovém počítání a jeho aplikace

Groverův algoritmus v kvantovém počítání a jeho aplika...

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作者： Katabira, Joseph Brno University of Technology

Kvantová výpočetní technika je rychle rostoucí obor informatiky, který přenáší principy kvantových jevu do našeho každodenního života. Díky své kvantové pods... 详细信息

Kvantová výpočetní technika je rychle rostoucí obor informatiky, který přenáší principy kvantových jevu do našeho každodenního života. Díky své kvantové podstatě získávají kvantové počítače převahu nad klasickými počítači. V této práci jsme se zaměřili na vysvětlení základů kvantového počítání a jeho implementaci na kvantovém počítači. Zejména se zaměřujeme na popis fungování, konstrukci a implementaci groverova algoritmu jako jednoho ze základních kvantových algoritmů. Demonstrovali jsme sílu tohoto kvantového algoritmu při prohledávání databáze a porovnávali ho s klasickými nekvantovými algoritmy pomocí implementace prostřednictvím simulačního prostředí QIsKit. Pro simulaci jsme použili QAsM simulator a state vector simulator Aer backends a ukázali, že získané výsledky korelují s dříve diskutovanými teoretickými poznatky. Toto ukazuje, že groverův algoritmus umožňuje kvadratické zrychlení oproti klasickému nekvantovému vyhledávacímu algoritmu, Použitelnost algoritmu stejně jako ostatních kvantových algoritmů je ale stále omezena několika faktory, mezi které patří vysoké úrovně dekoherence a chyby hradla.

关键词： Qubit superpozice grover’s algorithm Complexity Oracle Diffusion Operator Quantum circuit Quantum Gate grover Iterate Initialization Measurement algorithm search space Bra-Ket Notation. Qubit superposition grover’s algorithm Complexity O

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