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Near-Deterministic quantum search algorithm Without Phase Design

ADVANCED quantum TECHNOLOGIES 2025年第0期

作者： Wang, Zhen Zhang, Kun Korepin, Vladimir Xian Univ Sch Mech & Mat Engn Xian 710065 Peoples R China Northwest Univ Sch Phys Xian 710127 Peoples R China Shaanxi Key Lab Theoret Phys Frontiers Xian 710127 Peoples R China Peng Huanwu Ctr Fundamental Theory Xian 710127 Peoples R China SUNY Stony Brook CN Yang Inst Theoret Phys New York NY 11794 USA

Grover's algorithm solves the unstructured search problem. Grover's algorithm can find the target state with certainty only if searching one out of four. Designing the deterministic search algorithm can avoid any repetition of the algorithm, especially when Grover's algorithm is a subroutine in other algorithms. Grover's algorithm can be deterministic if the phase of the oracle or the diffusion operator is delicately designed. The precision of the phases could be a problem. A near-deterministic quantum search algorithm without the phase design is proposed. The algorithm has the same oracle and diffusion operators as Grover's algorithm. One additional component is the rescaled diffusion operator. It acts partially on the database. The success probability of Grover's algorithm is improved by the partial diffusion operator in two different ways. The possible cost is one or two more queries to the oracle. The deterministic search algorithm is also designed when searching one out of eight, sixteen, and thirty-two.

关键词： quantum search algorithm quantum partial search algorithm quantum deterministic search algorithm

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quantum search algorithm for Weighted Solutions

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IEEE ACCESS 2022年 10卷 16209-16224页

作者： Seo, Youngjin Kang, Yujin Heo, Jun Korea Univ Sch Elect Engn Seoul 02841 South Korea

This paper presents a quantum search algorithm (QSA) for weighted solutions. In a QSA, the final quantum state has an equal probability of solutions. However, solutions should have different probabilities in specific problems, such as dynamic spectrum management (DSM). We propose a method to make differences with probability in accordance with rewards for each solution, and present an application to DSM. The proposed algorithm has some error terms for the final quantum state, and we provide the error terms in accordance with the number of iterations. In addition, we present the simulation results of the proposed algorithm compared with a classical exact algorithm and QSA. The proposed algorithm has a lower complexity and relative difference than the classical exact algorithm. Furthermore, the proposed algorithm has a higher performance than the QSA in specific cases.

关键词： Heuristic algorithms Color Complexity theory Interference Image color analysis search problems Graph theory Dynamic spectrum management graph coloring problem quantum search algorithm

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First experimental demonstration of an exact quantum search algorithm in nuclear magnetic resonance system

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Science China(Physics,Mechanics & Astronomy) 2015年第7期58卷 11-16页

作者： LIU Yang ZHANG FeiHao School of Nuclear Science and Engineering North China Electric Power University State Key Laboratory of Intense Pulsed Radiation Simulation and Effect Northwest Institute of Nuclear Technology Department of Physics Tsinghua University

The success probability of searching an objective item from an unsorted database using standard Grover's algorithm is usually not exactly 1. It is exactly 1 only when it is used to find the target state from a database with four items. Exact search is always important in theoretical and practical applications. The failure rate of Grover's algorithm becomes big when the database is small, and this hinders the use of the commonly used divide-and-verify strategy. Even for large database, the failure rate becomes considerably large when there are many marked items. This has put a serious limitation on the usability of the Grover's algorithm. An important improved version of the Grover's algorithm, also known as the improved Grover algorithm, solves this problem. The improved Grover algorithm searches arbitrary number of target states from an unsorted database with full success rate. Here, we give the first experimental realization of the improved Grover algorithm, which finds a marked state with certainty, in a nuclear magnetic resonance system. The optimal control theory is used to obtain an optimized control sequence. The experimental results agree well with the theoretical predictions.

关键词： quantum search algorithm improved Grover algorithm nuclear magnetic resonance success rate

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A quantum search algorithm for future spacecraft attitude determination

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ACTA ASTRONAUTICA 2011年第7-8期68卷 1208-1218页

作者： Tsai, Jack Hsiao, Fu-Yuen Li, Yi-Ju Shen, Jen-Fu Tamkang Univ Dept Aerosp Engn Tamsui 251 Taiwan Taipei Natl Univ Arts Ctr Art & Technol Performance Technol Lab Beitou Taiwan

In this paper we study the potential application of a quantum search algorithm to spacecraft navigation with a focus on attitude determination. Traditionally, attitude determination is achieved by recognizing the relative position/attitude with respect to the background stars using sun sensors, earth limb sensors, or star trackers. However, due to the massive celestial database, star pattern recognition is a complicated and power consuming job. We propose a new method of attitude determination by applying the quantum search algorithm to the search for a specific star or star pattern. The quantum search algorithm, proposed by Grover in 1996, could search the specific data out of an unstructured database containing a number N of data in only O(root N) steps, compared to an average of N/2 steps in conventional computers. As a result, by taking advantage of matching a particular star in a vast celestial database in very few steps, we derive a new algorithm for attitude determination, collaborated with Grover's search algorithm and star catalogues of apparent magnitude and absorption spectra. Numerical simulations and examples are also provided to demonstrate the feasibility and robustness of our new algorithm. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： quantum computing quantum search algorithm Spaceflight Attitude determination Navigation and guidance

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From Schrodinger's equation to the quantum search algorithm

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PRAMANA-JOURNAL OF PHYSICS 2001年第2-3期56卷 333-348页

作者： Grover, LK Bell Labs Lucent Technol Phys Res Lab Murray Hill NJ 07974 USA

The quantum search algorithm is a technique for searching N possibilities in only O(rootN) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it, these are quite different from any of the generally known forms of the algorithm. This paper describes these steps, which start by discretizing Schrodinger's equation. This paper also provides a self contained introduction to quantum computing algorithms from a new perspective.

关键词： quantum computation quantum search algorithm

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An Exact quantum search algorithm with Arbitrary Database

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INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2014年第8期53卷 2571-2578页

作者： Liu, Yang North China Elect Power Univ Sch Nucl Sci & Engn Beijing 102206 Peoples R China

In standard Grover's algorithm for quantum searching, the probability of finding a marked state is not exactly 1, and some modified versions of Grover's algorithm that search a marked state from an evenly distributed database with full successful rate have been presented. In this article, we present a generalized quantum search algorithm that searches M marked states from an arbitrary distributed N-item quantum database with a zero theoretical failure rate, where N is not necessary to be the power of 2. We analyze the general properties of our search algorithm, we find that our algorithm has periodicity with a period of 2J + 1, and it is effective with certainty for J + (2J + 1)m times of iteration, where m is an arbitrary nonnegative number.

关键词： quantum search algorithm Grover algorithm Long algorithm Zero theoretical failure rate

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quantum Key Agreement Protocol Based on quantum search algorithm

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INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2021年第3期60卷 838-847页

作者： Huang, Xi Zhang, Shi-Bin Chang, Yan Qiu, Chi Liu, Dong-Mei Hou, Min Chengdu Univ Informat Technol Sch Cybersecur Chengdu 610225 Peoples R China

quantum key agreement (QKA) and quantum search algorithm (QSA) are two important branches in quantum topic. The former asks all participants to negotiate the agreement key equally, and none of them can fully determine the agreement key. The latter is used to provide an acceleration in searching the marked item in an unsorted database. To date, several QKA schemes based on either BB84 or entangled states have been proposed, the QKA protocol based on QSA is rare, only exists one multi-party QKA (MQKA) protocol based on QSA. In this paper, on the basis of the properties of Grover's QSA, the first two-party quantum key agreement protocol based on quantum search algorithm known as Grover's algorithm is proposed. The participants transmit a two-particle quantum state sequence directly by inserting decoy photons randomly. The initial-prepared two-particle quantum states are easy to be prepared with current technology. Moreover, there is no swapping entanglement technology used in this protocol, it only needs unitary operations and single-particle measurements. Compared with the existing two-party QKA protocol, the proposed QKA protocol is more efficient. In addition, the security analysis shows that the proposed protocol is secure against both external attacks and internal ones. Finally, the proposed protocol is generated to MQKA protocol based on quantum search algorithm.

关键词： quantum key agreement quantum search algorithm Two-particle quantum state

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Multiparty controlled quantum secure direct communication based on quantum search algorithm

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quantum INFORMATION PROCESSING 2013年第12期12卷 3791-3805页

作者： Kao, Shih-Hung Hwang, Tzonelih Natl Cheng Kung Univ Dept Comp Sci & Informat Engn Tainan 701 Taiwan

In this study, a new controlled quantum secure direct communication (CQSDC) protocol using the quantum search algorithm as the encoding function is proposed. The proposed protocol is based on the multi-particle Greenberger-Horne-Zeilinger entangled state and the one-step quantum transmission strategy. Due to the one-step transmission of qubits, the proposed protocol can be easily extended to a multi-controller environment, and is also free from the Trojan horse attacks. The analysis shows that the use of quantum search algorithm in the construction of CQSDC appears very promising.

关键词： quantum cryptography quantum communication quantum search algorithm

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Towards More Reliable Fixed Phase quantum search algorithm

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APPLIED MATHEMATICS & INFORMATION SCIENCES 2013年第1期7卷 93-98页

作者： Younes, Ahmed Univ Alexandria Fac Sci Dept Math & Comp Sci Alexandria Egypt

Building quantum devices using fixed operators is a must to simplify hardware construction of a quantum computer. quantum search engine is not an exception. In this paper, a fixed phase quantum search algorithm that searches for M matches in an unstructured list of size N will be proposed. Fixing phase shifts to 1.91684 pi in the standard amplitude amplification will make the minimum probability of success is 99.58% in O (root N / M) for 0 < M <= N better than any know fixed operator quantum search algorithm. The algorithm will be able to handle either a single match or multiple matches in the search space. The algorithm will find a match in O root N / M) whether the number of matches is known or not in advance.

关键词： quantum search algorithm amplitude amplification fixed phase

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quantum Secret Sharing Based on quantum search algorithm

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INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2012年第10期51卷 3101-3108页

作者： Tseng, Hsin-Yi Tsai, Chia-Wei Hwang, Tzonelih Li, Chuan-Ming 1 Univ Rd Tainan 701 Taiwan

quantum secret sharing (QSS) and quantum search algorithm (QSA) are considered as two important but different research topics in quantum information science. This paper recognizes an important feature in the well-known Grover's QSA and then applies it to propose a QSS protocol. In contrast to the existing QSA-based QSS protocols, the newly proposed protocol has the following two advantages: (1) no quantum memory is required by the agents, whereas the agents in the existing QSA-based QSS protocols need long-term quantum memories to store their secret shadows;(2) the agents can cooperate to recover the boss's secret by using shadows in classical bits, whereas, the others have to combine their shadows in photons and perform a unitary operation on the retained photons. The proposed QSS protocol is also shown to be secure against eavesdroppers or malicious agents.

关键词： quantum information science quantum secret sharing quantum search algorithm

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