本文選題：量子計算　切入點：量子集合算法　出處：《四川師范大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

【摘要】：量子計算與量子信息是涉及物理學(xué)、計算機(jī)科學(xué)、數(shù)學(xué)以及信息科學(xué)等多個學(xué)科的新興綜合性交叉研究領(lǐng)域。在處理眾多特殊問題上,量子計算機(jī)展示了它比傳統(tǒng)計算機(jī),更加優(yōu)越的巨大潛力。例如：1994年,petershor提出的算法能在量子計算機(jī)上有效的解決兩個非常重要的問題：整數(shù)質(zhì)因數(shù)分解、離散對數(shù)問題,這些問題在傳統(tǒng)計算機(jī)上都是不能有效的被解決的。在量子計算的研究中,計算性能的優(yōu)越性主要體現(xiàn)在算法的有效性上。目前為止,被公認(rèn)的最具代表性的量子算法有Shor的大數(shù)質(zhì)因子分解算法以及Grover提出的數(shù)據(jù)庫搜索量子算法。然而,Grover搜索算法在搜索復(fù)雜的數(shù)據(jù)庫時存在著很大的足限性,因為Grover搜索算法只能處理在全空間中的量子比特,而不能處理在子空間中的量子比特。例如,它在處理部分量子比特時不可能保持另一部分量子比特不變。此外,數(shù)據(jù)在被處理之前,必須先加載到寄存器中,才能完成處理任務(wù)。但由于經(jīng)典的數(shù)據(jù)是通過輸入輸出設(shè)備,被逐個的加載到寄存器中去的。輸入輸出設(shè)備由于其逐個加載數(shù)據(jù)的方式,嚴(yán)重地拖慢了計算機(jī)的運(yùn)算速度,從而成為經(jīng)典計算機(jī)的效率瓶頸。量子計算機(jī)又不能直接處理經(jīng)典的數(shù)據(jù)信息,只能對量子態(tài)進(jìn)行處理。要對量子態(tài)進(jìn)行處理必須把經(jīng)典數(shù)據(jù)加載到量子態(tài)上,因此必須有一個針對量子計算機(jī)的數(shù)據(jù)存儲方案。這正是本文將研究的量子數(shù)據(jù)加載方案(QLS)。數(shù)據(jù)庫操作、信號處理、圖像壓縮等領(lǐng)域,由于其數(shù)據(jù)庫的龐大性,在經(jīng)典計算機(jī)上處理這類問題是非常困難的。而這些問題最終又可以歸結(jié)為對集合的操作。因此在量子計算機(jī)上有效地處理集合問題,就成了解決上述問題的關(guān)鍵�；谝陨蠁栴},在這篇文章中,提出了基于量子裝載方案(QLS)和旋轉(zhuǎn)子空間理論的量子集合算法,能夠在量子計算機(jī)上有效地解決集合運(yùn)算類問題。 本文分為以下三個部分： 第一部分對量子計算的歷史概況進(jìn)行了簡述,以及量子計算的準(zhǔn)備知識。對歷史上比較重要的量子算法進(jìn)行了重點分析,如shor因子分解算法、Grover搜索算法等已被提出的算法。 第二部分這部分介紹了旋轉(zhuǎn)子空間理論和量子數(shù)據(jù)加載方案(QLS),同時也介紹了針對Grover量子搜索算法而提出來的Ggeneral,最后在這些算法的基礎(chǔ)上提出了一個新量子集合算法。 第三部分在文章最后對量子集合算法的一個運(yùn)用——模式識別進(jìn)行了分析。主要是從如何實現(xiàn)在包含大量的干擾信號中實時地識別出真實的目標(biāo)這方面進(jìn)行了詳細(xì)的分析。
[Abstract]:Quantum computation and quantum information is involved in physics, computer science, new comprehensive interdisciplinary research field of multiple disciplines of mathematics and information science and so on. In dealing with many special problems, quantum computer shows its great potential than traditional computers, more superior. For example: in 1994, petershor proposed the algorithm can effectively solve two a very important problem in quantum computer: integer factorization and discrete logarithm problems, these problems are not effectively solved in the traditional computer. Research in quantum computing, superior computing performance is mainly reflected in the effectiveness of the algorithm. So far, the most representative of the quantum algorithm the recognized Shor large number factorization algorithm and quantum algorithm proposed by Grover database search. However, the Grover search algorithm in the search of complex database storage In a big foot limiting, because Grover search algorithms can only handle qubits in whole space, it can not deal with the qubit in the subspace. For example, it is not possible to keep the other part of a quantum bit qubit constant in the processing part. In addition, the data before the treatment, must be loaded to register, to complete the processing tasks. But due to the classic data is through the input and output devices, one by one is loaded into the registers to input and output devices. Because of its loading data one by one way, seriously slow down the computer operation speed, thus becomes the efficiency bottleneck of classical computer. Classical quantum direct processing the computer can not only information on the quantum state for processing. For the quantum state must be loaded into the classic data processing of quantum state, so it must be for a quantum computer This is the data storage scheme. This paper will study the quantum data loading scheme (QLS). The database operation, signal processing, image compression and other fields, because of its huge database, it is very difficult to handle this kind of problem in classical computer. These problems can be attributed to as set operation. So in a quantum computer effectively deal with a collection of problems has become the key to solve the above problems. Based on the above problems, in this article, based on the proposed quantum loading scheme (QLS) and quantum rotation subspace theory set algorithm, can effectively solve the problem of set operations in a quantum computer.
This article is divided into the following three parts:
The first part introduces the history of quantum computing and the knowledge of preparation for quantum computation. The important algorithms in history are analyzed, such as shor factorization algorithm and Grover search algorithm.
The second part introduces the theory of spin subspace and the loading scheme of quantum data (QLS). At the same time, it also introduces the Ggeneral proposed for Grover quantum search algorithm. Finally, based on these algorithms, a new quantum set algorithm is proposed.
The third part, at the end of the paper, analyzes the application of quantum ensemble algorithm -- pattern recognition. It mainly analyzes how to reallocate real targets in a large number of interfering signals in real time.

【學(xué)位授予單位】：四川師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：O413;TP38

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本文編號：1587854