本文關(guān)鍵詞：量子算法的一些進展　出處：《中國科學(xué):信息科學(xué)》2017年10期 　論文類型：期刊論文

  更多相關(guān)文章： 量子計算 量子算法 龍算法 對偶量子計算

【摘要】：量子計算機利用量子力學(xué)原理進行計算,具有量子并行計算能力,有比經(jīng)典計算機更加強大的數(shù)據(jù)處理能力.量子計算機可以指數(shù)加速量子體系模擬,加速一些重要的經(jīng)典算法.傳統(tǒng)的量子計算運算是通過酉算子對信息進行處理,其計算過程是對量子計算機體系的初始量子態(tài)進行一系列的酉算子的乘積運算.20世紀(jì)90年代中期,量子算法取得重大突破,1994年Shor提出了大數(shù)分解量子算法,指數(shù)加快了大數(shù)分解,1996年Grover提出了量子搜索算法,平方根地加速了無序數(shù)據(jù)庫的搜索.量子算法的重大突破推動量子計算成為國際的持續(xù)研究熱點領(lǐng)域.之后量子算法的后續(xù)發(fā)展緩慢,Shor在2003年提出了著名的Shor之問,詢問為什么沒有發(fā)現(xiàn)更多的量子算法.2009年以后,多個重要的新量子算法被發(fā)現(xiàn),如求解線性方程組的量子算法,稀疏Hamiltonian體系的酉算符線性疊加算法,取得計算精度的指數(shù)改進的量子系統(tǒng)的新模擬算法.本文首先簡單介紹量子算法的基本原理,然后描寫Shor算法和Grover/Long搜索算法.這些算法都是傳統(tǒng)的量子算法,計算的過程就是一系列酉算子的乘積.接著介紹了2002年提出的對偶量子計算,不同于傳統(tǒng)的酉量子算法,對偶量子算法允許酉算子的線性組合.過去的量子計算只能使用酉算子的乘和除,而對偶量子計算可以使用酉算子的加減乘除四則運算.對偶量子計算為構(gòu)造量子算法提供了方便,可以將經(jīng)典算法中的技巧直接用于量子算法的構(gòu)造.我們最近的研究證明2009年以來的幾個新量子算法都屬于對偶量子計算.本文還介紹開放量子系統(tǒng)的對偶量子模擬算法,該算法不僅降低了計算復(fù)雜度,而且指數(shù)提高了精度.最后我們給出總結(jié)和展望.
[Abstract]:Quantum computer has the ability of quantum parallel computing and has more powerful data processing ability than classical computer. Quantum computer can accelerate quantum system simulation exponentially. Some important classical algorithms are accelerated. The traditional quantum computation is to process the information by unitary operator. The calculation process is a series of product operations of unitary operator for the initial quantum state of quantum computer system. In the middle of 90s, quantum algorithm made a great breakthrough. In 1994, Shor proposed the quantum algorithm of large number decomposition, exponentially accelerated the large number decomposition, and in 1996, Grover proposed a quantum search algorithm. Square root accelerates the search of unordered database. The great breakthrough of quantum algorithm has promoted quantum computing to become a hot research field in the world. After that, the follow-up development of quantum algorithm has been slow. In 2003, Shor put forward the famous question of Shor, asking why no more quantum algorithms were found. After 2009, several important new quantum algorithms were discovered. For example, the quantum algorithm for solving linear equations, the unitary operator linear superposition algorithm for sparse Hamiltonian system. The new simulation algorithm of exponentially improved quantum system is obtained. Firstly, the basic principle of quantum algorithm is introduced briefly in this paper. Then we describe the Shor algorithm and the Grover/Long search algorithm, which are all traditional quantum algorithms. The process of computing is the product of a series of unitary operators. Then the dual quantum computation proposed in 2002 is different from the traditional unitary quantum algorithm. Dual quantum algorithms allow linear combinations of unitary operators. In the past quantum calculations could only use the multiplication and division of unitary operators. Dual quantum computation can use the addition, subtraction, multiplication and division operation of unitary operator, and dual quantum computation provides convenience for constructing quantum algorithm. The techniques in classical algorithms can be directly used in the construction of quantum algorithms. Our recent studies have proved that several new quantum algorithms since 2009 are dual quantum computation. Even quantum simulation algorithm. The algorithm not only reduces the computational complexity, but also improves the accuracy of the index. Finally, we give a summary and prospect.
【作者單位】： 清華大學(xué)物理系低維量子物理國家重點實驗室;量子物質(zhì)科學(xué)協(xié)同創(chuàng)新中心;清華信息科學(xué)技術(shù)國家實驗室(籌);
【基金】：國家重點基礎(chǔ)研究發(fā)展計劃(973)(批準(zhǔn)號:2011CB9216002) 國家重點研發(fā)計劃(批準(zhǔn)號:2017YFA0303700) 國家自然科學(xué)基金(批準(zhǔn)號:91221205,11175094)資助項目
【分類號】：TP38
【正文快照】： 1引言量子計算是國際上的熱點研究領(lǐng)域,是結(jié)合了計算機科學(xué)、數(shù)學(xué)、物理學(xué)和工程技術(shù)等諸多學(xué)科的交叉學(xué)科,具有重要的科學(xué)意義和戰(zhàn)略意義.量子計算利用量子糾纏、量子干涉等獨特的量子力學(xué) 原理進行計算.它的主要的研究目標(biāo)是打破傳統(tǒng)的硅芯片電子計算機不可避免的發(fā)展極限,

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