量子计算机中的数据库处理
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摘要
在量子计算机中,数据库处理过程作为信息传输和信息处理的基本过程,一直是人们关注和研究的焦点。本文主要涉及量子数据库处理的四个方面,即量子线路的解析表示、在量子计算机上实现的数据库处理算法、利用对偶计算进行的数据库处理和非线性光学量子计算方案。
在量子线路方面,本文提出两种新的理论方案。第一种是任意量子完全受控门的解析分解方案,此方案以通用量子门的形式分别给出了指数复杂度和多项式复杂度的量子线路图和解析分解结果。第二种方案是基于量子逻辑门分解的纠缠Bell态、GHZ态和W态量子分析器方案,为在实验上制备和测量典型纠缠态提供了新的思路和方法。
在量子数据库处理算法方面,本文提出了五种新的算法,包括仅需一次查询实现的平均叠加态单目标态的量子删除算法、任意叠加态多目标态的广义量子删除算法、大数据库单目标态的近似量子删除算法、量子插入算法和广义确定性量子搜索算法。前四种算法与经典算法相比,可以实现计算的指数加速。后一种算法是对现有的确定性量子搜索算法的推广和改进,具有更广的适应范围和更高的搜索效率。
在利用对偶计算进行的数据库处理方面,本文提出在量子计算机上模拟对偶计算的模式,包括模拟2路对称对偶计算机的对偶模式和模拟多路非对称对偶计算机的广义对偶模式,进一步给出量子力学所允许的广义对偶门的概念。本文还提出三种在量子计算机上利用对偶模式实现的算法,即平均叠加态单目标态的定点搜索算法、平均叠加态单目标态的定点删除算法和任意叠加态多目标态的定点删除算法。
在非线性光学量子计算方面,本文提出一种利用Mach-Zehnder干涉仪、旋光器件、非线性正单轴晶体和负单轴晶体实现的量子计算方案。在理想的实验条件下,此方案是确定性或近确定性的。
Quantum database processing is the basic process of information transmissionand information processing in quantum computers. It is an important topic in researchareas and has attracted attention of scientists. In this thesis, we focus on four areasin quantum database processing, i.e., analytic construction of quantum gates, quan-tum database processing, database processing based on duality properties and quantumcomputation with nonlinear optics.
In the field of quantum circuit, we propose two theoretical protocols. Firstly,we present two analytic expressions that most generally simulate n-qubit controlled-Ugates using universal one-qubit gates and CNOT gates with exponential and polynomialcomplexity respectively. Based on analytic results of quantum gates, we present afull Bell, GHZ and W basis-states analyzer. It provides a new method and view forexperimental design of state initialization and quantum measurement.
In the field of quantum database processing algorithm, we propose five new al-gorithms, i.e., quantum deletion algorithm which deletes a marked basis-state from aneven superposition of all basis-states with a single query, generalized quantum dele-tion algorithm which deletes M marked basis-states from arbitrary initial superposedstate, approximate quantum deletion algorithm which uses a fixed phase rotationπ/3to approximately delete a marked basis-state from a large database, quantum insertionalgorithm which inserts a marked basis-state into a superposed state with a single queryand generalized quantum search algorithm which searches M marked basis-states fromarbitrary initial distribution with certainty. The former four algorithms can achieve anexponential speedup compared to classical computing, the latter one algorithm is thegeneralization of the Long quantum search algorithm.
In the field of database processing based on duality properties, to realize dualitycapability in quantum computers, we present duality mode and recycling mode of quan-tum computers to simulate a 2-slit symmetric duality computer. We present general- ized duality mode and generalized duality gates to simulate arbitrary duality computerin quantum computers. In addition, a fixed-point search algorithm and two fixed-pointdeletion algorithms in quantum computers using duality mode are presented.
In the field of quantum computation with nonlinear optics, we propose a schemeof nonlinear optics quantum computation implemented by Mach-Zehnder interferom-eter, magnetic-induced Faraday rotation device, positive and negative uniaxial crystalwith second susceptibility and polarization-plastic device. Under ideal conditions, thesuccess probability of our scheme is deterministic or near-deterministic.
在量子线路方面,本文提出两种新的理论方案。第一种是任意量子完全受控门的解析分解方案,此方案以通用量子门的形式分别给出了指数复杂度和多项式复杂度的量子线路图和解析分解结果。第二种方案是基于量子逻辑门分解的纠缠Bell态、GHZ态和W态量子分析器方案,为在实验上制备和测量典型纠缠态提供了新的思路和方法。
在量子数据库处理算法方面,本文提出了五种新的算法,包括仅需一次查询实现的平均叠加态单目标态的量子删除算法、任意叠加态多目标态的广义量子删除算法、大数据库单目标态的近似量子删除算法、量子插入算法和广义确定性量子搜索算法。前四种算法与经典算法相比,可以实现计算的指数加速。后一种算法是对现有的确定性量子搜索算法的推广和改进,具有更广的适应范围和更高的搜索效率。
在利用对偶计算进行的数据库处理方面,本文提出在量子计算机上模拟对偶计算的模式,包括模拟2路对称对偶计算机的对偶模式和模拟多路非对称对偶计算机的广义对偶模式,进一步给出量子力学所允许的广义对偶门的概念。本文还提出三种在量子计算机上利用对偶模式实现的算法,即平均叠加态单目标态的定点搜索算法、平均叠加态单目标态的定点删除算法和任意叠加态多目标态的定点删除算法。
在非线性光学量子计算方面,本文提出一种利用Mach-Zehnder干涉仪、旋光器件、非线性正单轴晶体和负单轴晶体实现的量子计算方案。在理想的实验条件下,此方案是确定性或近确定性的。
Quantum database processing is the basic process of information transmissionand information processing in quantum computers. It is an important topic in researchareas and has attracted attention of scientists. In this thesis, we focus on four areasin quantum database processing, i.e., analytic construction of quantum gates, quan-tum database processing, database processing based on duality properties and quantumcomputation with nonlinear optics.
In the field of quantum circuit, we propose two theoretical protocols. Firstly,we present two analytic expressions that most generally simulate n-qubit controlled-Ugates using universal one-qubit gates and CNOT gates with exponential and polynomialcomplexity respectively. Based on analytic results of quantum gates, we present afull Bell, GHZ and W basis-states analyzer. It provides a new method and view forexperimental design of state initialization and quantum measurement.
In the field of quantum database processing algorithm, we propose five new al-gorithms, i.e., quantum deletion algorithm which deletes a marked basis-state from aneven superposition of all basis-states with a single query, generalized quantum dele-tion algorithm which deletes M marked basis-states from arbitrary initial superposedstate, approximate quantum deletion algorithm which uses a fixed phase rotationπ/3to approximately delete a marked basis-state from a large database, quantum insertionalgorithm which inserts a marked basis-state into a superposed state with a single queryand generalized quantum search algorithm which searches M marked basis-states fromarbitrary initial distribution with certainty. The former four algorithms can achieve anexponential speedup compared to classical computing, the latter one algorithm is thegeneralization of the Long quantum search algorithm.
In the field of database processing based on duality properties, to realize dualitycapability in quantum computers, we present duality mode and recycling mode of quan-tum computers to simulate a 2-slit symmetric duality computer. We present general- ized duality mode and generalized duality gates to simulate arbitrary duality computerin quantum computers. In addition, a fixed-point search algorithm and two fixed-pointdeletion algorithms in quantum computers using duality mode are presented.
In the field of quantum computation with nonlinear optics, we propose a schemeof nonlinear optics quantum computation implemented by Mach-Zehnder interferom-eter, magnetic-induced Faraday rotation device, positive and negative uniaxial crystalwith second susceptibility and polarization-plastic device. Under ideal conditions, thesuccess probability of our scheme is deterministic or near-deterministic.
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